Hydraulic Practice

Circular Culvert Design Calculations Software Equations

Circular Culvert using Manning Equation

Uses Manning equation with circular culvert geometry Compute velocity discharge depth top width culvert diameter area wetted perimeter hydraulic radius Froude number Manning

coefficient channel slope

To LMNO Engineering home page (more calculations) Culvert Design using Inlet and Outlet Conrol Trapezoidal Channel Design Rectangular Channels

Unit Conversions

LMNOLMNOengcom phone (USA) (740) 592-1890 Trouble printing

Register to enable Calculate button

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Links on this page Introduction Variables Mannings n coefficients Error messages References

IntroductionThe equation beginning V= is called the Manning Equation It is a semi-empirical equation and is the most commonly used equation for uniform steady state flow of water in open channels (see Discussion and References for Open Channel Flow for further discussion) Because it is empirical the Manning equation has inconsistent units which are handled through the conversion factor k Uniform means that the water surface has the same slope as the channel bottom Uniform flow is actually only achieved in channels that are long and have an unchanging cross-section However the Manning equation is used in other situations despite not strictly achieving these conditions

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In our calculation most of the combinations of inputs have analytic (closed form) solutions to compute the unknown variables however some two require numerical solutions (Enter Q n S d and Enter V n S d) Our numerical solutions utilize a cubic solver that finds roots of the equations with the result accurate to at least 8 significant digits All of our calculations utilize double precision

It is possible to get two answers using Enter QnSd or Enter VnSd This is because maximum Q and V do not occur when the pipe is full Qmax occurs when yd=0938 If yd is more than that Q actually decreases due to friction Given a pipe with diameter d roughness n and slope S let Qo be the discharge when the pipe is flowing full (yd=1) As seen on the graph below discharge is also equal to Qo when yd=082 If the entered Q is greater than Qo (but less than Qmax) there will be two solution values of yd one between 082 and 0938 and the other between 0938 and 1 The same argument applies to V except that Vo occurs at yd=05 and Vmax occurs at yd=081 If the entered V is greater than Vo (but less than Vmax) there will be two solution values of yd one between 05 and 081 and the other between 081 and 1 For further information see Chow (1959 p 134)

The following graphs are valid for any roughness (n) and slope (S) Qo=full pipe discharge Vo=full pipe velocity

Variables To top of page

A = Flow cross-sectional area determined normal (perpendicular) to the bottom surface [L2]d = Culvert diameter [L]F = Froude number F is a non-dimensional parameter indicating the relative effect of inertial effects to gravity effects Flow with Flt1 are low velocity flows called subcritical Fgt1 are high velocity flows called supercritical Subcritical flows are controlled by downstream obstructions while supercritical flows are affected by upstream controls F=1 flows are called criticalg = acceleration due to gravity = 32174 fts2 = 98066 ms2 g is used in the equation for Froude numberk = unit conversion factor = 149 if English units = 10 if metric units Our software converts all inputs to SI units (meters and seconds) performs the computations using k=10 then converts the computed quantities to units specified by the user Required since the Manning equation is empirical and its units

are inconsistentn = Manning coefficient n is a function of the culvert material such as plastic concrete brick etc Values for n can be found in the table below of Mannings n coefficientsP = Wetted perimeter [L] P is the contact length (in the cross-section) between the water and the culvertQ = Discharge or flowrate [L3T]R = Hydraulic radius of the flow cross-section [L]S = Slope of channel bottom or water surface [LL] Vertical distance divided by horizontal distanceT = Top width of the flowing water [L]V = Average velocity of the water [LT]y = Water depth measured normal (perpendicular) to the bottom of the culvert [L] If the culvert has a small slope (S) then entering the vertical depth introduces only minimal errorOslash = Angle representing how full the culvert is [radians] A culvert with Oslash=0 radians (0o) contains no water a culvert with Oslash=pi radians (180o) is half full and a culvert with Oslash=2 pi radians (360o) is completely full

Mannings n Coefficients To top of page The table shows the Manning n values for materials most commonly used for culverts These values were compiled from the references listed under Discussion and References and in the references at the bottom of this web page (note the footnotes which refer to specific references) A more complete table of Manning n values can be found on our Manning n page

Material Manning n Material Manning n

Metals

Brass 0011 Smooth Steel 0012

Cast Iron 0013 Corrugated Metal 0022

Non-Metals

Corrugated Polyethylene (PE) with smooth inner walls ab 0009-0015

Corrugated Polyethylene (PE) with corrugated inner walls c 0018-0025

Polyvinyl Chloride (PVC) with smooth inner walls de 0009-0011

Glass 0010 Finished Concrete 0012

Clay Tile 0014 Unfinished Concrete 0014

Brickwork 0015 Gravel 0029

Asphalt 0016 Earth 0025

Masonry 0025 Planed Wood 0012

Unplaned Wood 0013

Error Messages To top of page Infeasible Input Td gt 1 Water top width cannot be greater than the culvert diameterAn input is lt= 0 Certain inputs must be positiveInfeasible Input T lt 0 Water top width cannot be negativeInfeasible Input yd gt 1 Water depth cannot exceed the pipe diameter

References (footnotes refer back to Manning n table) To top of page a Barfuss Steven and J Paul Tullis Friction factor test on high density polyethylene pipe Hydraulics Report No 208 Utah Water Research Laboratory Utah State University Logan Utah 1988

c Barfuss Steven and J Paul Tullis Friction factor test on high density polyethylene pipe Hydraulics Report No 208 Utah Water Research Laboratory Utah State University Logan Utah 1994

e Bishop RR and RW Jeppson Hydraulic characteristics of PVC sewer pipe in sanitary sewers Utah State University Logan Utah September 1975

Chow V T 1959 Open-Channel Hydraulics McGraw-Hill Inc

d Neale LC and RE Price Flow characteristics of PVC sewer pipe Journal of the Sanitary Engineering Division Div Proc 90SA3 ASCE pp 109-129 1964

b Tullis J Paul RK Watkins and S L Barfuss Innovative new drainage pipe Proceedings of the International Conference on Pipeline Design and Installation ASCE March 25-27 1990

LMNO Engineering Research and Software Ltd7860 Angel Ridge Rd Athens Ohio USA (740) 592-1890

LMNOLMNOengcom httpwwwlmnoengcom

Culvert Design Inlet and Outlet Control

Culvert DesignInlet and Outlet Control

Flow thru culverts and over road or damGraph Headwater depth vs Flow

Based on HDS-5 methodology

To LMNO Engineering home page Circular Culvert using Manning Equation LMNOLMNOengcom Unit Conversions Register Trouble printing

Diagram of Flow through a Culvert

Register to fully enable Calculate buttonDemonstration mode for 09 m lt D lt 11 m and Nlt3 (D is pipe diameter N is number of pipes)

Links on this page Introduction Equations Variables Values of Coefficients and Manning n Error Messages and Validity References

In the calculation abovemiddot Culvert Types Conc Sq edge Wall = Concrete pipe with square edged inlet and headwall Conc Groove Wall = Concrete pipe with groove end at inlet and headwall Conc Groove Proj = Concrete pipe with groove end projecting at inlet

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CMP Headwall = Corrugated metal pipe with headwall at inlet CMP Mitered = Corrugated metal pipe mitered to slope at inlet CMP Projecting = Corrugated metal pipe projecting at inlet

middot Unitsm=meters ft=feet ls=litersec cfm=cubic feet per minute cfs=cubic feet per second gpm=US gallons per minute gph=US gallons per hour gpd=US gallons per day MGD=Millions of US gallons per day

middot You can enter tailwater depth (Yt) as a negative number if flow from the culvert drops down to a receiving channel You dont

need to know the exact elevation drop entering any negative number for Yt will have the same effect

middot The phrase Inlet Control or Outlet Control that appears in the upper right hand corner of the calculation refers to the type of control for the total flow (Qt) entered in the calculations upper left hand corner The graph below the calculation plots headwater

depth (Yh) for the range of Qt min to Qt max entered in the bottom right hand corner The type of control may change from one part

of the graph to another as Qt changes

Introduction Culverts have been utilized for thousands of years as a means to transmit water under walkways or roads Often a culvert is simply installed without much thought to how much water it needs to convey under extreme conditions If a culvert cannot convey all of the incoming water then the water will flow over or around the pipe or simply back up behind the culvert creating a pond or reservoir If any of these conditions are unacceptable then the proper culvert diameter and number of culverts must be selected prior to installation in order to convey all of the anticipated water through the pipe(s) This calculation helps the designer size culverts as well as present a headwater depth vs discharge rating curve

The LMNO Engineering calculation is primarily based on the methodology presented in Hydraulic Design of Highway Culverts by Normann (1985) and published by the US Department of Transportations Federal Highway Administration It is also known as HDS-5 (Hydraulic Design Series No 5) HDS-5 focuses on culvert design Culvert design is usually based on the maximum acceptable discharge - thus the HDS-5 methodology is geared toward culverts flowing full with water possibly flowing over the road above the culvert In addition to programming the HDS-5 methodology LMNO Engineering wished to compute headwater depths for lesser flows Therefore in addition to the HDS-5 methodology we have added the Manning equation for culverts flowing partially full The HDS-5 methodology also assumes that the user knows the tailwater depth (Yt) before using the

methodology Though Yt can be found by field measurements it is often computed in the office using Mannings equation based on

bottom width side slopes channel roughness and channel slope Therefore LMNO Engineering added the additional feature of a built-in subroutine for computing Yt for trapezoidal channels Note that for the graphing portion of our calculation Yt is re-

computed for the entire range of flows (Qt) shown on the graph (unless the user specifically inputs Yt)

As explained in Normann 1985 (also known as HDS-5) the discharge through a culvert is controlled by either inlet or outlet conditions Inlet control means that flow through the culvert is limited by culvert entrance characteristics Outlet control means that flow through the culvert is limited by friction between the flowing water and the culvert barrel The term outlet control is a bit of a misnomer because friction along the entire length of the culvert is as important as the actual outlet condition (the tailwater depth) Inlet control most often occurs for short smooth or greatly downward sloping culverts Outlet control governs for long rough or slightly sloping culverts The type of control also depends on the flowrate For a given culvert installation inlet control may govern for a certain range of flows while outlet control may govern for other flowrates If the flowrate is large enough water could go over the road (or dam) In this case the calculation automatically computes the amount of water going over the road and through each culvert as well as the headwater depth

