Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Manifold Hydraulics Cayuga Lake Ithaca WWTP Outfall Cayuga Lake Ithaca WWTP Outfall.

Monroe L. Weber-Shirk

School of Civil and

Environmental Engineering

Manifold HydraulicsManifold Hydraulics

Cayuga Lake

Ithaca WWTP Outfall

Cayuga Lake

Ithaca WWTP Outfall

ManifoldsManifolds

Examples Sprinkler and drip irrigation systems wastewater discharge (multiport diffuser)

Design objectives distribute a given discharge through

multiple ports choose pipe size given constraints of head loss,

flow distribution, and cost

Examples Sprinkler and drip irrigation systems wastewater discharge (multiport diffuser)

Design objectives distribute a given discharge through

multiple ports choose pipe size given constraints of head loss,

flow distribution, and cost

uniformlyuniformly

Multiport DiffuserMultiport Diffuser

Objectives Minimize detrimental

effects of the discharge on the environment

Maximize initial Meet regulatory

requirements

Objectives Minimize detrimental

effects of the discharge on the environment

Maximize initial Meet regulatory

requirements

Pollutants treated wastewater

Cooling water from power plant

Sites Rivers, Lakes,

Oceans

Pollutants treated wastewater

Cooling water from power plant

Sites Rivers, Lakes,

Oceans

dilutiondilution

BOD, N, P, metalsBOD, N, P, metals

HeatHeat

Multiport DiffuserMultiport Diffuserenergy grade lineenergy grade linehydraulic grade linehydraulic grade line

z = 0z = 0??

Representation of EGL and HGL for multiport diffuser. Does it make sense?What happens to HGL across the ports?

Representation of EGL and HGL for multiport diffuser. Does it make sense?What happens to HGL across the ports?

Remember Expansions

Multiport Diffuser:Flow CalculationsMultiport Diffuser:Flow Calculations

We will derive equations in terms of ________ because pressure controls the port flow

Port flow based on ______ equation head loss through port (possibly including a riser)

Piezometric head change (H) across port flow expansion

Piezometric head change ( H) between ports Darcy-Weisbach and Swamee-Jain

We will derive equations in terms of ________ because pressure controls the port flow

Port flow based on ______ equation head loss through port (possibly including a riser)

Piezometric head change (H) across port flow expansion

Piezometric head change ( H) between ports Darcy-Weisbach and Swamee-Jain

energyenergy

In diffuser

HGLHGLpz

g+

Port typesPort types

Nozzle riser diffuser can be buried nozzle can give direction to discharge

Port cast in wall of diffuser pipe can’t be used if diffuser pipe is buried generally not recommended

Nozzle riser diffuser can be buried nozzle can give direction to discharge

Port cast in wall of diffuser pipe can’t be used if diffuser pipe is buried generally not recommended

The ProblemThe Problem

Given a desired discharge Calculate the head (pressure) required Calculate the flow from each port

Develop a strategy to solve this problem Simple Solution

________ ________ in the diffuser pipe Each port is an ________________

Complete Solution Determine HGL for the diffuser pipe

Given a desired discharge Calculate the head (pressure) required Calculate the flow from each port

Develop a strategy to solve this problem Simple Solution

________ ________ in the diffuser pipe Each port is an ________________

Complete Solution Determine HGL for the diffuser pipe

exit (minor losses)

Constant pressure

StrategyStrategy

The diffuser has many ports. If we can develop equations describing pressures and flows at one port we can then apply them to all of the ports.

We need equations describing Flow from a port as a function of pressure (HGL) in the

diffuser Head loss (and pressure drop) in the diffuser Flow in the diffuser _________________

The diffuser has many ports. If we can develop equations describing pressures and flows at one port we can then apply them to all of the ports.

We need equations describing Flow from a port as a function of pressure (HGL) in the

diffuser Head loss (and pressure drop) in the diffuser Flow in the diffuser _________________(mass conservation)

Port FlowPort Flow

H

p

z H

p

z

Vr Vr

riserriser

portport

diffuser pipediffuser pipe

Vd Vd

Lp

pa

d hg

VH

g

VH

22

22

Lp

pa

d hg

VH

g

VH

22

22

L

p

p

paa

a hg

Vz

p

g

Vz

p 22

22

L

p

p

paa

a hg

Vz

p

g

Vz

p 22

22

Hd

Vp2

2ghL

Hd

Vp2

2ghL

piezometric headpiezometric head

z = 0 at water surfacez = 0 at water surface

aVaV

pVpV

p p

00pa VV pa VV

Control volume?

