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Contents:
Lesson 1 Single Pipe Calculation (5)
Lesson 2 Pipes in Parallel & Series (5)
Lesson 3 Branched Network Layouts (2)
Lesson 4 Looped Network Layouts (3)
Introduction
The spreadsheet hydraulic lessons have been developed as an aid for steady state hydraulic calculatio
These problems are elaborated during the workshop sessions and should normally be calculated manu
More than the however, the spreadsheet lessons help the teacher to demonstrate a wider range of pro
as well as they enable students to continue analysing them at home. Ultimately, through playing with th
should be reached.
Some forty problems have been classified in eight groups/worksheets according to the contents of the
This package is lectured in the Water Supply Engineering specialisation and is separately offered as a
Brief accompanying instructions for each problem are given in the "About" worksheet (below).
The layout of each lesson covers app. one full screen (30 rows) consisting of drawings, tables and grap
The green colour indicates input cells. These cells are unprotected and their contents are u
The brown colour indicates output cells. These cells contain fixed formulas and are therefor
Moreover, some intermediate calculations are moved further to the right in the worksheet, being irrelev
Each lesson serves a kind of a "chess problem" in which the "check-mate" should be reached within a f
takes more time than the execution, which was the main concept of development. Introduced simplifica
SpreadsheetHydraulic Lessons in
Water Transport & DPart I
N.Trifunovic, Senior Lecturer UNESCO-IHE Delft, The Netherlands
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were meant to facilitate this process. In addition, the worksheets are designed without complicated rout
just initial knowledge of spreadsheets is required.
This is the first edition and any suggestion on improvement or extension will obviously be welcome.
N. Trifunovic
Lesson 1-1 Hydraulic Grade Line
Contents:Calculation of the friction losses in a single pipe (the Darcy-Weisbach formula applied).
Goal:Sensitivity analysis of the basic hydraulic parameters, namely the pipe length, diameter, internal rough
Abbreviations:L (m) Pipe length v (m/s) Flow veloci
D (mm) Pipe diameter vis (m2/s) Kinematick (mm) Internal roughness Re Reynolds n
Q (l/s) Flow rate lambda Darcy-Wei
T (deg C) Water temperature (degrees Celsius) hf (mwc) Friction los
H2 (msl) Downstream piezometric head (metres above sea level) S Hydraulic g
Remarks:The calculation ultimately yields the upstream piezometric head required to maintain the specified dow
Lesson 1-2 Friction Loss Formulas
Contents:Single pipe calculation of the hydraulic gradients by the Darcy-Weisbach, Hazen-Williams and Mannin
Goal:Comparison of the calculation accuracy and sensitivity of the Darcy-Weisbach, Hazen-Williams and Ma
Abbreviations:D (mm) Pipe diameter v (m/s) Flow veloci
Q (l/s) Flow rate vis (m2/s) Kinematic
T (deg C) Water temperature Re Reynolds n
k (mm) Internal roughness Sdw Hydraulic g
Chw Hazen-Williams friction factor Shw Hydraulic g
N(m-1/3s) Manning friction factor Sma Hydraulic g
Remarks:The percentage shows the difference between the lowest and the highest value of the three hydraulic g
Lesson 1-3 Maximum Capacity
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Contents:Single pipe calculation by using the Darcy-Weisbach formula.
Goal:Determination of the maximum flow rate in a pipe of specified diameter and hydraulic gradient.
Abbreviations:L (m) Pipe length hf (mwc) Friction los
D (mm) Pipe diameter vis (m2/s) Kinematic
k (mm) Internal roughness Re Reynolds n
S Hydraulic gradient lambda Darcy-Wei
T (deg C) Water temperature v (m/s) Calculated
H2 (msl) Downstream piezometric head Q (l/s) Flow rate
v (m/s) Assumed flow velocity
Remarks:The iterative procedure starts by assuming the flow velocity (commonly at 1 m/s), required for determin
The velocity calculated afterwards by the Darcy-Weisbach formula serves as an input for the next iteratThe iterative process is achieved by typing the value of the calculated velocity into the cell of the assu
Message Iteration complete appears once the difference between the velocities in two iterations drop
Lesson 1-4 Optimal Diameter
Contents:Single pipe calculation by using the Darcy-Weisbach formula.
Goal:Determination of the optimal pipe diameter for specified flow rate and hydraulic gradient.
Abbreviations:L (m) Pipe length hf (mwc) Friction los
k (mm) Internal roughness vis (m2/s) Kinematic
Q (l/s) Flow rate D (mm) Pipe diame
S Hydraulic gradient Re Reynolds n
T (deg C) Water temperature lambda Darcy-Wei
H2 (msl) Downstream piezometric head v (m/s) Calculated
v (m/s) Assumed flow velocity
Remarks:The same iterative procedure as in Lesson 1-3, except that the pipe diameter is determined from the a
Message Iteration complete appears once the difference between the velocities in two iterations drop
Lesson 1-5 Pipe Characteristics
Contents:Friction loss calculation in a single pipe of specified length, diameter and roughness.
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Goal:Determination of the pipe characteristics diagram.
Abbreviations:L (m) Pipe length v (m/s) Flow veloci
D (mm) Pipe diameter vis (m2/s) Kinematic
k (mm) Internal roughness Re Reynolds n
Q (l/s) Flow rate lambda Darcy-Wei
T (deg C) Water temperature hf (mwc) Friction los
H2 (msl) Downstream piezometric head S Hydraulic g
Remarks:The friction loss is calculated for the flow range 0-1.5Q (specified), in the same way as in Lesson 1-1, a
The three points selected in the graph show the upstream heads required to maintain the specified do
Assumption of the reference level at the pipe axis equals the downstream piezometric head with the pr
The friction loss at the same curve represents its dynamic head.