If you have surfed around our website you may have noticed our other calculations for circular culverts We have a calculation using Mannings equation for design of circular culverts Since it uses Mannings equation it assumes the culvert is long enough so that normal depth is achieved We also have a calculation for computing discharge from the exit depth (end depth) in a circular culvert - very useful for flowrate measurement in the field For flows under pressure we have several calculations listed under the Pipe Flow category on our home page

Equations and Methodology Back to calculationThe LMNO Engineering methodology generally follows that of Normann (1985 also known as HDS-5) However the Normann methodology is mainly for culvert design Culvert design usually involves the largest expected flowrate We wanted to write a calculation that also determines headwater depth for small flowrates Therefore in addition to the Normann methodology we have incorporated Mannings equation for outlet control when the headwater depth is less than 093 times the culvert diameter 093D is used since it is the depth at which discharge through a partially full culvert is a maximum (Chow 1959) At depths greater than 093D and for full flow the Nomann (1985) equation is used for outlet control For inlet control our calculation uses Normanns equations

Many of the equations shown below are empirical and require US Customary units (feet seconds and radians) Some of the equations are based on first principles and are compatible with any consistent set of units (eg SI) However to keep this web page from being too busy we have refrained from indicating which equations are empirical and which are fundamental If you work through the equations by hand please use feet seconds and radians in all of them to avoid any problem with units [Our calculation (above) allows many different types of units the units are internally converted before and after using the equations]

Since total flowrate (Qt) is entered and headwater depth (Yh) is computed the equations below are solved simultaneously to

determine Yh Outlet versus inlet control is determined by the equation resulting in a larger value for Yh

All of the variables are defined below in the Variables section Pipe downstream invert elevation is defined as 00

General EquationsQt = Qr + N Qp Sp = Sc - Yf Lp Ei = Lp Sp Eh = Ei + Yh V=Qp Av

Tailwater Depth Yt

Yt can be computed or input If it is computed Mannings equation is used (Chow 1959)

Since Qt is input the above equations are solved numerically (backwards) for Yt

Headwater depth Yh

Yh is computed independently based on inlet and outlet control equations The equation that gives the larger value of Yh is

considered to be the controlling mechanism and is reported

Inlet Control (see below for values of constants C1 C2 C3 C4 C5)

Outlet velocity (V) is computed based on what we call the velocity depth Yv Normann (1985) suggests computing Yv using the

Manning equation If Yv is greater than D then Yv is set to D

Unsubmerged Inlet (Normann 1985)

Submerged Inlet (Normann 1985)

Outlet ControlOutlet velocity (V) is computed based on what we call the velocity depth Yv Normann (1985) suggests If Ytlt=Yc then Yv=Yc If

YcltYtltD then Yv=Yt If Ytgt=D then Yv=D

If Yhlt093D then Mannings equation (Chow 1959) is used

Since Qp is input the above equations are solved numerically for Yt

If Yhgt=093D Normann (1985) is used

Flow over Road (or Dam)If water flows over the road (or dam) then flow over the road is computed by (Normann 1985)

Note that instead of using a constant value of 3 Normann (1985) uses a coefficient that varies from 25 to 31 depending on the water depth above the road and whether the road is paved or gravel

Variables Back to calculation

A=Flow area [ft2]Ac=Flow area in one pipe based on critical depth [ft2]

Av=Flow area in one pipe used for computing outlet velocity [ft2]

b=Width of channel bottom [ft] Used for computing Yt

C1 C2 C3 C4 C5=Constants for inlet control equations See values below

D=Diameter of each pipe (culvert) [ft]Eh=Headwater elevation relative to invert of pipe outlet [ft] Pipe outlet invert elevation is defined at 00 ft

Ei=Elevation of pipe inlet invert relative to pipe outlet invert [ft] Pipe outlet invert elevation is defined at 00 ft

Er=Elevation of road (or dam) crest relative to pipe outlet invert [ft] Pipe outlet invert elevation is defined at 00 ft

g=Acceleration due to gravity 32174 fts2H=Head loss computed from outlet control equation [ft]Ke=Minor loss coefficient for pipe inlet (used for outlet control equations) See values below

Lp=Pipe (culvert) length [ft] If there is more than one culvert they all must have the same length Lp is the length of one of them

(not the sum of the lengths)Lw=Weir length [ft] Length of the road (or dam) that water could flow over Lw is the width that the water sees as it flows over

the roadnc=Channel Manning n coefficient See values below

np=Pipe (culvert) Manning n coefficient See values below

N=Number of pipes (culverts) next to each otherP=Wetted perimeter [ft]Qp=Flowrate through each pipe [cfs ft3s]

Qr=Flowrate over the road (or dam) [cfs]

Qt=Total flowrate [cfs] Sum of flows through pipes plus flow over road

Sc=Slope of existing channel [elevation changelength] Longitudinal slope not side slopes

Sp=Pipe slope [elevation changelength] Longitudinal slope not side slopes

Tc=Top width of flow in one pipe based on critical depth [ft]

V=Pipe outlet velocity [fts]Vc=Pipe velocity based on critical depth [fts]

Yavg=Average water depth [ft]

Yc=Critical water depth [ft]

Yf=Fall [ft] Vertical distance that inlet pipe invert is lowered below the existing channel bottom

Yh=Headwater depth [ft]

Yo=Water outlet depth [ft]

Yt=Tailwater depth [ft] Depth of water in existing channel at culvert outlet

Yv=Depth used for computing outlet velocity [ft]

z1=Left side slope of existing natural channel [horizontalvertical]

z2=Right side slope of existing natural channel [horizontalvertical]

Values of Coefficients and Manning n Back to calculationManning n values are from Chow (1950) French (1985) Mays (1999) Normann (1985) and Streeter (1998) C1 through C5 and

Ke are from Normann (1985)

Pipe material and inlet type Manning n C1 C2 C3 C4 C5 Ke

Concrete Square edge inlet with headwall 0013 00098 20 -05 00398 067 05

Concrete Groove end inlet with headwall 0013 00078 20 -05 00292 074 02

Concrete Groove end projecting at inlet 0013 00045 20 -05 00317 069 02

Corrugated metal (CMP) Headwall at inlet 0022 00078 20 -05 00379 069 05

Corrugated metal (CMP) Mitered to slope at inlet 0022 00210 133 07 00463 075 07

Corrugated metal (CMP) Projecting at inlet 0022 00340 150 -05 00553 054 09

Channel Material Manning n Material Manning nNatural Streams Excavated Earth Channels

Clean and Straight 0030 Clean 0022

Major Rivers 0035 Gravelly 0025

Sluggish with Deep Pools 0040 Weedy 0030

Stony Cobbles 0035

Floodplains

Pasture Farmland 0035 Heavy Brush 0075

Light Brush 0050 Trees 015

Error Messages and Validity Back to calculationInput checks in top half of calculation If one of these messages appears the calculation and graphing is haltedNeed 0lt=Qtlt10000 m3s Total flow cannot be negative or must be less than 10000 m3s

Need 0ltNlt1001 Must have at least one pipe but no more than 1000 pipesNeed 0ltDlt100 m Pipe diameter must be positive and less than 100 mNeed 0ltLplt10000 m Pipe length must be positive and less than 10000 mNeed 0ltPipe nlt005 Pipe Manning n must be positive and less than 005Need YtltEr Tailwater depth cannot be higher than the road crest

Need Ei+DltEr Upstream pipe invert plus culvert diameter cannot exceed road crest elevation If Ei+D is greater than Er then

the top of the culvert is pushing through the road which is unacceptableNeed 0ltLwlt10000 m Weir length of road (or dam) must be positive and less than 10000 m

Need Ytlt10000 m Tailwater depth must be less than 10000 m Negative values are acceptable Negatives simulate culverts

discharging to a lower channelNeed Sclt05 Channel bottom slope cannot exceed 05 mm (vertical to horizontal ratio) This is the longitudinal slope not the

side slopesNeed Scgt0 Channel cannot be horizontal

Need 0ltChan nlt05 Channel Manning n must be positive and less than 05Need 0ltblt10000 m Channel bottom width must be positive and less than 10000 mNeed 0ltz1lt10000 Need 0ltz2lt10000 Channel side slopes can be neither exactly vertical (z=0) nor nearly flat (zgt10000) z

is defined as horizontal to vertical ratioNeed 1e-7ltSplt05 Pipe slope must be between these limits

Input checks for graph If one of these messages appears the graph will not proceed Note that if any value is out of range in the upper portion of the calculation a graph will not be shownNeed min Qtgt=0 Minimum total flow for graph was entered as a negative number

Max Qtgt10000 m3s Maximum total flow for graph cannot exceed 10000 m3s

Min must be lt Max Minimum Qt entered for graph must be less than maximum Qt entered for graph

Need MinMaxlt099 Minimum Qt entered for graph must be less than 099 times maximum Qt entered for graph Otherwise the

minimum and maximum are too close together to have good axis labels for the graph

Run-time errors The following message may be generated by the graphing portion of the calculationYtgtEr for some Qt Tailwater depth exceeds road (or dam) crest for large values of Qt Yh cannot be computed or graphed when

YtgtEr since the equations are only valid for Ytlt=Er

References Back to calculationChow V T 1959 Open-Channel Hydraulics McGraw-Hill Inc (the classic text)

French R H 1985 Open-Channel Hydraulics McGraw-Hill Book Co

Mays L W editor 1999 Hydraulic design handbook McGraw-Hill Book Co

Normann J M 1985 Hydraulic design of highway culverts HDS-5 (Hydraulic Design Series 5) FHWA-IP-85-15 NTIS publication PB86196961 Obtainable at httpwwwntisgov

Streeter V L E B Wylie and K W Bedford 1998 Fluid Mechanics WCBMcGraw-Hill 9ed

LMNO Engineering Research and Software Ltd7860 Angel Ridge Rd Athens Ohio 45701 USA (740) 592-1890

Design of Circular Water Pipes using Hazen Williams Equation

Design of Circular Pressurized Water Pipes

Calculation uses Hazen-Williams friction loss equation (commonly used by Civil Engineers) Valid for water at

temperatures typical of city water supply systems (40 to 75 oF 4 to 25 oC)