Redo this w/ cs1 at entrance

Riser Head LossRiser Head Loss

gV

Kh relel 2

2

gV

Kh relel 2

2

hriserf

Lr

Dr

Vr2

2g hriserf

Lr

Dr

Vr2

2g

VrDr2 VpDp

2

VrDr2 VpDp

2

Vr

2 Vp2 Dp

Dr

4

Vr

2 Vp2 Dp

Dr

4

continuitycontinuity Vp Vp

hL hentrance hriser helbowhcontraction hL hentrance hriser helbowhcontraction

hL Ken f

Lr

Dr

Kel

Vr

2

2g Kc

Vp2

2g hL Ken f

Lr

Dr

Kel

Vr

2

2g Kc

Vp2

2g

g

VK

D

DK

D

LfKh p

c

r

pel

r

renL

2

24

g

VK

D

DK

D

LfKh p

c

r

pel

r

renL

2

24

hc Kc

Vp2

2g hc Kc

Vp2

2g

g

VKh renen

2

2

g

VKh renen

2

2

p p

Riser Head Loss CoefficientRiser Head Loss Coefficient

Hd Kr

Vp2

2g

r

dp

K

gHV

2

(riser loss coefficient)Note that the riser coefficient is a function of ________ number.

(riser loss coefficient)Note that the riser coefficient is a function of ________ number.

Port velocity (or flow) given piezometric head in diffuser and a riser loss coefficient

Port velocity (or flow) given piezometric head in diffuser and a riser loss coefficient

r

dpp

K

gHDQ

2

4

2

Hd

Vp2

2ghL

g

VK

D

DK

D

LfKH p

c

r

pel

r

rend

21

24

Kr 1 Ken f

Lr

Dr

Kel

Dp

Dr

4

Kc

ReynoldsReynolds

Orifice equation!

Head Loss across PortHead Loss across Port

_________ applied over entire cross section

_________ applied over entire cross section

___________ transferred over smaller area

___________ transferred over smaller area

Flow ____________ Same equation applies

as derived previously The velocities

upstream and downstream from the port are determined from continuity

Flow ____________ Same equation applies

as derived previously The velocities

upstream and downstream from the port are determined from continuity

( )2

1

2i

i iL

V Vh

g+-

=( )2

1

2i

i iL

V Vh

g+-

=

1 2

separationseparation

Vi Vi+1

PressurePressure MomentumMomentum

expansionexpansion

HGL in Diffuser across PortHGL in Diffuser across Port

Head loss occurs between section 1 and section 2 some distance downstream (~5 times the diameter of the diffuser)

We will treat this head loss as if it all occurred immediately after the port

Although there is head loss past the port the pressure (HGL) will __________ (proof coming up)

Head loss occurs between section 1 and section 2 some distance downstream (~5 times the diameter of the diffuser)

We will treat this head loss as if it all occurred immediately after the port

Although there is head loss past the port the pressure (HGL) will __________ (proof coming up)

hLi

Vi Vi1 2

2g hLi

Vi Vi1 2

2g

H from pressure recovery

H from pressure recovery

EGLEGL

HGLHGL

1 2

ViVi Vi+1Vi+1

increaseincrease

HGL in Diffuser across PortHGL in Diffuser across Port

ii Lii

ii hg

V

g

VHHH

22

2

1

2

1expansion ii Lii

ii hg

V

g

VHHH

22

2

1

2

1expansion

gVVV

H iii 11expansion i

gVVV

H iii 11expansion i

________ equation using definition of piezometric head

________ equation using definition of piezometric head

pressure increase across abrupt expansionpressure increase across abrupt expansion

g

VV

g

V

g

VH iiii

222

2

1

2

1

2

expansioni

g

VV

g

V

g

VH iiii

222

2

1

2

1

2

expansioni

hLi

Vi Vi1 2

2g hLi

Vi Vi1 2

2g

Li

ii

i hgV

HgV

H 22

2

11

2

Li

ii

i hgV

HgV

H 22

2

11

2

energyenergy

1 ii VV 1 ii VV

HGL in Diffuser across PortHGL in Diffuser across Port

Vi Vi1

Qpi

Ad Vi Vi1

Qpi

Ad

gVVV

H iii

i

11expansion

gVVV

H iii

i

11expansion

d

pi

gA

QVH i

i

1

expansion

d

pi

gA

QVH i

i

1

expansion

Vi1 Vi

Qpi

Ad Vi1 Vi

Qpi

Ad

continuitycontinuityHow can we find velocity downstream of port i? ___________How can we find velocity downstream of port i? ___________