Lesson 2-1a Pipes in Parallel - Maximum Capacity
Contents:Hydraulic calculation of two pipes connected in parallel.
Goal:Resulting from the demand growth, a new pipe (B) of specified diameter is to be laid in parallel, next to
The task is to find the maximum flow rate in this pipe by maintaining the same hydraulic gradient as in t
Abbreviations:L (m) Pipe length hf (mwc) Friction los
D (mm) Pipe diameter vis (m2/s) Kinematick (mm) Internal roughness Re Reynolds n
Q (l/s) Flow rate in the existing pipe lambda Darcy-Wei
T (deg C) Water temperature v (m/s) Calculated
H2 (msl) Downstream piezometric head Q (l/s) Flow rate in
v (m/s) Assumed flow velocity in the new pipe S Hydraulic g
Remarks:The friction loss in the existing pipe is calculated as in Lesson 1-1. Its hydraulic gradient is used as an i
The same iterative procedure as in Lesson 1-3 applies for the new pipe.
Message Iteration complete appears once the difference between the velocities in two iterations drop
Lesson 2-1b Pipes in Parallel - Pipe Characteristics
Contents:Hydraulic calculation of two pipes connected in parallel.
Goal:Determination of the pipe characteristics diagrams for the system from Lesson 2-1b.
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Abbreviations:L (m) Pipe length
D (mm) Pipe diameter
k (mm) Internal roughness
Q (l/s) Flow rate in the existing pipe
Remarks:The pipe characteristics diagram is presented for each of the pipes and both of them operating in parall
The three points selected in the graph show the upstream heads required to maintain the specified do
Flow rate in each of the pipes can be determined in this way.
Lesson 2-2 Pipes in Parallel - Optimal Diameter
Contents:Hydraulic calculation of two pipes connected in parallel.
Goal:Resulting from the demand growth, a new pipe (B) is to be laid in parallel, next to the existing one (A).The task is to determine optimal diameter of this pipe for given flow rate, by maintaining the same hydr
Abbreviations:L (m) Pipe length hf (mwc) Friction los
D (mm) Diameter of the existing pipe vis (m2/s) Kinematic
k (mm) Internal roughness Re Reynolds n
Q (l/s) Flow rate lambda Darcy-Wei
T (deg C) Water temperature v (m/s) Calculated
H2 (msl) Downstream piezometric head D (mm) Diameter o
v (m/s) Assumed flow velocity in the new pipe S Hydraulic g
Remarks:The friction loss in the existing pipe is calculated as in Lesson 1-1. Its hydraulic gradient is used as an i
The same iterative procedure as in Lesson 1-4 applies for the new pipe.
Message Iteration complete appears once the difference between the velocities in two iterations drop
Lesson 2-3 Pipes in Parallel - Equivalent Diameter
Contents:Calculation of hydraulically equivalent pipe.
Goal: Alternatively to the system in Lesson 2-2, one larger pipe can be laid instead of the two parallel pipes.
The task is to determine optimal diameter of this pipe for given flow rate, by maintaining the same hydr
Abbreviations:The same as in Lesson 2-2.
Remarks:The total flow rate and hydraulic gradient from Lesson 2-2 are used as an input for calculation of the op
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The same iterative procedure as in Lesson 1-4 applies.
Message Iteration complete appears once the difference between the velocities in two iterations drop
Lesson 2-4 Pipes in Series - Hydraulic Grade Line
Contents:Calculation of the friction losses in two pipes connected in series.
Goal:Resulting from the system expansion, a new pipe (B) of specified diameter is to be laid in series, followi
The task is to determine the piezometric head at the upstream side (H1), required to maintain the mini
Abbreviations:L (m) Pipe length v (m/s) Flow veloci
D (mm) Pipe diameter Re Reynolds n
k (mm) Internal roughness lambda Darcy-Wei
Q (l/s) Flow rate hf (mwc) Friction los
H3 (msl) Downstream piezometric head S Hydraulic gT (deg C) Water temperature vis (m2/s) Kinematic
Remarks:By maintaining the same flow rate in pipes A & B, the same calculation procedure as in Lesson 1-1 app
Lesson 2-5 Pipes in Series - Equivalent Diameter
Contents:Calculation of hydraulically equivalent pipe.
Goal: Alternatively to the system in Lesson 2-4, one longer pipe can be laid instead of the two serial pipes.
The task is to determine optimal diameter of this pipe for given flow rate, by maintaining the existing he
Abbreviations:The same as in Lesson 2-4.
Remarks:The flow rate and piezometric head difference (H1-H3 i.e. hfA+hfB) from Lesson 2-4 are used as an inp
The same iterative procedure as in Lesson 1-4 applies.
Message Iteration complete appears once the difference between the velocities in two iterations drop
Lesson 3-1 Branched Network Layouts - Residual Pressures
Contents:Calculation of the friction losses in a branched network configuration.
Goal:For specified network configuration, distribution of nodal demands and piezometric head fixed in a num
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Abbreviations:NODES Node data PIPES Pipe data
X (m) Horizontal co-ordinate Nups Upstream
Y (m) Vertical co-ordinate Ndws Downstrea
Z (msl) Altitude Lxy(m) Length cal
Qn (l/s) Nodal demand L (m) Length adoH (msl) Piezometric head D (mm) Diameter
p (mwc) Nodal pressure Q (l/s) Flow rate
v (m/s) Flow veloci
Qn total Total demand of the system Re Reynolds n
T (deg C) Water temperature lambda Darcy-Wei
vis(m2/s) Kinematic viscosity S Hydraulic g
hf (mwc) Friction los
PATH Pipes selected to be plotted with their piezometric heads.
(order from the upstream to the downstream pipes)
k (mm) Internal roughness (uniform)
Remarks:The nodes are plotted based on the X/Y input (origin of the graph is at the lower left corner). Any node
The first node in the list of nodes simulates the source and has therefore fixed piezometric head.