ToOther single pipe calculators Hazen-Williams with pump curve Darcy-Weisbach without pump curve

Darcy-Weisbach with pump curveMultiple pipes Bypass Loop Pipe Network

LMNO Engineering home page Unit Conversions Page Trouble printing

Topics Scenarios Common Questions Equations H-W Coefficients Minor Loss Coefficients

Piping Scenarios

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Common Questions Back to CalculationsI took fluid mechanics a long long time ago What is head Why does it have units of length Head is energy per unit weight of fluid (ie Force x LengthWeight = Length) The program on this page solves the energy equation (shown below) we call energy headWhy is Pressure=0 for a reservoir A reservoir is open to the atmosphere so its gage pressure is zeroWhy is Velocity=0 for a reservoir This is a common assumption in fluid mechanics and is based on the fact that a reservoir has a large surface area Therefore the water level drops very little even if a lot of water flows out of the reservoir A reservoir may physically be a lake or a large diameter tankWhat is a main and a lateral A main is a large diameter water supply pipe that has many smaller diameter laterals branching off of it to supply water to individual residences businesses or sub-divisions In fluid mechanics we set V=0 for the main since it has a large diameter (relative to the lateral) and thus a very small velocity To further justify the V=0 assumption the mains pressure is typically high so the velocity head in the main is negligible The main is drawn such that it is coming out of your computer monitor

Can I model flow between two reservoirs using either Scenario B or E Yes you can If using Scenario E just set P1-P2=0 Scenario B automatically sets P1-P2=0Can I model flow between two mains using either Scenario B or E Only if the pressure is the same in both mainsHow do I model a pipe discharging freely to the atmosphere Use Scenario A C or F Since P2=0 (relative to atmospheric pressure) P1-P2 that is input or output will be P1What are minor losses Minor losses are head (energy) losses due to valves pipe bends pipe entrances (for water flowing from a tank to a pipe) and pipe exits (water flowing from a pipe to a tank) as opposed to a major loss which is due to the friction of water flowing through a length of pipe Minor loss coefficients (Km) are tabulated below For our program all of the pipes have the same diameter so you can add up all your minor loss coefficients and enter the sum in the Minor Loss Coefficient input boxIm confused about pumps Only input Pump Head if the pump is between points 1 and 2 Otherwise enter 0 for Pump HeadYour program is great What are its limitations Pipes must all have the same diameter Pump curves cannot be implemented The fluid must be waterWhere can I find additional information ReferencesWhat is Driving Head See below

Steady State Energy Equation used for this page Back to CalculationsObtained from References

Driving Head (DH) = left side of the first equationg = acceleration due to gravity = 32174 fts2 = 98066 ms2

k = unit conversion factor = 1318 for English units = 085 for Metric unitsS = Specific Weight of Water (ie weight density weight per unit volume) = 624 lbftsup3 for English units = 9800 Nmsup3 for Metric unitsPump Power = SQHp Note that 1 horsepower = 550 ft-lbs

All of the calculations on this page have analytic (closed form) solutions except for Solve for V Q and Q known Solve for Pipe Diameter These two calculations required a numerical solution Our solution utilizes a modified implementation of Newtons method that finds roots of the equations with the result accurate to 8 significant digits All of the calculations utilize double precision

Table of Hazen-Williams Coefficients (C is unit-less) Back to CalculationsCompiled from References

Material C Material C

Asbestos Cement 140 Copper 130-140

Brass 130-140 Galvanized iron 120

Brick sewer 100 Glass 140

Cast-Iron Lead 130-140

New unlined 130 Plastic 140-150

10 yr old 107-113 Steel

20 yr old 89-100 Coal-tar enamel lined 145-150

30 yr old 75-90 New unlined 140-150

40 yr old 64-83 Riveted 110

ConcreteConcrete-lined

Steel forms 140 Tin 130

Wooden forms 120 Vitrif clay (good condition) 110-140

Centrifugally spun 135 Wood stave (avg condition) 120

Table of Minor Loss Coefficients (Km is unit-less) Back to CalculationsCompiled from References

Fitting Km Fitting Km

Valves Elbows

Globe fully open 10 Regular 90deg flanged 03

Angle fully open 2 Regular 90deg threaded 15

Gate fully open 015 Long radius 90deg flanged 02

Gate 14 closed 026 Long radius 90deg threaded 07

Gate 34 closed 17 Regular 45deg threaded 04

Swing check forward flow 2

Swing check backward flow infinity Tees

Line flow flanged 02

180deg return bends Line flow threaded 09

Flanged 02 Branch flow flanged 10

Threaded 15 Branch flow threaded 20

Pipe Entrance (Reservoir to Pipe) Pipe Exit (Pipe to Reservoir)

Square Connection 05 Square Connection 10

Rounded Connection 02 Rounded Connection 10

Re-entrant (pipe juts into tank) 10 Re-entrant (pipe juts into tank) 10

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Gradually Varied Flow Calculation Backwater profile

Gradually Varied Flow in Trapezoidal Channel

Plot Water depth Velocity Froude Top width vs DistanceCompute GVF profile (M1 M2 S2 S3 C1 C3)

Compute normal and critical depths

To LMNO Engineering home page (more calculations) Trapezoidal Channel Design Hydraulic Jump Unit Conversions

LMNOLMNOengcom phone (USA) +1(740) 592-1890 Trouble printing

Cross-Section of Trapezoidal Channel

Gradually Varied Flow Profiles

CalculationRegister to fully enable the Calculate button Demonstration mode for B=3 m

middot If x-axis says Distance in m divided by 10^2 then multiply the value shown on the axis by 10^2 in order to get the actual value Therefore 50 on the axis is actually 500 meters Likewise for the y-axismiddot Elevation graph shows bottom of channel (ie channel invert) and water surface elevations relative to channel invert elevation of 00 at Xmax

middot Units cm=centimeter cfs=cubic feet per second ft=feet gpm=US gallons per minute gph=US gallons per hour gpd=US gallons per day km=kilometer m=meter MGD=Millions of US gallons per day s=second

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Links on this page Equations Variables Manning n coefficients Error messages References

Introduction In long prismatic (constant cross-sectional geometry) channels flowing water will attempt to reach the normal depth (also known as the uniform flow depth) Normal depth is the water depth determined using Mannings equation (please see our other web page for design of trapezoidal channels using Mannings equation) A gradually varied flow (GVF) profile is a plot of water depth versus distance along the channel as the water depth gradually achieves normal depth A GVF computation in a trapezoidal channel involves starting at a known depth Ys and making successive water depth computations at small distance intervals The method involves the continuity

equation and energy slope equations The LMNO Engineering calculation initially computes normal depth critical depth and GVF profile type Then it computes the water depth profile and plots it The calculation also displays channel properties (depth velocity Froude number etc) at a specific location Xp entered by the user A GVF profile is also known as a water depth profile backwater

calculation and non-uniform flow computation It is for steady state flows (discharge remains constant)

The LMNO Engineering calculation plots GVF profiles for M1 M2 S2 S3 C1 and C3 curves M3 and S1 curves cross over the critical depth in order to achieve normal depth Flows crossing the critical depth are called rapidly varied flows and cannot be computed using GVF methods

Equations and MethodologyFundamental flow equations are first presented followed by equations for computing the critical depth Yc and normal depth Yn Then

using the input value of Ys the GVF profile type is determined and the GVF profile is computed using the Improved Euler method

References for the equations are shown alongside the equations Mannings equation for Yn and the equation for the friction slope Sf are

empirical they are shown in the form that uses meters and seconds for units Units for all other equations can be from any consistent set of units

Fundamental equationsThe following equations are always valid for trapezoidal channels (Chanson 1999 Chow 1959 Simon and Korom 1997)

Critical depth computationTo compute critical depth Yc the Froude number F is set to 10 Then we use the Newton method (Kahaner Moler and Nash 1989 Rao

1985) along with the fundamental equations above to solve for Yc

Normal depth computationTo compute normal depth Yn a cubic solution technique (Rao 1985) is used to solve the fundamental equations above in conjunction with

the Manning Equation (Chanson 1999 Chaudhry 1993 Chow 1959 Simon and Korom 1997)

Gradually varied flow profile determination (Chanson 1999 Chaudhry 1993 Chow 1959 Simon and Korom 1997)If YngtYc then the channel is considered to have a mild (M) slope If YnltYc the slope is steep (S) If Yn=Yc then the slope is termed

critical (C) The slopes are further classified by a number (1 2 or 3) as follows

For mild slopes (YngtYc)

If YsgtYn then the slope is an M1 The GVF calculation starts downstream at Xmax at a depth of Ys and proceeds upstream to X=0 The

water depth gets closer to Yn as the calculation proceeds further and further upstream

If YngtYs gtYc then the slope is an M2 The GVF calculation starts downstream at Xmax at a depth of Ys and proceeds upstream to X=0

The water depth gets closer to Yn as the calculation proceeds further and further upstream

If YcgtYs then the slope is an M3 This is an unstable GVF calculation since the water depth begins below both Yn and Yc Since the slope

is mild an hydraulic jump will occur Hydraulic jumps are rapidly varied flow situations that cannot be modeled by a GVF calculator Therefore the message Cannot plot S1 or M3 will be shown

For steep slopes (YcgtYn)

If YsgtYc then the slope is an S1 This is an unstable GVF calculation since the water depth begins above both Yc and Yn Since the slope

is steep the water depth will have to pass through the critical depth in order to reach the normal depth Passing through the critical depth is a rapidly varied flow situation that cannot be modeled by a GVF calculator Therefore the message Cannot plot S1 or M3 will be shown

If YcgtYsgtYn then the slope is an S2 The GVF calculation starts upstream at X=0 at a depth of Ys and proceeds downstream to Xmax The

water depth gets closer to Yn as the calculation proceeds further and further downstream

If YngtYs then the slope is an S3 The GVF calculation starts upstream at X=0 at a depth of Ys and proceeds downstream to Xmax The

For critical slopes (Yc=Yn)

If YsgtYc then the slope is a C1 The GVF calculation starts downstream at Xmax at a depth of Ys and proceeds upstream to X=0 The

If YcgtYs then the slope is a C3 The GVF calculation starts upstream at X=0 at a depth of Ys and proceeds downstream to Xmax The