1 ipi QQQi 1 ipi QQQi

Now we have the velocity downstream of the next portNow we have the velocity downstream of the next port

And we can calculate the increase in HGL across the port

And we can calculate the increase in HGL across the port

HGL between PortsHGL between Ports

HGL is parallel to EGL so H = E between diffusers

E = -hf and is due to friction loss (major losses)

HGL is parallel to EGL so H = E between diffusers

E = -hf and is due to friction loss (major losses)

2

9.0Re

74.5

7.3log

25.0

D

f

2

9.0Re

74.5

7.3log

25.0

D

f

Re

VD

ReVD

hf fLD

V2

2g hf f

LD

V2

2g

Multiport Diffuser: SolutionMultiport Diffuser: Solution The diffuser number, spacing, and jet velocity would be

determined in part by the mixing required in the ambient water (Environmental Fluid Mechanics)

Available head and total flow would be determined by the water source hydraulics

A criteria may also be established for uniformity of flow from the ports

Alternate design criteria may dictate different solution methods

The diffuser number, spacing, and jet velocity would be determined in part by the mixing required in the ambient water (Environmental Fluid Mechanics)

Available head and total flow would be determined by the water source hydraulics

A criteria may also be established for uniformity of flow from the ports

Alternate design criteria may dictate different solution methods

Multiport Diffuser: SolutionMultiport Diffuser: Solution Given total discharge, pipe

diameter, port size... Calculate the piezometric

head (measured from the water surface) required to give the necessary discharge in the first port loss coefficient for port head required to get

desired flow from port

Given total discharge, pipe diameter, port size...

Calculate the piezometric head (measured from the water surface) required to give the necessary discharge in the first port loss coefficient for port head required to get

desired flow from port

r

dpp

K

gHDQ

2

4

2

r

dpp

K

gHDQ

2

4

2

Hd

Kr

2g

4Qp

Dp2

2

Hd

Kr

2g

4Qp

Dp2

2

Kr 1 Ken f

Lr

Dr

Kel

Dp

Dr

4

Kc Kr 1 Ken f

Lr

Dr

Kel

Dp

Dr

4

Kc

Multiport Diffuser: SolutionMultiport Diffuser: Solution

Starting with the first port and proceeding to the last port ... Calculate the discharge from port i Calculate velocity change in

diffuser past port i Calculate the piezometric head

increase across port i Calculate the piezometric head

decrease between ports i and i+1 Calculate the piezometric head at

port i+1

Starting with the first port and proceeding to the last port ... Calculate the discharge from port i Calculate velocity change in

diffuser past port i Calculate the piezometric head

increase across port i Calculate the piezometric head

decrease between ports i and i+1 Calculate the piezometric head at

port i+1

d

pi

gA

QVH i

i

1expansion

d

pi

gA

QVH i

i

1expansion

Vi1 Vi

Qpi

Ad Vi1 Vi

Qpi

Ad

Hpipe f

LDd

Vi12

2g Hpipe f

LDd

Vi12

2g

iiii pipedd HHHH expansion1 iiii pipedd HHHH expansion1

r

dpp

K

gHDQ i

i

2

4

2

r

dpp

K

gHDQ i

i

2

4

2

Multiport Diffuser: SolutionMultiport Diffuser: Solution

ViVi

r

dpp

K

gHDQ i

i

2

4

2

r

dpp

K

gHDQ i

i

2

4

2

Vi1 Vi

Qpi

Ad Vi1 Vi

Qpi

Ad

HGLHGL1

5

g

V

D

LfH i

d

pipe

2

21g

V

D

LfH i

d

pipe

2

21

3

2

4

(_________ in pressure)(_________ in pressure)

(__________ in pressure)(__________ in pressure)

idH

idH

d

pi

gA

QVH i

i

1expansion

d

pi

gA

QVH i

i

1expansion

iiii pipedd HHHH expansion1 iiii pipedd HHHH expansion1

Known from previous stepKnown from previous step

increaseincrease

decreasedecrease

Multiport Diffuser: SolutionMultiport Diffuser: Solution

Calculate the total discharge from the ports Compare with design discharge Adjust the _________ ____ at first port to give design

discharge (use goal seeking, solver, or trial and error on spreadsheet). Alternately, set velocity past last port = 0 by changing piezometric head at first port.

It may be necessary to adjust diffuser or port diameter. It will likely be possible to decrease the size of the

diffuser pipe as the flow decreases. This may also help increase the discharge uniformity of the ports.

Calculate the total discharge from the ports Compare with design discharge Adjust the _________ ____ at first port to give design

discharge (use goal seeking, solver, or trial and error on spreadsheet). Alternately, set velocity past last port = 0 by changing piezometric head at first port.