The pipes are plotted based on the Nups/Ndws input. This input determines connectivity between the n
From the determined pipe flows, the friction losses and consequently the nodal heads/pressures will be
Each node may appear only once as a downstream node (Ndws). Otherwise suggests a system consis
Lesson 3-2 Branched Network Layouts - Optimal Diameters
Contents:Hydraulic calculation of a branched network configuration.
Goal:For specified network configuration, distribution of nodal demands and uniform (= design) hydraulic gra
Abbreviations:NODES Node data PIPES Pipe data
X (m) Horizontal co-ordinate Nups Upstream
Y (m) Vertical co-ordinate Ndws Downstrea
Z (msl) Altitude Lxy(m) Length cal
Qn (l/s) Nodal demand L (m) Length ado
H (msl) Piezometric head Q (l/s) Flow rate
p (mwc) Nodal pressure v (m/s) Flow veloci
D (mm) Calculated
Qn total Total demand of the system Re Reynolds nT (deg C) Water temperature lambda Darcy-Wei
vis(m2/s) Kinematic viscosity v (m/s) Flow veloci
hf (mwc) Friction los
PATH Pipes selected to be plotted with their piezometric heads. D (mm) Adopted di
(order from the upstream to the downstream pipes)
S Design hydraulic gradient (uniform)
k (mm) Internal roughness (uniform)
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Remarks:Procedure of the network building is the same as in Lesson 3-1. The order of the nodes from upstream
The first node in the list of nodes simulates the source and has therefore fixed piezometric head.
The hydraulic calculation follows the principles of the single pipe calculation from Lesson 1-4; the iterati
That can be done at once, by copying the entire column of the "i+1" velocities, and pasting it subseque
"Excel" command "Edit/Paste Special (Values)" should only be used in this case (the ordinary "Paste"Message Iteration complete appears once the total difference between the velocities in two iterations
Lesson 4-1 Looped Network Layouts - Method of Balancing H
Contents:Hydraulic calculation of a looped network configuration by the Hardy-Cross Method of Balancing Head
Goal:For specified network configuration, nodal demands and piezometric head fixed in a source node, the fl
Abbreviations:NODES Node data PIPES Pipe data p
X (m) Horizontal co-ordinate N1cw Upstream
Y (m) Vertical co-ordinate N2cw Downstrea
Z (msl) Altitude Lxy(m) Length cal
Qn (l/s) Nodal demand L (m) Length ado
H (msl) Piezometric head D (mm) Diameter
p (mwc) Nodal pressure Q (l/s) Flow rate o
v (m/s) Flow veloci
Qtot(l/s) Total demand of the system hf (mwc) Friction los
T (deg C) Water temperature Q (l/s) Flow rate o
vis(m2/s) Kinematic viscosity
dQ (l/s) Flow rate c
k (mm) Internal roughness (uniform) Sum Sum of frict
Remarks:The table with the nodal data is prepared in the same way as in Lessons 3-1 and 3-2.
The pipes are plotted based on the N1cw/N2cw input. As a convention, this input has to be made in a c
The pipes shared by neighbouring loops should appear in both tables (with opposite flow directions).
The first node in the list of nodes and pipes (in loop 1) simulates the source and has therefore fixed pie
To provide correct spreadsheet calculation of nodal piezometric heads, the tables of loops 2 & 3 should
The iterative process starts by distributing the pipe flows "i" arbitrarily, but satisfying the continuity equa
Negative flows, velocities and friction losses, indicate anti-clockwise flow direction.
The flow correction (dQ) is calculated from the friction losses/piezometric heads, and flows for iteration
Both dQ corrections are applied in case of the shared pipes (with opposite signs!).
The iteration proceeds by copying the entire column of the "i+1" flows, and pasting it subsequently to th"Excel" command "Edit/Paste Special (Values)" should only be used in this case (the ordinary "Paste"
Message Iteration complete appears once the sum of friction losses in the loop drops below 0.01 mw
Lesson 4-2 Looped Network Layouts - Method of Balancing Fl
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Contents:Hydraulic calculation of a looped network configuration by the Hardy-Cross Method of Balancing Flows
Goal:For specified network configuration, nodal demands and piezometric head fixed in a source node, the fl
Abbreviations:NODES Node data PIPES Pipe data
X (m) Horizontal co-ordinate N1 Node nam
Y (m) Vertical co-ordinate N2 Node nam
Z (msl) Altitude Lxy(m) Length cal
Qn (l/s) Nodal demand L (m) Length ado
H (msl) Piezometric head of iteration "i" D (mm) Diameter
p (mwc) Nodal pressure hf (mwc) Friction los
dQ (l/s) Balance of the flow continuity equation S Hydraulic g
dH (msl) Piezometric head correction. Hi+1 = Hi + dH v (m/s) Flow veloci
H (msl) Piezometric head of iteration "i+1" Re Reynolds n
lambda Darcy-Wei
Qn total Total demand of the system v (m/s) Flow veloci
T (degC) Water temperature Q (l/s) Flow rate
vis(m2/s) Kinematic viscosity Q/hf Ratio used
dH total Sum of all dH-corrections k (mm) Internal rou
Remarks:The table with the nodal data is prepared in the same way as in Lesson 4-1
The pipes are plotted based on the N1/N2 input. Unlike in Lesson 4-1, the order of nodes/pipes is not c
The first node in the list of nodes simulates the source and has therefore fixed piezometric head.