There is no such thing as a C2 slope - sinceYc=Yn Ys cannot be between Yc and Yn

Gradually varied flow profile (graph) computationTo compute the gradually varied flow profile (graph) the Improved Euler method (Chaudhry 1993) is used

At control section i=1 and Yi=Ys

Repeat for i=2 to n in increments of distance dX where dX is negative for downstream control and dX is positive for upstream controlCompute Ti Ai and Pi using the fundamental equations shown above using Y=Yi

Compute the friction slope depth increment and intermediate depth (note for the friction slope equation shown the friction slope variables must be in meters and seconds)

Compute T2 A2 and P2 using the fundamental equations shown above with Y=Y2 Then compute the friction slope based on T2 A2 and

P2 followed by computation of a second depth increment Finally compute the water depth Yi+1 by using the average of the two

differential depth increments (this is the basis of the Improved Euler method)

Then repeat the loop by incrementing i

The LMNO Engineering calculation uses an unequal node spacing so that more nodes are used at the beginning of the calculation to improve accuracy The first node spacing is approximately 10-10 m and there are 4500 distance increments The results have been checked against hand calculations spreadsheets and results shown in Chaudhry (1993) Chow (1959) French (1985) Henderson (1966) and Simon and Korom (1997)

Variables Back to calculationVariables are shown below in SI units (metric) If you work through the above equations by hand use the SI units shown - since many of the equations are empirical and are valid only with the indicated units (The calculation performs internal unit conversions which allow you to select a variety of different units)A=Channel cross-sectional area [m2]Ai=Area computed at successive i intervals in Improved Euler method [m2]

Ap=Area at Xp [m2]

A2=Area for intermediate computation in Improved Euler method [m2]

dX=Distance increment for Improved Euler method [m] Negative for M1 M2 and C1 since computation proceeds upstream Positive for S2 S3 and C3 since computation proceeds downstream(dYdX)1=First depth increment for Improved Euler method [m]

(dYdX)2=Second depth increment for Improved Euler method [m]

B=Channel bottom width [m]E=Elevation [m] The calculation automatically sets the channel invert elevation to 00 at Xmax

Epi=Elevation of channel invert at Xp [m] Invert means bottom of the channel

Epy=Elevation of water surface at Xp [m]

F=Froude number [dimensionless]Fp=Froude number at Xp [dimensionless]

g=Acceleration due to gravity 98066 ms2i=Loop index for computing GVF profilen=Mannings n value [dimensionless] See table below for valuesP=Channel wetted perimeter [m]Pi=Wetted perimeter computed at successive i intervals in Improved Euler method [m]

P2=Second wetted perimeter computed in Improved Euler method [m]

Q=Discharge (flowrate) of water in the channel [m3s]So=Slope of bottom of channel (vertical to horizontal ratio) [mm]

Sf1=First energy slope for Improved Euler method [dimensionless]

Sf2=Second energy slope for Improved Euler method [dimensionless]

T=Top width of water in channel [m]Ti=Top width computed at successive i intervals in Improved Euler method [m]

T2=Second top width computed in Improved Euler method [m]

Tp=Top width at Xp [m]

V=Average velocity of water [ms]Vp=Velocity at Xp [ms]

X=Distance along channel [m]Xmax=Maximum distance for computing GVF profile [m] Profile is always plotted from X=0 to Xmax For M1 M2 and C1 profiles Ys

is at X=Xmax For S2 S3 and C3 profiles Ys is at X=0

Xp=Distance entered by user for showing channel properties [m] Cannot exceed Xmax If user enters XpgtXmax the calculation will

automatically set Xp to Xmax

Y=Water depth [m]Yc=Critical depth [m]

Yi=Water depth computed at successive i intervals in Improved Euler method [m]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Ys=Starting depth [m] This is also known as the depth at the control section It is the depth that GVF calculations start at

Y2=Second depth computed in Improved Euler method [m]

Z1=One channel side slope (horizontal to vertical ratio) [mm]

Z2=The other channel side slope (horizontal to vertical ratio) [mm]

Manning n Coefficients Back to calculationThe Mannings n coefficients were compiled from Chaudhry (1993) Chow (1959) French (1985) and Mays (1999)

Natural Streams Excavated Earth Channels

Stony Cobbles 0035

Metals Floodplains

Brass 0011 Pasture Farmland 0035

Cast Iron 0013 Light Brush 0050

Smooth Steel 0012 Heavy Brush 0075

Corrugated Metal 0022 Trees 015

Non-Metals

Unplaned Wood 0013

Error Messages Back to calculationInitial input checks The following messages are generated from improper input valuesNeed 1e-20ltQlt1e50 m3s Need 1e-20ltBlt1e6 m Need Z1 Z2 gt=0 Z1 Z2 cannot both be 0 Need 1e-9ltnlt20 Need 1e-

20ltSolt1e99 Need 0001ltXmaxlt1e6 m Need 1e-20ltYslt100 m Need Xpgt=0

Run-time messages The following messages may be generated during executionInfeasible input Inputs are unusually large or small causing the program to have trouble computing Yn or Yc

Cannot plot S1 or M3 As discussed above these two GVF profiles encounter rapidly varied flow where the water depth crosses through critical depthNo graph Ys=Yn This is a uniform flow situation not a GVF calculation Water depth will remain at normal depth so the GVF profile

is not computedYn at x=874231 m This is the distance where the water depth is within 001 of the normal depth

References Back to calculationChanson H 1999 The Hydraulics of Open Channel Flow John Wiley and Sons Inc

Chaudhry M H 1993 Open-Channel Flow Prentice-Hall Inc

Chow V T 1959 Open-Channel Hydraulics McGraw-Hill Inc (the classic text)

Henderson F M 1966 Open Channel Flow MacMillan Publishing Co

Kahaner D C Moler and S Nash 1989 Numerical Methods and Software Prentice-Hall Inc 2ed

Rao S 1985 Optimization Theory and Applications Wiley Eastern Limited 2ed

Simon A and S Korom 1997 Hydraulics Prentice-Hall Inc 4ed

Hydraulic Jump Calculation

Hydraulic Jump in Horizontal Rectangular Channel

Hydraulic jump for water in rectangular horizontal channel Enter discharge channel width upstream depth Compute downstream depth Froude numbers depth ratio velocities

jump length and energy loss

To LMNO Engineering home page (all calculations) Related open channel calculations

Rectangular Channel Design Trapezoidal Channel DesignGradually varied flow in trapezoidal channel Unit Conversions

Photograph from Ohio Universitys Fluid Mechanics Laboratory Athens Ohio USA

fileE|engineeringhydraulicsHydraulic20Jump20Calculationhtm (1 of 3)12112007 40633 PM

Equations

Equations for hydraulic jump in horizontal rectangular channel (Chaudhry 1993 Chow 1959)

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

where (subscript 1 indicates upstream of jump subscript 2 indicates downstream of jump)B=Channel width (m) F=Froude number (dimension-less) g=acceleration due to gravity (98066 ms2) h=Head loss (m) L=Length of jump (m) Q=Discharge (m3s) tanh=Hyperbolic tangent trigonometric function V=Velocity (ms) y=Water depth (m)

Note Equations require consistent units such as ft and seconds or meters and seconds LMNO Engineering calculation allows a wide variety of other units Most units are self-explanatory MGD is Millions Gallons (US) per Day

What is a Hydraulic Jump

A hydraulic jump occurs when the upstream flow is supercritical (Fgt1) To have a jump there must be a flow impediment downstream The downstream impediment could be a weir a bridge abutment a dam or simply channel friction Water depth increases during a hydraulic jump and energy is dissipated as turbulence Often engineers will purposely install impediments in channels in order to force jumps to occur Mixing of coagulant chemicals in water treatment plants is often aided by hydraulic jumps Concrete blocks may be installed in a channel downstream of a spillway in order to force a jump to occur thereby reducing the velocity and energy of the water Flow will go from supercritical (Fgt1) to subcritical (Flt1) over a jump

According to Chow (1959) a strong jump occurs when F1gt9 a steady jump occurs when 45ltF1lt9 an

oscillating jump occurs when 25ltF1lt45 a weak jump occurs when 17ltF1lt25 and an undular jump

occurs when 1ltF1lt17 According to Chaudhry (1993) the best jumps occur when 45ltF1lt9

MessagesNeed Bgt0 Channel width must be a positive numberNeed Qgt0 Discharge must be positiveNeed y1gt0 Upstream depth must be positive

Need F1 gt1 Upstream flow must be supercritical

ReferencesChaudhry M H 1993 Open Channel Flow Prentice-Hall Inc

Chow V T 1959 Open Channel Hydraulics McGraw-Hill Inc

Manning Equation

Mannings Equation Calculator Software The open channel flow software website

LMNO Engineering Home Page Manning n values Unit Conversions Trouble printing More calculations Design of Rectangular Channels Design of Trapezoidal Channels

Circular Culverts using Manning Equation Culvert Design using Inlet and Outlet Control Q=VA simple flowrate calculator

The Manning Equation is the most commonly used equation to analyze open channel flows It is a semi-empirical equation for simulating water flows in channels and culverts where the water is open to the atmosphere ie not flowing under pressure and was first presented in 1889 by Robert Manning The channel can be any shape - circular rectangular triangular etc The units in the Manning equation appear to be inconsistent however the value k has hidden units in it to make the equation consistent The Manning Equation was developed for uniform steady state flow (see Discussion and References for Open Channel Flow) S is the slope of the energy grade line and S=hfL where hf is energy (head) loss

and L is the length of the channel or reach For uniform steady flows the energy grade line = the slope of the water surface = the slope of the bottom of the channel

The product AP is also known as the hydraulic radius Rh

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Non-Circular Open Channel Geometry

Geometric Calculations for Non-Circular Partially Filled Channels

The open channel flow calculations software website

Manning Equation Calculator Design of Rectangular Channels Calculation Unit Conversions LMNO Engineering Home Page Trouble printing

You may enter numbers in any units so long as you are consistent (L) means that the variable has units of length (eg meters) (L2) means that the variable has units of length squared (eg m2)

Equations (note that R=AP)

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Pipe Network Calculator Hardy Cross Darcy Weisbach or Hazen Williams losses