It may be necessary to adjust diffuser or port diameter. It will likely be possible to decrease the size of the

diffuser pipe as the flow decreases. This may also help increase the discharge uniformity of the ports.

piezometric headpiezometric head

Multiport Diffuser:Example Solution (1 m pipe)

Multiport Diffuser:Example Solution (1 m pipe)

total flow (Q) 2.5port velocity (Vp) 3port diameter (Dp) 0.230port area (Ap) 0.04number of ports 20port flow (Qp) 0.13terminal piezometric head (H) 0.8distance between ports (L) 4pipe roughness () 0diffuser diameter (Dd) 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 20 40 60 80distance along diffuser (m)

(m)

EGL

HGL

SI units

Multiport Diffuser:Example Solution (0.63 m pipe)

Multiport Diffuser:Example Solution (0.63 m pipe)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 20 40 60 80distance along diffuser (m)

(m)

EGL

HGLtotal flow (Q) 2.5port velocity (Vp) 3port diameter (Dp) 0.230port area (Ap) 0.04number of ports 20port flow (Qp) 0.13terminal piezometric head (H) 1.2distance between ports (L) 4pipe roughness () 0diffuser diameter (Dd) 0.63

SI units

Design GuidelinesDesign Guidelines The port discharge velocity should be _______ to achieve

good mixing with the ambient water. The sum of all port areas must be less than the diffuser pipe

area. The best area ratio (port area/diffuser area) is usually between 1/3 and 2/3.

The effects of pipe friction and pressure recovery will tend to cancel when Ld is the total length of the diffuser pipe and the friction factor, f, is

obtained by iteration since it is a function of the pipe diameter. If the diffuser area obtained using this method is less than 1.5 x

port area then this design criteria can not be used.

The port discharge velocity should be _______ to achieve good mixing with the ambient water.

The sum of all port areas must be less than the diffuser pipe area. The best area ratio (port area/diffuser area) is usually between 1/3 and 2/3.

The effects of pipe friction and pressure recovery will tend to cancel when Ld is the total length of the diffuser pipe and the friction factor, f, is

obtained by iteration since it is a function of the pipe diameter. If the diffuser area obtained using this method is less than 1.5 x

port area then this design criteria can not be used.

f3d

d

LD =

f3d

d

LD =

~3 m/s~3 m/s

Multiport Diffuser:Thought ExperimentsMultiport Diffuser:

Thought Experiments What happens to the uniformity of flow rates from the

ports as the size of the diffuser pipe decreases? (Assume the pressure in the feeder pipe is varied to maintain constant flow while the port size remains the same.) ______________

What happens to the uniformity of flow rates from the ports as the size of the ports decreases? ______________

If the goal is uniform flow distribution why not use very small ports? ____________________

Which port will have the highest flow rate? _____________

What happens to the uniformity of flow rates from the ports as the size of the diffuser pipe decreases? (Assume the pressure in the feeder pipe is varied to maintain constant flow while the port size remains the same.) ______________

What happens to the uniformity of flow rates from the ports as the size of the ports decreases? ______________

If the goal is uniform flow distribution why not use very small ports? ____________________

Which port will have the highest flow rate? _____________

First or last!

Energy requirements

More Uniform

Less Uniform

Diffuser HomeworkDiffuser Homework

Hometown WWTP

300 m 95 m

20 ports20 ports

QuizQuiz

The friction factor for major losses in pipe flow is relatively constant for a given geometry at high Reynolds numbers. Head loss is proportional to the friction factor. Therefore head loss is independent of Reynolds number at high Reynolds numbers. Explain why this is or isn’t true.

In large multiport diffusers the diameter of the main diffuser pipe is decreased in increments as the flow decreases (due to discharge from the ports). If you compare discharge from a port upstream from a decrease in diffuser pipe diameter with the port just downstream from a diameter change which port will have the highest flow? You may assume the transition in diffuser pipe diameter is smooth. Explain your answer.

The friction factor for major losses in pipe flow is relatively constant for a given geometry at high Reynolds numbers. Head loss is proportional to the friction factor. Therefore head loss is independent of Reynolds number at high Reynolds numbers. Explain why this is or isn’t true.

In large multiport diffusers the diameter of the main diffuser pipe is decreased in increments as the flow decreases (due to discharge from the ports). If you compare discharge from a port upstream from a decrease in diffuser pipe diameter with the port just downstream from a diameter change which port will have the highest flow? You may assume the transition in diffuser pipe diameter is smooth. Explain your answer.