The heads in other nodes are distributed arbitrarily in the 1st iteration, except that no nodes should be
The calculation starts by iterating the velocities in order to determine the pipe flows for given piezometi
Message Iteration complete appears once the total difference between the velocities in two iterations After the pipe flows have been determined, the correction (dH) is calculated and the iteration of piezom
A consecutive iteration is done node by node, by typing the current "Hi+1" value into "Hi" cell. Copying
The new values of nodal piezometric heads should result in gradual reduction of the "dH total" value; t
Message Iteration complete appears once the sum of dH corrections for all nodes drops below 0.01
Lesson 4-3 Looped Network Layouts - Linear Theory
Contents:Hydraulic calculation of a looped network configuration based on the linear theory (solution by the Newt
Goal:For specified network configuration, nodal demands and piezometric head fixed in a source node, the fl
Abbreviations:NODES Node data PIPES Pipe data
X (m) Horizontal co-ordinate N1 Node nam
Y (m) Vertical co-ordinate N2 Node nam
Z (msl) Altitude Lxy(m) Length cal
Qn (l/s) Nodal demand L (m) Length ado
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H (msl) Piezometric head of iteration "i" D (mm) Diameter
p (mwc) Nodal pressure Q(l/s) Flow rate o
dQ (l/s) Balance of the flow continuity equation v (m/s) Flow veloci
H (msl) Piezometric head of iteration "i+1" Re Reynolds n
lambda Darcy-Wei
Qn total Total demand of the system 1/U Linearisatio
T (degC) Water temperature H1/U Ratio usedvis(m2/s) Kinematic viscosity H2/U Ratio used
hf (mwc) Friction los
dH total Total error between two iterations (dH = ABS(Hi+1 - Hi)) S Hydraulic g
v (m/s) Flow veloci
Omega Successive over-relaxation factor (value range 1.0-2.0) Q (l/s) Flow rate o
k (mm) Internal rou
Remarks:The table with the nodal and pipe data is prepared in the same way as in Lesson 4-2
The first node in the list of nodes simulates the source and has therefore fixed piezometric head.
The heads in other nodes are distributed arbitrarily in the 1st iteration, except that no nodes should be
The pipe flows in the 1st iteration are also distributed arbitrarily (commonly to fit the velocities around 1
The calculation starts by iterating piezometric heads in the nodes, in order to determine the pipe flows i A consecutive iteration is done node by node, by typing the current "Hi+1" value into "Hi" cell.
Alternative approach, by copying the entire column ("Excel" command "Edit/Paste Special (Values)"), i
The new values of nodal piezometric heads should result in gradual reduction of the "dH total" value; th
That is done by copying the entire "Qi+1" column into "Qi" cells ("Excel" command "Edit/Paste Special
Messages Iteration complete appear once the total difference between the heads (flows) in two iterati
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Version 1.0
January 2003
Scroll-down
ns of simple water transport and distribution problems.
ally; the spread-sheet serves here as a fast check of the results.
lems during the lectures, in a clear (and clean) way,
e data, a real understanding of the hydraulic concepts
ater Transport and Distribution package at UNESCO-IHE.
short course of duration between 1 to 3 weeks.
hs. In the tables:
ed for calculations.
e protected.
nt for educational purposes.
ew right moves. This suggests a study process where thinking
tions (neglected minor losses, pump curve definition, etc.)
stribution
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s
iscosity
umber
bach friction factor
flow velocity
ation of the Reynolds number i.e. the lambda factor.
ion.ed velocity.
below 0.01 m/s.
s
iscosity
ter
umber
bach friction factor
flow velocity
sumed/calculated velocity (and specified flow rate).
below 0.01 m/s.
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lel, in the range 0-1.5Q (=Qa+Qb).
nstream head for 0.5Q, Q and 1.5Q, respectively.
ulic gradient as in the existing pipe.
s
iscosity
umber
bach friction factor
flow velocity
f the new pipe
radient
nput for calculation of the maximum capacity in the new pipe.
below 0.01 m/s.
ulic gradient as in the existing pipe.
timal pipe diameter.
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below 0.01 m/s.
ing the existing one (A).
um head at the downstream side (H3).
ty
umber
bach friction factor
s
radientiscosity
lies.
ad difference between the points 1 & 3.
ut for calculation of the optimal pipe diameter.
below 0.01 m/s.
ber of nodes, pressures in the system should be determined.
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ode name
node name
ulated from the X/Y co-ordinates
pted for hydraulic calculation
ty
umber
bach friction factor
radient
s
ame can be used.
odes and hence the flow rates/directions.
calculated.
ing of more than one source, or from loops.
dient, the pipe diameters in the system should be determined.
ode name
node name
ulated from the X/Y co-ordinates
pted for hydraulic calculation
ty of iteration "i"
diameter
umber bach friction factor
ty of iteration "i+1"
s
meter (manufactured size)
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to downstream has to be respected in the list of pipes.
ion procedure has to be conducted for all pipes.
tly to the column of "i" velocities.
ommand also copies the cell formulas, which is wrong).drops below 0.01 m/s.
eads
(Loop Oriented Method).
ows and pressures in the system should be determined.
er loop
ode name (clockwise direction)
node name (clockwise direction)
ulated from the X/Y co-ordinates
pted for hydraulic calculation
f iteration "i"
ty
s
f iteration "i+1"
orrection. Qi+1 = Qi + dQ
ion losses in the loop (clockwise direction)
lockwise direction for each loop.
zometric head.
start with previously filled (shared) pipe.
tion in each node.
"i+1" are determined for all loops simultaneously.
e column of "i" flows.ommand also copies the cell formulas).
.
ows
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(Node Oriented Method).
ows and pressures in the system should be determined.
1
2
ulated from the X/Y co-ordinates
pted for hydraulic calculation
s
radient
ty of iteration "i"
umber
bach friction factor
ty of iteration "i+1"
for calculation of dH-corrections
ghness (uniform)
rucial in this case.
llocated the same value.
heads. This is done in the same way as in Lesson 3-2.
drops below 0.01 m/s.etric heads proceeds.
he entire column does not lead to a convergence.
e velocities (flows) have to be re-iterated.
wc.
on-Raphson/successive over-relaxation method).
ows and pressures in the system should be determined.