Pipe Network CalculatorDarcy Weisbach or Hazen Williams friction

losses

Compute pressure and hydraulic head at each node and flow in each pipe Enter node flows elevations pressure Select Darcy Weisbach (Moody diagram) or Hazen Williams friction losses Include minor losses by equivalent length of

pipe Dont have to use all the pipes or nodes

To Darcy-Weisbach single pipe Hazen-Williams single pipe Bypass Loop LMNO Engineering home page (more calculations) Unit Conversions Page Trouble printing

Enter positive values for inflows at nodes (negative values for outflows) Enter pipe diameter of 00 to make a pipe non-existent

Register to fully enable Calculate button

Demonstration mode for Fluid mercury Pipe material wood Losses Darcy-Weisbach Head loss units m of fluid Flow units m3s Diameter units meters Length units meters Elevation units meters Pressure units m of fluid Z+PS (hydraulic head) units m of fluid To enable other fluids materials units and Hazen-Williams losses please register Click shift-Reload on your browser to reload the default values

Topics on this page Introduction Equations and Methodology (Hardy Cross method friction losses (Darcy Weisbach and Hazen Williams) pressure computation minor losses and calculator) Applications Built-in fluid and material properties Units Variables Error Messages References

IntroductionPipe Network simulates steady flow of liquids or gases under pressure It can simulate city water systems car exhaust manifolds long pipelines with different diameter pipes in series parallel pipes groundwater flow into a slotted well screen soil vapor extraction well design and more Enter flows at nodes as positive for inflows and negative for outflows Inflows plus outflows must sum to 0 Enter one pressure in the system and all other pressures are computed All fields must have a number but the number can be 0 You do not need to use all the pipes or nodes Enter a diameter of 00 if a pipe does not exist If a node is surrounded on all sides by non-existent pipes the nodes flow must be entered as 00 The program allows a wide variety of units After clicking Calculate the arrows lt-- --gt v ^ indicate the direction of flow through each pipe (to the left right down or up)

Losses can be computed by either the Darcy-Weisbach or Hazen-Williams (HW) method selectable by clicking on the Roughness e drop-down menu If HW is used then the fluid must be selected as Water 20C (68F)

The HVRe output field is scrollable using the left and right arrow keys on your keyboard Velocity is in ms if metric units are selected for flowrate Q and fts if English units are selected for Q

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Equations and Methodology Back to CalculationThe pipe network calculation uses the steady state energy equation Darcy Weisbach or Hazen Williams friction losses and the Hardy Cross method to determine the flowrate in each pipe loss in each pipe and node pressures Minor losses (due to valves pipe bends etc) can be accounted for by using the equivalent length of pipe method

Hardy Cross Method (Cross 1936 Viessman and Hammer 1993)The Hardy Cross method is also known as the single path adjustment method and is a relaxation method The flowrate in each pipe is adjusted iteratively until all equations are satisfied The method is based on two primary physical laws

1 The sum of pipe flows into and out of a node equals the flow entering or leaving the system through the node2 Hydraulic head (ie elevation head + pressure head Z+PS) is single-valued This means that the hydraulic head at a node is the same whether it is computed from upstream or downstream directions

Pipe flows are adjusted iteratively using the following equation

until the change in flow in each pipe is less than the convergence criterian=20 for Darcy Weisbach losses or 185 for Hazen Williams losses

Friction Losses HOur calculation gives you a choice of computing friction losses H using the Darcy-Weisbach (DW) or the Hazen-Williams (HW) method The DW method can be used for any liquid or gas while the HW method can only be used for water at temperatures typical of municipal water supply systems HW losses can be selected with the menu that says Roughness e (m) The following equations are used

Hazen Williams equation (Mays 1999 Streeter et al 1998 Viessman and Hammer 1993) where k=085 for meter and seconds units or 1318 for feet and seconds units

Darcy Weisbach equation (Mays 1999 Munson et al 1998 Streeter et al 1998)

where log is base 10 logarithm and ln is natural logarithm Variable definitions

Pressure computationAfter computing flowrate Q in each pipe and loss H in each pipe and using the input node elevations Z and known pressure at one node pressure P at each node is computed around the network

Pj = S(Zi - Zj - Hpipe) + Pi where node j is down-gradient from node i S = fluid weight density [FL3]

Minor LossesMinor losses such as pipe elbows bends and valves may be included by using the equivalent length of pipe method (Mays 1999) Equivalent length (Leq) may be computed using the following calculator which uses the formula Leq=KDf f is the

Darcy-Weisbach friction factor for the pipe containing the fitting and cannot be known with certainty until after the pipe network program is run However since you need to know f ahead of time a reasonable value to use is f=002 which is the default value We also recommend using f=002 even if you select Hazen-Williams losses in the pipe network calculation K values are from Mays (1999)

For example there is a 100-m long 10-cm diameter (inside diameter) pipe with one fully open gate valve and three regular 90o elbows Using the minor loss calculator Leq is 10 m and 125 m for the fully open gate valve and each elbow respectively

The pipe length you should enter into the pipe network calculator is 100 + 10 + 3(125) = 10475 m The calculator allows a variety of units such as m cm inch and ft for diameter and m km ft and miles for equivalent length If a fitting is not listed select User enters K and enter the K value for the fitting

ApplicationsThe pipe network calculation has many applications Two examples will be provided

1 Municipal water supply system A water tower is located at node D The other nodes could represent industries or homes Enter the water withdrawals at all the nodes as negative numbers then enter the inflow to the network from the water tower at node D as a positive number equal to the sum of the withdrawals from the other nodes Usually cities require a certain minimum pressure everywhere in the system often 40 psi Use the drop-down menu to select the node that you expect will have the lowest pressure - possibly the node furthest from D or the one at the highest elevation well use node I Enter the pressure at node I as 40 psi Enter all the pipe lengths diameters and node elevations Then click Calculate You can use your right and left arrow keys to scroll to the left and right to see the velocity in each pipe Typically you want pipe velocities to be around 2 fts If you are designing a system (as opposed to analyzing a system that is already in place) vary the pipe diameters until the pipe velocities are reasonable and pressure at node D is as low as possible to minimize the height of the water tower There will be a trade-off between pressure at D and pipe diameters Smaller diameter pipes will save money on

pipes but will require a taller water tower The water tower height is proportional to the pressure at D according to h=PS where P is the pressure at D S is the weight density of the water and h is the water tower height required A more detailed example

2 Manifold A manifold has multiple inflows at various positions along the same pipeline and one outflow Let node I be the outflow and use all other nodes A-H as inflow locations so flow is from node A through pipes 1 2 5 7 6 8 11 and 12 and out node I Enter the diameters and lengths of these pipes and the desired inflows at nodes A-H Enter the outflow at node I as a positive number equal to the sum of the inflows at nodes A-H Enter the diameters of pipes 3 4 9 and 10 as 00 since they are non-existent pipes Enter the elevations of all nodes For a horizontal pipe set all the elevations to the same value or just to 00 to keep it simple From the drop-down menu select the node where you know the pressure and enter its pressure Clicking Calculate will give the flowrate in all pipes and the pressure at all the nodes

Built-in fluid and material propertiesThe user may manually enter fluid density and viscosity or select one of the common liquids or gases from the drop-down menu Density and viscosity for the built-in fluids were obtained from Munson et al (1998) Likewise the user may manually enter material roughness or Hazen-Williams C or select one of the common pipe materials listed in the other drop-down menu Surface roughnesses for the built-in materials were compiled from Munson et al (1998) Streeter et al (1998) and Mays (1999)

Unitsbblsday=barrelsday cfm=ft3min cfs=ft3s cm=centimeter cP=centipoise cSt=centistoke in=inch in H2O=inch water at 60F in Hg=inch mercury at 60F ft=foot g=gram gpd=gallon (US)day gph=gallon (US)hr gpm=gallon (US)min hr=hour kg=kilogram km=kilometer lb=pound lb(f)=pound (force) m=meter mbar=millibar mm=millimeter mm H2O=mm water at 4C min=minute N=Newton psi=lb(f)in2 s=second

Variables [] indicates units F=force L=length P=pressure T=time Back to Calculation

Fluid density and viscosity may be entered in a wide choice of units Some of the density units are mass density (gcm3 kgm3 slugft3 lb(mass)ft3) and some are weight density (Nm3 lb(force)ft3) There is no distinction between lb(mass)ft3 and lb(force)ft3 in the density since they have numerically equivalent values and all densities are internally converted to Nm3 Likewise fluid viscosity may be entered in a wide variety of units Some of the units are dynamic viscosity (cP poise N-sm2 (same as kgm-s) lb(force)-sft2 (same as slugft-s) and some are kinematic viscosity (cSt stoke (same as cm2s) ft2s m2s) All viscosities are internally converted to kinematic viscosity in SI units (m2s) If necessary the equation Kinematic viscosity = Dynamic viscosityMass density is used internally

A = Pipe area [L2]C = Hazen Williams coefficient Selectable as last item in drop-down menu saying Roughness eD = Pipe diameter [L]e = Pipe roughness [L] All pipes must have the same roughnessf = Moody friction factor used in Darcy Weisbach friction loss equationg = Acceleration due to gravity = 32174 fts2 = 98066 ms2H = Head losses in pipe [L] Can also be expressed in pressure units [P]k = Constant in Hazen Williams equation for computing HK = Minor loss coefficientL = Pipe length [L]Leq = Equivalent length of pipe for minor losses [L]

n = Constant used in Hardy Cross equationP = Node pressure [P] Can also be expressed in length units [L]Q = Flowrate through pipe or into or out of node [L3T] Also known as discharge or capacityRe = Reynolds numberS = Specific Weight of Fluid (ie weight density weight per unit volume) [FL3] Typical units are Nm3 or lb(force)ft3

Note that S=(mass density)(g)V = Velocity in pipe [LT]Z = Elevation of node [L]Z+PS = Hydraulic head [L] Also known as piezometric head Can also be expressed in pressure units [P]v = Kinematic viscosity of fluid [L2T] Greek letter nu Note that kinematic viscosity is equivalent to dynamic (or absolute) viscosity divided by mass density Mass density=Sg