1
2
ulated from the X/Y co-ordinates
pted for hydraulic calculation
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f iteration "i"
ty of iteration "i"
umber
bach friction factor
n coefficient
for calculation of "Hi+1" (from N1)for calculation of "Hi+1" (from N2)
s
radient
ty of iteration "i+1"
f iteration "i+1"
ghness (uniform)
llocated the same value.
m/s).
n the next iteration
likely to yield slower convergence.
e velocities (flows) have to be re-iterated.
Values)").
ons drops below 0.1 mwc (l/s).
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Turbulent flow
INPUT OUTPUT
L (m) 3299.5 v (m/s) 2.52 640.80 m3/hD (mm) 300 vis (m2/s) 9.16E-07
k (mm) 0.1 Re 824299
Q (l/s) 178 lambda 0.0162
T (deg C) 24 hf (mwc) 57.56
H2 (msl) 0 S 0.0174
57.56
0.00
Lesson 1-1Hydraulic Grade Line
1 2
Lesson 1-2Friction Loss Formulas
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Difference
73.4%
Turbulent flow
INPUT OUTPUT
D (mm) 800 v (m/s) 1.99 3600.00 m3/hQ (l/s) 1000 vis (m2/s) 1.31E-06
T (deg C) 10 Re 1218155
k (mm) 0.2 Sdw 0.0038
Chw 115 Shw 0.0048
N(m-1/3s) 0.014 Sma 0.0066
INPUT OUTPUT
L (m) 1500.3 hf (mwc) 80.96
D (mm) 300 vis (m2/s) 9.16E-07
k (mm) 0.1 Re 1466477
S 0.05396 lambda 0.0158
DW
HW
MA
1 2
80.96
Lesson 1-3Maximum Capacity
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Turbulent flow T (deg C) 24 v (m/s) 4.48
H2 (msl) 0 Q (l/s) 316.50
Assumption
v (m/s) 4.48
1139.42 m3/hIteration complete
INPUT OUTPUT
L (m) 1236.3 hf (mwc) 76.03
k (mm) 0.15 vis (m2/s) 8.58E-07
Q (l/s) 200 D (mm) 249
S 0.0615 Re 1191195
Turbulent flow T (deg C) 27 lambda 0.0179
H2 (msl) 752.756 v (m/s) 4.10
Assumption
v (m/s) 4.1
0.001 2
Lesson 1-4Optimal Diameter
1 2
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720.00 m3/hIteration complete
Turbulent flow
INPUT OUTPUT
L (m) 275 v (m/s) 4.07 180.00 m3/hD (mm) 125 vis (m2/s) 1.24E-06
k (mm) 0.01 Re 412295
Q (l/s) 50 lambda 0.0146
27.53
47.21
78.24
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
0 20 40 60 80
H
( m s l )
Q (l/s)
47.21
20.00
Lesson 1-5Pipe Characteristics
1 2
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T (deg C) 12 hf (mwc) 27.21
H2 (msl) 20 S 0.0989
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0 57.56
1 0.00
0 0.00 0.00 0.01
1 0 0 0
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0 80.96
1 0.00
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0 828.79
1 752.76
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0 47.21
1 20.00
0 0.00 0.00 0.00E+00 0.0000 2
0.1 5.00 0.41 4.12E+04 0.0220 2
0.2 10.00 0.81 8.25E+04 0.0190 20.3 15.00 1.22 1.24E+05 0.0176 22
0.4 20.00 1.63 1.65E+05 0.0168 2
0.5 25.00 2.04 2.06E+05 0.0162 2
0.6 30.00 2.44 2.47E+05 0.0157 3
0.7 35.00 2.85 2.89E+05 0.0154 34
0.8 40.00 3.26 3.30E+05 0.0151 3
0.9 45.00 3.67 3.71E+05 0.0148 42
1 50.00 4.07 4.12E+05 0.0146 4
1.1 55.00 4.48 4.54E+05 0.0144 52
1.2 60.00 4.89 4.95E+05 0.0143 5
1.3 65.00 5.30 5.36E+05 0.0141 64
1.4 70.00 5.70 5.77E+05 0.0140 7
1.5 75.00 6.11 6.18E+05 0.0139 7
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INPUT - A OUTPUT - A
L (m) 275 v (m/s) 1.13
D (mm) 150 Re 148934k (mm) 0.1 lambda 0.0203
H2 (msl) Q (l/s) 20 hf (mwc) 2.43
Turbulent flow 30 S 0.0088
72.00 m3/h Maximum Capacity
T(deg C) INPUT - B OUTPUT - B
15 L (m) 275 Re 76325
vis(m2/s) D (mm) 100 lambda 0.0230
1.14E-06 k (mm) 0.1 v (m/s) 0.87
v (m/s) 0.87 Q (l/s) 6.82
S 0.0088
Turbulent flow Iteration complete
24.55 m3/h
96.55 m3/h
32.43 30.00
Lesson 2-1aMaximum Capacity
hf = hf A = hf B ; Q = Q A + QB
Lesson 2-1bPipes Characteristics
35.2835.0
36.0
1 2
A
B
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Turbulent flow
72.00 m3/h
From Lesson 2-1a
PIPE - A PIPE - B
Turbulent flow L (m) 275 L (m) 275
24.55 m3/h D (mm) 150 D (mm) 100
96.55 m3/h k (mm) 0.100 k (mm) 0.100
Q (l/s) 20.00 Q (l/s) 6.82
INPUT - A OUTPUT - A
L (m) 1400 v (m/s) 1.20
D (mm) 500 Re 459391
k (mm) 0.1 lambda 0.0157
71.00 67.78
Lesson 2-2Optimal Diameter
32.43 30.00
30.65
32.43
29.0
30.0
31.0
32.0
33.0
34.0
0 10 20 30 40 50
H
( m s l )
Q (l/s)
A
B
A+B
hf = hf A = hf B ; Q = Q A + QB
1 2
A
B
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H2 (msl) Q (l/s) 235.7 hf (mwc) 3.22
Turbulent flow 67.78 S 0.0023
848.52 m3/h Optimal Diameter
T(deg C) INPUT - B OUTPUT - B
10 L (m) 1400 D (mm) 360
vis(m2/s) k (mm) 0.1 Re 270365
1.31E-06 Q (l/s) 100 lambda 0.0171v (m/s) 0.98 v (m/s) 0.98
S 0.0023
Turbulent flow Iteration complete
360.00 m3/h
1208.52 m3/h
From Lesson 2-2
T (deg C) 10 vis (m2/s) 1.31E-06
H2 (msl) 67.78 hf (mwc) 3.22
PIPE - A PIPE - B
Turbulent flow L (m) 1400 L (m) 1400
D (mm) 500 D (mm) 360
71.00 67.78
Lesson 2-3Equivalent Diameter
21
hf = hf A = hf B ; Q = Q A + QB
1 2
A
B
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k (mm) 0.100 k (mm) 0.100
v (m/s) 1.20 v (m/s) 0.98
Q (l/s) 235.70 Q (l/s) 100.00
INPUT - C OUTPUT - C
L (m) 1000 D (mm) 563 1208.52 m3/hk (mm) 0.1 Re 581407
v (m/s) 1.35 lambda 0.0151Q (l/s) 335.70 v (m/s) 1.53
Iterate the velocity(diamater)!
T (deg C) Q (l/s)10 235.7
vis (m2/s) H3 (mwc)
1.31E-06 61.4
Turbulent flow Turbulent flow
INPUT - A OUTPUT - A INPUT - B OUTPUT - B
L (m) 1400 v (m/s) 1.20 L (m) 900 v (m/s) 1.88 848.52 m3/hD (mm) 500 Re 459391 D (mm) 400 Re 574238
C
71.00 67.7861.40
Lesson 2-4Pipes in Series
1 2 3
A B
hf C = hf A = hf B ; QC = Q A + QB
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k (mm) 0.1 lambda 0.0157 k (mm) 0.1 lambda 0.0158
hf (mwc) 3.22 hf (mwc) 6.38
S 0.0023 S 0.0071
From Lesson 2-4
T (deg C) 10 vis (m2/s) 1.31E-06
H3 (msl) 61.4 Q (l/s) 235.70
PIPE - A PIPE - B
Turbulent flow L (m) 1400 L (m) 900
D (mm) 500 D (mm) 400
k (mm) 0.100 k (mm) 0.100
v (m/s) 1.20 v (m/s) 1.88
hf (mwc) 3.22 hf (mwc) 6.38
INPUT - C OUTPUT -C
L (m) 550 D (mm) 359 848.52 m3/hk (mm) 0.01 Re 640023
v (m/s) 2.33 lambda 0.0131
hf (mwc) 9.60 v (m/s) 3.07
Iterate the velocity(diamater)!
hf = hf A + hf B ; Q = Q A = QB
71.0061.40
Lesson 2-5Equivalent Diameter
21
C
hf C = hf A = hf B ; QC = Q A + QB
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0 32.43
1 30.00
0.00 0.00 0.00E+00 0.000
2.00 0.11 1.49E+04 0.029
4.00 0.23 2.98E+04 0.025
6.00 0.34 4.47E+04 0.023
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8.00 0.45 5.96E+04 0.022
10.00 0.57 7.45E+04 0.021
12.00 0.68 8.94E+04 0.021
14.00 0.79 1.04E+05 0.021
16.00 0.91 1.19E+05 0.020
18.00 1.02 1.34E+05 0.020
20.00 1.13 1.49E+05 0.02022.00 1.24 1.64E+05 0.020
24.00 1.36 1.79E+05 0.019
26.00 1.47 1.94E+05 0.019
28.00 1.58 2.09E+05 0.019
30.00 1.70 2.23E+05 0.019
0 71.00
1 67.78
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0 71.00
1 67.78
2 61.40
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0 71.00
1 61.40
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0.00 0.00
0.68 2.68
1.36 5.36
2.05 8.05
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2.73 10.73
30.65 3.41 13.41
4.09 16.09
4.77 18.77
5.46 21.46
6.14 24.14
32.43 6.82 26.827.50 29.50
8.18 32.18
8.87 34.87
9.55 37.55
35.28 10.23 40.23
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Qn total T (deg C) vis(m2/s) PATH
131 10 1.3E-06 ups p3
p5p6
NODES X (m) Y (m) Z (msl) Qn (l/s) H (msl) p (mwc)n1 45 135 54 0 54 0.00
n2 25 200 12 10.4 52.46 40.46
n3 60 46 22 18.5 49.68 27.68n4 65 88 17 12.2 52.91 35.91 dws
n5 100 100 25 22.1 47.06 22.06
n6 130 20 20 14.4 41.41 21.41
n7 81 39 22 13.8 43.95 21.95n8 99 154 38 12.5 52.89 14.89
n9 60 180 33 19.1 49.19 16.19 k (mm)n10 12 134 28 8 44.35 16.35 0.1
PIPES Nups Ndws Lxy(m) L (m) D (mm) Q (l/s) v (m/s) Re lambda S hf (mwc)
p1 n1 n8 57 570 250 34.60 0.70 134874 0.0192 0.0019 1.11
p2 n8 n5 54 540 150 22.10 1.25 143580 0.0203 0.0108 5.84
p3 n1 n4 51 510 300 58.90 0.83 191332 0.0181 0.0021 1.09p4 n4 n3 42 420 150 18.50 1.05 120191 0.0207 0.0077 3.24
p5 n4 n7 52 520 150 28.20 1.60 183211 0.0199 0.0172 8.96
p6 n7 n6 53 530 150 14.40 0.81 93554 0.0213 0.0048 2.54
p7 n1 n2 68 680 250 37.50 0.76 146179 0.0190 0.0023 1.54
p8 n2 n10 67 670 100 8.00 1.02 77962 0.0229 0.0121 8.11
p9 n2 n9 40 400 150 19.10 1.08 124089 0.0206 0.0082 3.27
Qn total T (deg C) vis(m2/s) PATH
131 10 1.3E-06 ups p3
p5p6
NODES X (m) Y (m) Z (msl) Qn (l/s) H (msl) p (mwc)
n1 50 135 54 0 54 0.00
n2 25 200 12 10.4 48.56 36.56
n3 60 46 22 18.5 46.56 24.56n4 65 88 17 12.2 49.92 32.92 dws