Error Messages in Pipe Network calculation Back to CalculationNode Qs must sum to 0 Check the node flowrates that you entered Total flow into pipe network must equal total flow out of pipe networkTotal inflow must be gt0 Check that you have positive flow into the system You have entered all node flows as 00 or negativeNode i must have Q=0 Node i is completely surrounded by pipes having diameters less than 0001 m which is the criteria the program uses for treating pipes as being non-existent You cannot have flow in or out of a node that is surrounded by non-existent pipes|Q| must be lt 1e9 m3s Node flows cannot exceed 109 m3s | | is absolute valueP at isolated node Be sure that the P known at node x drop-down menu indicates a node that is surrounded by at least one existing pipe (ie a pipe having a diameter greater than 0001 m) If you dont know the pressure anywhere in your system just enter 00 for the pressure All the other node pressures will be computed relative to the pressure you enterDensity must be gt 0 Density too high Viscosity must be gt 0 Viscosity too high These messages can only occur if Another fluid is selected from the fluid drop-down menu Be sure the density and viscosity you enter are greater than zero but less than 1010 kgm3 and 1010 m2s respectivelyD must be lt 1e6 m Individual pipe diameters cannot exceed 106 mL must be lt 1e7 m Individual pipe lengths cannot exceed 107 m|Z| must be lt 1e20 |P| must be lt 1e20 m The absolute value of each node elevation and pressure that are input cannot exceed 1020 mNeed Water (20C) if H-W If Hazen-Williams C is selected from the Roughness drop-down menu you must also select Water 20C (68F) from the fluid drop-down menu The Hazen-Williams method for head losses is only valid for water at typical city water supply temperatures such as 20CC out of range e out of range These messages can only occur if you selected Another material from the pipe material drop-down menu Valid ranges are 0ltClt1000 and 0 lt= e lt 100 m Normally C will not exceed 150 and e will not exceed 0001 m but we allow high ranges for those who like to experimentPipe i eD out of range See the equations above for Friction loss computation using Darcy-Weisbach eD cannot exceed 005 unless Reynolds number is less than 4000 Also eD cannot be 00 (ie e cannot be 00) if Reynolds number is greater than 108Unusual input If you experiment with the calculation long enough you may enter some very unusual input combinations Some situations are physically not possible but the calculation will continue iterating to compute the pipe flows and losses After 5000 iterations (a few seconds of real time) the program will stop running and give you this error message so you can check your input and enter more realistic numbers The program has been designed so that it will not lock upOther things If the calculation doesnt seem to run when you click Calculate check your inputs If you accidentally entered two decimal points or a letter in an input field then it wont run and wont give an error message

References Back to CalculationCross Hardy Analysis of flow in networks of conduits or conductors University of Illinois Bulletin No 286 November 1936

Munson BR D F Young and T H Okiishi 1998 Fundamentals of Fluid Mechanics John Wiley and Sons Inc 3ed

Viessman W and M J Hammer 1993 Water Supply and Pollution Control HarperCollins College Publishers 5ed

Pressurized Liquid or Gas Pipes with Pump Curve Darcy Weisbach (Moody diagram) friction losses

Circular Pressurized Liquid or Gas Pipe with Pump Curve (Darcy

Weisbach - Moody friction losses)

Compute flow (ie discharge capacity) velocity pipe diameter length elevation difference pressure difference major losses

(using Darcy-Weisbach friction loss ie Moody Diagram) minor losses total dynamic head net positive suction head User enters two points on pump curve - Head at no flow and Flow at no head

Parabolic shaped pump curve is formed from the two points

ToOther single pipe calculators Darcy-Weisbach without pump curve Hazen-Williams without pump

curve Hazen-Williams with pump curve

Multiple pipes Bypass Loop Pipe Network LMNO Engineering home page (more calculations) Unit Conversions Page Trouble printing

Topics Piping Scenarios Equations and Methodology Variables Minor Loss Coefficients Error Messages References

IntroductionThis program automatically intersects a system curve with a pump curve to tell you the operating point If you have a pump already installed or want to investigate system performance of a certain pump before purchasing it you can enter two points on its pump curve along with piping system information to determine the actual flowrate through the system Or if you know the flowrate or velocity you can solve for diameter pipe length pressure difference elevation difference or the sum of the minor loss coefficients

A pump curve (blower curve for gases) is incorporated into the calculation to simulate systems containing a centrifugal pump or other pump that has a pump curve To keep the calculations input relatively simple we only require you to enter two points on the pump curve - flow at zero head and head at zero flow A parabolic curve is then formed between the two points as shown in equations below The calculation also asks for information specifically about the pipe on the suction side of the pump This information is used to compute the net positive suction head available (NPSHA) for liquids

For a pump to properly function the NPSHA must be greater than the NPSH required by the pump

(obtained from the pump manufacturer) If your system does not require a pump or uses a pump that does not have a parabolically shaped pump curve then our other Darcy Weisbach design calculation may be more helpful

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Piping ScenariosPipe A is the pipe upstream from the pump (ie the suction side pipe)Convention for Z1-Z2 and Z1-Z3 If location 1 is above location 2 then Z1-Z2 should be entered as

positive If location 2 is above location 1 then Z1-Z2 should be entered as negative Likewise for Z1-Z3

Equations and Methodology Back to CalculationsThe calculation on this page uses the steady state energy equation Minor losses (due to valves pipe bends etc) and major losses (due to pipe friction) are included The Darcy Weisbach equation for friction losses is used and the calculation includes both laminar and turbulent flow The equations are standard equations which can be found in most fluid mechanics textbooks (see references below) A pump curve is included in the calculation Determination of the pump curve requires that the user enter the two extreme points on the curve - head when capacity is zero and capacity when head is zero Then a parabola with a negative curvature is fit through the two points This parabola is used since it is a good approximation of a typical pump curve and does not require users to enter a multitude of data points And oftentimes pump catalogs only give the two extreme points on the curve rather than a graph showing the complete curve

Energy equation with Darcy-Weisbach friction lossesAll equations were compiled from references except for parabolic pump curve equation which is our development The Colebrook equation is an equation representation of the Moody diagram

Pump CurveTo provide an example of a pump curve developed using the equation H=Hmax[1-(QQmax)2] let

Qmax=1500 gpm (when head is zero) and Hmax=900 ft (when Q is zero) The pump curve used in the

calculation will look like

The Colebrook equation is solved for f using Newtons method (Kahaner et al 1989) The remaining calculations are analytic (ie closed form) except Solve for V Q Q known Solve for Diameter and V known Solve for Diameter These three calculations required a numerical solution Our solution utilizes a cubic solver (Rao 1985) with the result accurate to 8 significant digits Multiple solutions are possible for the three numerical solutions All solutions for both laminar and turbulent flow are automatically determined and shown if they exist All of the calculations utilize double precision

Built-in fluid and material propertiesThe user may enter his own fluid properties or select one of the common liquids or gases from the drop-down menu Weight density kinematic viscosity and vapor pressure (if a liquid) for the built-in fluids were obtained from references Likewise the user may enter his own material roughness or select one of the common pipe materials listed in the other drop-down menu Surface roughnesses for the built-in materials were compiled from references

Net Positive Suction HeadNPSH is the sum of the heads that push fluid into a pump less the suction side losses Most pumps have a minimum requirement for NPSH called NPSHR If the NPSH available by the piping system (NPSHA)

is lower than NPSHR then the pump will not function properly and may overheat NPSH is only

defined for liquids

Variables Units F=force L=length P=pressure T=time Back to Calculations

Fluid density and viscosity may be entered in a wide choice of units Some of the density units are mass density (gcm3 kgm3 slugft3 lb(mass)ft3) and some are weight density (Nm3 lb(force)ft3) There

is no distinction between lb(mass)ft3 and lb(force)ft3 in the density since they have numerically equivalent values and all densities are internally converted to Nm3 Likewise fluid viscosity may be entered in a wide variety of units Some of the units are dynamic viscosity (cP poise N-sm2 (same as kgm-s) lb(force)-sft2 (same as slugft-s) and some are kinematic viscosity (cSt stoke (same as cm2s) ft2s m2s) All viscosities are internally converted to kinematic viscosity in SI units (m2s) If necessary the equation Kinematic viscosity = Dynamic viscosityMass density is used

A = Pipe area [L2]D = Pipe diameter [L]e = Pipe roughness [L]f = Moody friction factor used in Darcy-Weisbach friction loss equationg = Acceleration due to gravity = 32174 fts2 = 98066 ms2

hf = Major losses for entire pipe [L] Also known as friction losses

hfA = Major losses for pipe upstream of pump (pipe A) only [L]

hm = Minor losses for entire pipe [L]

hmA = Minor losses for pipe upstream of pump (pipe A) only [L]

H = Total dynamic head [L] Also known as system head or head supplied by pumpHmax = Maximum head that pump can provide [L] It is the head when Q=0

K = Sum of minor loss coefficients for entire pipe See table below for valuesKA = Sum of minor loss coefficients for pipe upstream of pump (pipe A) Same as Ka Only required

for liquidsL = Total pipe length [L]LA = Length of pipe upstream of pump (pipe A) [L] Same as La Only required for liquids

NPSH = Net positive suction head [L] The calculation computes NPSHA (NPSH available)

Patm = Atmospheric (or barometric) pressure [P] Standard atmospheric pressure = 147 psi = 2992 inch

Hg = 760 mm Hg = 1 atm = 101325 Pa = 101 bar Note that your local atmospheric pressure is different from standard atmospheric pressure Be careful - if you change the units of Patm and Pv be sure to enter Patm in the selected units Only required for liquidsPv = Vapor pressure of fluid [P] Expressed as an absolute pressure Only required for liquids

P1 = Gage pressure at location 1 of the system [P] Location 1 could be the surface of a reservoir open

to the atmosphere (thus P1=0) or the pressure in a supply main (same as a tank under pressure) or

location 1 could simply be a location in a pipe upstream of the pump Only required for liquidsP1-P3 = Pressure difference between locations 1 and 3 [P]

Q = Flowrate [L3T] Also known as discharge or capacityQmax = Maximum flowrate on pump curve [L3T] Corresponds to point on pump curve where head is

zeroRe = Reynolds numberS = Specific Weight of Fluid (ie weight density weight per unit volume) [FL3] Typical units are Nm3 or lb(force)ft3 Note that S=(mass density)(g)