n5 100 100 25 22.1 45.12 20.12n6 130 20 20 14.4 42.80 22.80
n7 81 39 22 13.8 45.76 23.76 Sn8 99 154 38 12.5 49.44 11.44 0.008
n9 60 180 33 19.1 45.36 12.36 k (mm)n10 12 134 28 8 43.20 15.20 0.1
Iteration complete
PIPES Nups Ndws Lxy(m) L (m) Q (l/s) v (m/s) D (mm) Re lambda v (m/s) hf (mwc)
p1 n1 n8 53 570 34.60 1.24 189 178786 0.0193 1.24 4.56
p2 n8 n5 54 540 22.10 1.11 159 135267 0.0203 1.11 4.32
p3 n1 n4 49 510 58.90 1.41 231 248841 0.0182 1.41 4.08
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p4 n4 n3 42 420 18.50 1.06 149 121088 0.0207 1.06 3.36
p5 n4 n7 52 520 28.20 1.18 175 157426 0.0197 1.18 4.16
p6 n7 n6 53 370 14.40 1.00 135 103586 0.0213 1.00 2.96
p7 n1 n2 70 680 37.50 1.26 194 187962 0.0191 1.26 5.44
p8 n2 n10 67 670 8.00 0.86 109 71786 0.0229 0.86 5.36
p9 n2 n9 40 400 19.10 1.07 151 123519 0.0206 1.07 3.20
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D (mm)
200
200
250
1722 20
52.91
43.9541.41
500 1000 1500 2000
L (m)
X-Y
1722 20
49.9245.76
42.80
500 1000 1500
L (m)
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150
200
150
200
150
150
X-Y
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0.00 n4 n8
0.00 n4 n7
0.00 n7 n4
0.00 n1 n1
0.00 n2 n2
0.00 n2 n2
0.00 0.00 #N/A
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0 0 54.00508.66 508.66 52.91
519.98 1028.63 43.95
530.00 1558.63 41.41
#VALUE! #VALUE! #N/A#VALUE! #VALUE! #N/A
#VALUE! #VALUE! #N/A#VALUE! #VALUE! #N/A
0 0 54.00
508.66 508.66 49.92519.98 1028.63 45.76
369.99 1398.63 42.80
#VALUE! #VALUE! #N/A#VALUE! #VALUE! #N/A
#VALUE! #VALUE! #N/A
#VALUE! #VALUE! #N/A
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k (mm) 0.1
Qn total T (degC) vis(m2/s) PIPES N1cw N2cw Lxy(m)
72.9 10 1.3E-06 p1 n1 n4 40
p2 n4 n2 50
NODES X (m) Y (m) Z (msl) Qn (l/s) H (msl) p (mwc) p3 n2 n3 40
n1 40 80 54 0 60 6.00 p4 n3 n1 50n2 80 30 12 10.4 55.84 43.84
n3 40 30 17 12.2 58.05 41.05 LOOP 1
n4 80 80 25 22.1 56.04 31.04 Iteration complete
n5 120 80 20 14.4 52.65 32.65
n6 120 30 22 13.8 50.10 28.10 PIPES N1cw N2cw Lxy(m)
p2 n2 n4 50
p5 n4 n5 40
p6 n5 n6 50
p7 n6 n2 40
LOOP 2
Iteration complete
PIPES N1cw N2cw Lxy(m)
LOOP 3
Iteration complete
Qn total T (degC) vis(m2/s) dH total72.9 10 1.3E-06 0.01
Iteration complete
NODES X (m) Y (m) Z (msl) Qn (l/s) H (msl) p (mwc) dQ (l/s) dH (msl) H (msl)
n1 40 80 54 0 60 6.00 -72.86 0.00 60.00
n2 80 30 12 10.4 55.85 43.85 -0.04 0.00 55.85
n3 40 30 17 12.2 58.05 41.05 0.01 0.00 58.05
n4 80 80 25 22.1 56.04 31.04 -0.01 0.00 56.04
n5 120 80 20 14.4 52.65 32.65 0.00 0.00 52.65
n6 120 30 22 13.8 50.10 28.10 0.01 0.00 50.10
Iteration complete
PIPES N1 N2 Lxy(m) L (m) D (mm) hf (mwc) S v (m/s) Re lambda v (m/s)
p1 n1 n4 40 400 200 3.96 0.0099 1.44 220102 0.0188 1.44
p2 n4 n2 50 500 150 0.19 0.0004 0.21 23622 0.0264 0.21
p3 n2 n3 40 400 150 -2.20 0.0055 0.88 100560 0.0211 0.88
p4 n3 n1 50 500 200 -1.95 0.0039 0.88 134885 0.0197 0.88p5 n4 n5 40 400 150 3.39 0.0085 1.10 126362 0.0206 1.10
p6 n5 n6 50 500 100 2.55 0.0051 0.64 49208 0.0242 0.64
Lesson 4-1Method of
Balancing Heads
Lesson 4-2
Method of Balancing Flows
X-Y
X-Y
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p7 n6 n2 40 400 100 -5.75 0.0144 1.11 85335 0.0227 1.11
0.00 0.00
0.00 0.000.00 0.00
Qn total T (degC) vis(m2/s) dH total72.9 10 1.3E-06 0.06
Iteration complete
NODES X (m) Y (m) Z (msl) Qn (l/s) H (msl) p (mwc) dQ (l/s) H (msl)
n1 40 70 54 0 60 6.00 -72.59 60.00
n2 80 20 12 10.4 55.88 55.87 -0.25 55.87
n3 40 20 17 12.2 58.07 41.07 -0.11 58.06
n4 80 70 25 22.1 56.06 31.06 -0.12 56.06
n5 120 70 20 14.4 52.64 32.64 0.04 52.65n6 120 20 22 13.8 50.04 28.04 0.13 50.08
Omega1
k (mm)0.1
PIPES N1 N2 Lxy(m) L (m) D (mm) Q(l/s) v (m/s) Re lambda 1/U H1/U
p1 n1 n4 40 400 200 45.05 1.43 219531 0.0188 0.0114 0.69
p2 n4 n2 50 500 150 3.54 0.20 23017 0.0265 0.0196 1.10
p3 n2 n3 40 400 150 -15.44 -0.87 100333 0.0211 0.0071 0.39
p4 n3 n1 50 500 200 -27.54 -0.88 134170 0.0197 0.0143 0.83p5 n4 n5 40 400 150 19.54 1.11 126952 0.0206 0.0057 0.32
p6 n5 n6 50 500 100 5.11 0.65 49790 0.0242 0.0020 0.10
p7 n6 n2 40 400 100 -8.83 -1.12 86071 0.0227 0.0015 0.08
Lesson 4-3Linear Theory
X-Y
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L (m) D (mm) Q (l/s) v (m/s) hf (mwc) Q (l/s)
400 200 45.20 1.44 3.96 45.20
500 150 3.65 0.21 0.19 3.66
400 150 -15.50 -0.88 -2.20 -15.50
500 200 -27.70 -0.88 -1.95 -27.700.00 0.00
Q (l/s)= 0.00 Sum= 0.00
L (m) D (mm) Q (l/s) v (m/s) hf (mwc) Q (l/s)
500 150 -3.65 -0.21 -0.19 -3.66
400 150 19.45 1.10 3.39 19.45
500 100 5.05 0.64 2.55 5.05
400 100 -8.75 -1.11 -5.75 -8.75
0.00 0.00
Q (l/s)= 0.00 Sum= 0.00
L (m) D (mm) Q (l/s) v (m/s) hf (mwc) Q (l/s)
0.00
0.00
0.00
0.00
0.00
Q (l/s)= 0.00 Sum= 0.00
Q (l/s) Q/hf k (mm)
45.18 11.41 0.1
3.64 19.14
-15.48 7.04
-27.69 14.2019.45 5.74
5.05 1.98
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-8.76 1.52
Iteration complete
H2/U hf (mwc) S v (m/s) Q (l/s)
0.64 3.94 0.0098 1.43 45.06
1.09 0.18 0.0004 0.20 3.53
0.41 -2.19 0.0055 0.87 -15.44
0.86 -1.93 0.0039 0.88 -27.540.30 3.42 0.0086 1.11 19.54
0.10 2.60 0.0052 0.65 5.10
0.08 -5.84 0.0146 1.12 -8.83
0.00
0.000.00
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56.04 220246 0.0188 0.0877 40 80 80 80 0
55.84 23742 0.0264 0.052435 80 80 80 30 0.000648
58.05 100696 0.0211 0.142262 80 40 30 30 0
60.00 134968 0.0197 0.07046 40 40 30 80 0#VALUE! #VALUE! - 0 #N/A #N/A #N/A #N/A 0
56.04 23742 0.0264 0.052435 80 80 30 80 0.001289
52.65 126340 0.0206 0.174239 80 120 80 80 0
50.10 49178 0.0242 0.504756 120 120 80 30 0
55.85 85306 0.0227 0.656382 120 80 30 30 0
#VALUE! #VALUE! - 0 #N/A #N/A #N/A #N/A 0
#N/A #VALUE! - 0 #N/A #N/A #N/A #N/A 0
#N/A #VALUE! - 0 #N/A #N/A #N/A #N/A 0
#N/A #VALUE! - 0 #N/A #N/A #N/A #N/A 0
#N/A #VALUE! - 0 #N/A #N/A #N/A #N/A 0
#N/A #VALUE! - 0 #N/A #N/A #N/A #N/A 0
40 80 80 8080 80 80 30
80 40 30 3040 40 30 80
80 120 80 80
120 120 80 30
0.00 120 80 30 30
0.00 #N/A #N/A #N/A #N/A
0.00 #N/A #N/A #N/A #N/A
0.00 #N/A #N/A #N/A #N/A
0.00
0.00
0.00
0.00
0.00
0.00
0.00 45.18
0.00 3.64
0.00 15.48
0.00 27.690.00 19.45
0.00 5.05
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0.00 8.76
0.00 0.00
0.00 0.000.00 0.00
40 80 70 7080 80 70 20
80 40 20 2040 40 20 70
80 120 70 70
120 120 70 20
0.00 120 80 20 20
0.01 #N/A #N/A #N/A #N/A
0.01 #N/A #N/A #N/A #N/A
0.00 #N/A #N/A #N/A #N/A
0.010.04
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7/28/2019 hles1-4
http://slidepdf.com/reader/full/hles1-4 321/322
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7/28/2019 hles1-4
http://slidepdf.com/reader/full/hles1-4 322/322