V1 = Velocity of fluid at location 1 This is determined when you select a scenario If location 1 is a

reservoir or main (Scenarios B C E and F) then V1 is automatically set to 0 because the velocity head

of the fluid in the reservoir or main (or pressure tank) is much smaller than in the attached pipeline This is a standard assumption in fluid mechanics However if location 1 is inside the suction side pipeline then V1 is automatically computed as QA

reservoir or main (Scenarios B D E and G) then V3 is automatically set to 0 because the velocity head

of the fluid in the reservoir or main (or pressure tank) is much smaller than in the attached pipeline This is a standard assumption in fluid mechanics However if location 3 is inside your discharge side pipeline then V3 is automatically computed as QA

Z1-Z2 = Elevation of location 1 minus elevation of pump [L] If the pump is above location 1 then enter

this value as negative Only required for liquidsZ1-Z3 = Elevation of location 1 minus elevation of location 3 [L]

v = Kinematic viscosity of fluid [L2T] greek letter nu Note that kinematic viscosity is equivalent to dynamic (or absolute) viscosity divided by mass density Mass density=Sg

Table of Minor Loss Coefficients (K is unit-less) Back to CalculationsCompiled from references

Fitting K Fitting K

Valves Elbows

Error Messages Back to CalculationsThe following are input checks and will appear if an input is physically impossible such as a negative lengthQ V D L must be gt 0 Density Viscosity must be gt 0 K must be gt= 0 e must be gt= 0 Qmax Hmax must be gt 0 Q must be lt= Qmax

The following are input checks for liquids onlyLa Ka must be gt= 0 Vapor and Atm P must be gt 0

Need Lalt=L and Kalt=K Length of the suction pipe (Pipe A) was entered as being longer than all of

the pipe or K for the suction pipe was entered as greater than K for the entire system

Other messagesK must be gt=1 If Q known Solve for D and V

3=0 then K must be gt 1 in order to solve

Tanks open so P1-P3=0 for B Cannot solve for pressure difference if using Scenario B since

reservoirs are defined to be at zero pressure thus zero pressure difference

Infeasible input Hlt0 Infeasible input hmlt0 Infeasible input hf lt=0 Re or eD out of range

Infeasible Losses will be lt=0 f wont be 0008 to 01 f will be too small f will be too large Re will be gt 1e8 Infeasible input One of these messages will appear if each of your inputs is okay but they combine to give no possible solution For instance if you are solving for pipe diameter and your input data will result in negative losses regardless of pipe diameter then your data are infeasible

References Back to CalculationsNumerical methods citationsKahaner D C Moler S Nash 1989 Numerical methods and software Prentice-Hall Inc

Rao S S 1985 Optimization theory and applications Wiley Eastern Limited 2ed

Fluid mechanics referencesGerhart P M R J Gross and J I Hochstein 1992 Fundamentals of Fluid Mechanics Addison-Wesley Pubishing Co 2ed

Potter M C and D C Wiggert 1991 Mechanics of Fluids Prentice-Hall Inc

Roberson J A and C T Crowe 1990 Engineering Fluid Mechanics Houghton Mifflin Co

White F M 1979 Fluid Mechanics McGraw-Hill Inc

Pressurized Water Pipes with Pump Curve Calculation uses Hazen Williams equation

Circular Pressurized Water Pipes with Pump Curve

(Hazen Williams)

(using Hazen Williams coefficient) minor losses total dynamic head net positive suction head User enters two points on pump curve - Head at no flow and Flow at no head Parabolic shaped pump curve is formed from the two points Valid for water at

ToOther single pipe calculators Hazen-Williams without pump curve Darcy-Weisbach without pump

curve Darcy-Weisbach with pump curve

Multiple pipes Bypass Loop Pipe NetworkLMNO Engineering home page Unit Conversions Page Trouble printing

Topics Scenarios Common Questions Equations Variables Hazen Williams Coefficients Minor Loss Coefficients Error Messages

IntroductionThe Hazen Williams equation for major (friction) losses is commonly used by engineers for designing and analyzing piping systems carrying water at typical temperatures of municipal water supplies (40 to 75 oF 4 to 25 oC) A pump curve is incorporated into the calculation to simulate flows containing centrifugal pumps or other pumps that have a pump curve To keep the calculations input relatively simple we only require you to enter two points on the pump curve - flow at zero head and head at zero flow A parabolic curve is then formed between the two points as shown in Equations below The calculation also asks for information specifically about the pipe on the suction side of the pump This information is used to compute the net positive suction head available (NPSHA) For a pump to properly

function the NPSHA must be greater than the NPSH required by the pump (obtained from the pump

manufacturer) If your system does not require a pump or uses a pump that does not have a parabolically shaped pump curve then our other Hazen Williams design calculation may be more helpful

Piping ScenariosPipe A is the pipe upstream from the pump (ie the suction side pipe)

fileE|engineeringhydraulicsPressurized20Water20Calculation20uses20Hazen20Williams20equationhtm (1 of 8)12112007 40851 PM

Convention for Z1-Z2 and Z1-Z3 If location 1 is above location 2 then Z1-Z2 should be entered as

Equations and Methodology Back to Calculations

The calculation on this page uses the steady state energy equation Minor losses (due to valves pipe bends etc) and major losses (due to pipe friction) are included The Hazen Williams equation for friction losses is used The equations are standard equations which can be found in most fluid mechanics textbooks (see References) A pump curve is included in the calculation Determination of the pump curve requires that the user enter the two extreme points on the curve - head when capacity is zero and capacity when head is zero Then a parabola with a negative curvature is fit through the two points This parabola is used since it is a good approximation of a typical pump curve and does not require users to enter a multitude of data points And oftentimes pump catalogs only give the two extreme points on the curve rather than a graph showing the complete curve

All of the calculations on this page have analytic (closed form) solutions except for Solve for V Q Q known Solve for Diameter and V known Solve for Diameter These three calculations required a numerical solution Our solution utilizes a modified implementation of Newtons method that finds roots of the equations with the result accurate to 8 significant digits All of the calculations utilize double precision V known Solve for Diameter may find two diameters which give the same velocity - if this is the case both diameters are shown

Variables Units L=length P=pressure T=time Back to Calculations

A = Pipe area [L2]C = Hazen-Williams coefficient See table belowD = Pipe diameter [L]DH = Driving Head [L] = left side of the first equation above

g = Acceleration due to gravity = 32174 fts2 = 98066 ms2

hf = Major losses for entire pipe [L]

k = Unit conversion factor = 1318 for English units = 085 for Metric unitsK = Sum of minor loss coefficients for entire pipe See table below for valuesKA = Sum of minor loss coefficients for pipe upstream of pump (pipe A) Same as Ka

L = Total pipe length [L]LA = Length of pipe upstream of pump (pipe A) [L] Same as La

Hg = 760 mm Hg = 1 atm = 101325 Pa = 101 bar Note that your local atmospheric pressure is

different from standard atmospheric pressurePv = Vapor pressure of fluid [P] Expressed as an absolute pressure This value is built-in to the

program as 2000 Nm2 (absolute) for water at 15oCP1 = Gage pressure at location 1 of the system [P] Location 1 could be the surface of a reservoir open

location 1 could simply be a location in a pipe upstream of the pumpP1-P3 = Pressure difference between locations 1 and 3 [P]

zeroS = Specific Weight of Water (ie weight density weight per unit volume) = 624 lbftsup3 for English units = 9800 Nmsup3 for Metric unitsV1 = Velocity of fluid at location 1 This is determined when you select a scenario If location 1 is a

this value as negativeZ1-Z3 = Elevation of location 1 minus elevation of location 3 [L]

Common Questions Back to CalculationsWhat is net positive suction head It is the sum of the heads that push fluid into the pump less the suction side losses Most pumps have a minimum requirement for NPSH called NPSHR If the NPSH

available by the piping system (NPSHA) is lower than NPSHR then the pump will not function properly

and may overheatWhat is Driving Head DH is the sum of heads supplied by the pump elevation pressure and velocity differences between the inlet and outlet system boundaries DH is equivalent to the sum of minor and major lossesHow is Total dynamic head different than Driving head Total dynamic head H is the head that the pump must provide to overcome major losses minor losses and elevation pressure and velocity head differences between outlet and inlet H may be more or less than DH depending on whether the elevation pressure andor velocity head differences are beneficial or must be overcomeYour program is great What are its limitations Pipes must all have the same diameter The fluid must be water Our approximation for the pump curve may not be close enough to your actual pump

curve to give sufficiently accurate resultsDo you have more common questions and answers somewhere else on your website Yes see our Hazen Williams calculation without pump curvesWhere can I find additional information References

Table of Hazen Williams Coefficients (C is unit-less) Back to CalculationsCompiled from References

Table of Minor Loss Coefficients (K is unit-less) Back to CalculationsCompiled from References

Fitting K Fitting K

Valves Elbows

Error Messages Back to CalculationsAn input is lt 0 The following values must be entered as gt= 0 K and KA One or more of them was

entered as lt0An input is lt= 0 The following values must be entered as positive Q V D L C Qmax Hmax LA

One or more of them was entered as lt=0KA must be lt= K Minor loss coefficient for pipe A cannot exceed the minor loss coefficient for the

entire pipe systemLA must be lt= L The length of pipe A cannot exceed the length of the entire pipe

P1+Patm must be gt0 The sum of P1+Patm gives P1 in absolute pressure It is physically impossible

to have an absolute pressure lt= 0 since that implies a complete vacuum at location 1Q must be lt= Qmax System flowrate cannot be entered as greater than the maximum flowrate that

the pump can deliverTanks open so P1-P3=0 for B This message occurs if Scenario B (reservoir to reservoir) is selected

and Solve for P1-P3 is selected Reservoirs are defined to be open to the atmosphere so they have a

pressure difference of zero by default If you have tanks that are under pressure select Scenario E (main to main) insteadPump not needed H will be lt=0 The system characteristics that were entered result in a negative total dynamic head which means that a pump is not necessary to deliver the flow There are enough elevation pressure andor velocity head differences to overcome the major and minor losses without the need of a pump For this situation it would be better to run our Hazen-Williams calculation that doesnt incorporate a pump curveInfeasible Input DH will be lt=0 Driving head (the left hand side of the first equation shown above in Equations) must be positive in order for fluid to flow The system and pump characteristics entered

result in DH being lt= 0Infeasible Input (DH-hm)lt=0 The difference (DH-hm) is lt= 0 implying that major losses will also

be lt=0 which is impossible for a flowing fluidInfeasible Input (DH-hf )lt0 The difference (DH-hf ) is lt 0 implying that minor losses will also be

lt0 which is impossibleInfeasible input Driving head andor major losses are lt=0 or minor losses are lt 0

Trapezoidal Open Channel Design Calculations Software Manning equation Rivers streams

Trapezoidal Open Channel Design Calculation

Uses Manning Equation Compute velocity discharge depth top width bottom width area wetted perimeter hydraulic radius

Froude number Manning coefficient channel slope

To LMNO Engineering home page (more calculations) Gradually varied flow in trapezoidal channel

Culvert Design using Inlet and Outlet Control Circular Culvert using Manning Equation Rectangular Channel Design Hydraulic Jump Unit Conversions

Links on this page Introduction Variables Manning n coefficients Error Messages References

IntroductionMany natural and man-made channels are approximately trapezoidal This calculation uses the most commonly used equation for analyzing open channels - the Manning equation It is the equation

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beginning with V= above The Manning equation is best used for uniform steady state flows Uniform means that the cross-section geometry of the channel remains constant along the length of the channel and steady state means that the velocity discharge and depth do not change with time Though these assumptions are rarely ever strictly achieved in reality the Manning equation is still used to model most open channel flows where conditions are relatively steady and for reaches (portions of rivers) that have a reasonably constant cross-section for a long enough distance that the depth remains fairly constant

The Manning equation is a semi-empirical equation Thus its units are inconsistent The factor k has units which allow the equation to be used properly Our calculation takes care of all the unit conversions for you and allows you to enter and compute variables in a wide variety of units

In our calculation most of the combinations of inputs have analytic (closed form) solutions to compute the unknown variables however some require numerical solution Our numerical solutions utilize a cubic solver that finds roots of the equations with the result accurate generally to at least 8 significant digits All of our calculations utilize double precision Two depths and bottom widths are possible for certain combinations of entered values when Q T n and S or V T n and S are entered

Variables [] indicates dimensions To calculation

A = Flow cross-sectional area determined normal (perpendicular) to the bottom surface [L2]b = Channel bottom width [L]F = Froude number F is a non-dimensional parameter indicating the relative effect of inertial effects to gravity effects Flows with Flt1 are low velocity flows called subcritical Fgt1 are high velocity flows called supercritical Subcritical flows are controlled by downstream obstructions while supercritical flows are affected by upstream controls F=1 flows are called criticalg = acceleration due to gravity = 32174 fts2 = 98066 ms2 g is used in the equation for Froude numberk = unit conversion factor = 149 if English units = 10 if metric units Our software converts all inputs to SI units (meters and seconds) performs the computations using k=10 then converts the computed quantities to units specified by the usern = Manning coefficient n is a function of the channel material such as grass concrete earth etc Values for n can be found in the table of Mannings n coefficients shown belowP = Wetted perimeter [L] P is the contact length between the water and the channel bottom and sidesQ = Discharge or flowrate [L3T]R = Hydraulic radius of the flow cross-section [L]S = Slope of channel bottom or water surface [LL] Vertical distance divided by horizontal distanceT = Top width of the flowing water [L]V = Average velocity of the water [LT]y = Water depth measured normal (perpendicular) to the bottom of the channel [L] If the channel has a small slope (S) then using the vertical depth introduces only minimal errorz1 z2 = Side slopes of each bank of the channel These slopes are computed as horizontal distance

divided by vertical distance

Oslash = Angle formed by S

Mannings n Coefficients To calculationThe Mannings n coefficients were compiled from the references listed under Discussion and References and in the references at the bottom of this web page (note the footnotes which refer to specific references)

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Error Messages To calculationInvalid boxes checked This message is displayed if too many or too few variables are selected to be entered A problem cannot be over-stated or under-stated In all there are 30 combinations of inputs which are acceptable This message can be displayed to both registered and non-registered users

The following messages are displayed if an entered value lies outside the acceptable range for the variable These messages are only displayed when the Calculate button is clicked - for registered usersb must be gt 0 b must be 1e-9 to 10000 m n must be 1e-9 to 100 Q must be gt 0 Q must be 1e-9 to 1e9 m3s S must be 1e-9 to 1e9 T must be gt 0 T must be 1e-9 to 10000 m V must be gt 0 V must be 1e-9 to 1e9 ms y must be lt 0 y must be 1e-9 to 1e9 m z1 z2 must be gt=0 z1 z2

cannot both be 0 Note that the channel cannot have both z1=0 and z2=0 However if you wish to

simulate a rectangular channel you can set one of them to 00 and the other to a very small positive number such as 000001 Or you can use our rectangular open channel calculation Triangular channels can be modeled by setting the bottom width b to a very small positive number such as 0001 m or as low as 10-9 m

The following messages are displayed if the values entered result in an infeasible situation For instance entering certain combinations of values for T Q n and S can result in an impossible flow situation indicated by a negative bottom width or negative depth These messages are only displayed when the Calculate button is clicked - for registered usersb will be lt 0 T will be gt 10000 m y will be lt 0 y will be lt= 0 y or b will be lt 0 The calculation uses an upper limit of 10000 m for top width

References To calculationA further discussion of open channel flow Mannings equation and trapezoidal channel geometry can be found in these references and on our discussion page The Mannings n coefficients shown above are compiled from the references shown here The footnotes refer to specific values shown in the Manning n table above

a Barfuss Steven and J Paul Tullis Friction factor test on high density polyethylene pipe Hydraulics Report No 208 Utah Water Research Laboratory Utah State University Logan Utah 1988

Chaudhry M H 1993 Open Channel Flow Prentice-Hall Inc

Chow V T 1959 Open Channel Hydraulics McGraw-Hill Inc (the classic text)

French R H 1985 Open Channel Hydraulics McGraw-Hill Book Co

Streeter V L E B Wylie and K W Bedford 1998 WCBMcGraw-Hill 9ed

7860 Angel Ridge Rd Athens Ohio USA (740) 592-1890LMNOLMNOengcom httpwwwlmnoengcom

Waterhammer surge analysis and transient analysis pipe flow modeling software

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Waterhammer analysis tools of the past have been noted for being difficult to use and requiring extensive specialized knowledge As a result this critical aspect of piping system design and operation has often been overlooked But no longer Now AFT Impulsetrade offers the ease-of-use of a drag-and-drop interface and built-in waterhammer modeling expertise AFT Impulse helps you design and operate your systems with greater reliability and safety by avoiding the potentially catastrophic effects of waterhammer and other undesirable system transients

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fileE|engineeringhydraulicsWaterhammer20surgnt20analysis20pipe20flow20modeling20softwarehtm (1 of 2)12112007 40933 PM

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file____E__engineering_hydraulics_Culvert20Design_20Inlet20and20Outlet20Controlpdf
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Manning Equation
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In our calculation most of the combinations of inputs have analytic (closed form) solutions to compute the unknown variables however some two require numerical solutions (Enter Q n S d and Enter V n S d) Our numerical solutions utilize a cubic solver that finds roots of the equations with the result accurate to at least 8 significant digits All of our calculations utilize double precision

It is possible to get two answers using Enter QnSd or Enter VnSd This is because maximum Q and V do not occur when the pipe is full Qmax occurs when yd=0938 If yd is more than that Q actually decreases due to friction Given a pipe with diameter d roughness n and slope S let Qo be the discharge when the pipe is flowing full (yd=1) As seen on the graph below discharge is also equal to Qo when yd=082 If the entered Q is greater than Qo (but less than Qmax) there will be two solution values of yd one between 082 and 0938 and the other between 0938 and 1 The same argument applies to V except that Vo occurs at yd=05 and Vmax occurs at yd=081 If the entered V is greater than Vo (but less than Vmax) there will be two solution values of yd one between 05 and 081 and the other between 081 and 1 For further information see Chow (1959 p 134)

The following graphs are valid for any roughness (n) and slope (S) Qo=full pipe discharge Vo=full pipe velocity

Variables To top of page

A = Flow cross-sectional area determined normal (perpendicular) to the bottom surface [L2]d = Culvert diameter [L]F = Froude number F is a non-dimensional parameter indicating the relative effect of inertial effects to gravity effects Flow with Flt1 are low velocity flows called subcritical Fgt1 are high velocity flows called supercritical Subcritical flows are controlled by downstream obstructions while supercritical flows are affected by upstream controls F=1 flows are called criticalg = acceleration due to gravity = 32174 fts2 = 98066 ms2 g is used in the equation for Froude numberk = unit conversion factor = 149 if English units = 10 if metric units Our software converts all inputs to SI units (meters and seconds) performs the computations using k=10 then converts the computed quantities to units specified by the user Required since the Manning equation is empirical and its units

Metals

Non-Metals

Unplaned Wood 0013

Tailwater Depth Yt

Headwater depth Yh

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

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Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

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Manning Equation
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Metals

Non-Metals

Unplaned Wood 0013

Tailwater Depth Yt

Headwater depth Yh

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Tailwater Depth Yt

Headwater depth Yh

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Tailwater Depth Yt

Headwater depth Yh

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Tailwater Depth Yt

Headwater depth Yh

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Tailwater Depth Yt

Headwater depth Yh

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Floodplains

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Piping Scenarios

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Valves Elbows

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Home Features

Download

Buy Now

Other Products

Contact Info

Suggestion Box

Forums

Revision History

Buy Online

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Ap=Area at Xp [m2]

Yn=Normal depth [m]

Yp=Depth at Xp [m]

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Equations

V=Q(yB) F=V(gy)05 y2y1 = 05 [(1+8F12 )05 - 1]

L = 220 y1 tanh[(F1-1)22] h = (y2-y1)3 (4y1y2)

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Manning Equation

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

losses

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

defined for liquids

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Fitting K Fitting K

Valves Elbows

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

(Hazen Williams)

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Fitting K Fitting K

Valves Elbows

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Stony Cobbles 0035

Metals Floodplains

Non-Metals

Unplaned Wood 0013

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Products

TitanUtilities

Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Manning Equation
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk
Local Disk

Hydraulic Practice

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existing natural

utah state

minor loss

total dynamic

computing

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