Hydraulics Lecture Material

8/2/2019 Hydraulics Lecture Material

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HYDRAULICSYDRAULICSIntroductionntroductionBasic Hydraulicsasic HydraulicsHead Lossead LossPipelinesipelinesLateral Designateral DesignMainline Designainline Design

HYDRAULICSYDRAULICSIntroductionntroductionAn understanding and use ofn understanding and use of hydraulicsydraulics issabsolutely essential for proper developmentbsolutely essential for proper developmentand operation of modern irrigation systemsnd operation of modern irrigation systems

Irrigation hydraulics involves the determinationrrigation hydraulics involves the determinationof the pressure distribution in the system, thef the pressure distribution in the system, theselection of pipe sizes and fittings to conveyelection of pipe sizes and fittings to conveyand regulate water delivery, and thend regulate water delivery, and thedetermination of the power and energyetermination of the power and energyrequirements to pressurize and lift water.equirements to pressurize and lift water.

HYDRAULICSYDRAULICSMistakes made in setting up an irrigation systemMistakes made in setting up an irrigation system

are often very expensive to correct, whereas theare often very expensive to correct, whereas the

cost of appropriate planning to avoid errors iscost of appropriate planning to avoid errors is

small.small.


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HYDRAULICSYDRAULICSBasic Hydraulicsasic Hydraulics


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HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsOne of the most important considerations inne of the most important considerations inthe hydraulics of irrigation systems is thehe hydraulics of irrigation systems is theamount ofmount of energynergy that is available in the waterhat is available in the waterat any point within the system. With watert any point within the system. With waterflow, energy can be in the following forms:low, energy can be in the following forms:

1.. Kinetic energy due to velocityinetic energy due to velocity2.. Potential energy due to elevationotential energy due to elevation3.. Potential energy due to waterotential energy due to water

pressure.ressure.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsIn this class, the energy in water is expressedn this class, the energy in water is expressedas energy per unit weight of water. Energy hass energy per unit weight of water. Energy hasthe units of FL (force times length) and weighthe units of FL (force times length) and weighthas the units of Force (F).as the units of Force (F). Thus, energy perhus, energy perunit weight has the units of FL / F or just thenit weight has the units of FL / F or just thedimension of L (LENGTH).imension of L (LENGTH).Hence, the energy of water in an irrigationence, the energy of water in an irrigationsystem includes velocity head, elevation head,ystem includes velocity head, elevation head,and pressure head.nd pressure head.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsThehe potential energyotential energy due to elevation is aue to elevation is aresult of the location of the water relativeesult of the location of the water relativeto an arbitrary reference plane. Water at ao an arbitrary reference plane. Water at ahigher elevation has more potentialigher elevation has more potentialenergy than water at a lower elevation.nergy than water at a lower elevation.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsThe water has the ability to do work as ithe water has the ability to do work as itflows downhill, such as eroding the soillows downhill, such as eroding the soilsurface, generating power, etc. Theurface, generating power, etc. Thepotential energy of the water decreasesotential energy of the water decreasesas it flows downhill. The letter Z will bes it flows downhill. The letter Z will beused to represent elevation head orsed to represent elevation head orcalledalled gravitational headravitational head.


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HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsThe potential energy due to the pressurization ofhe potential energy due to the pressurization ofwater can be a very large component in anater can be a very large component in anirrigation system. Pressure is the force per unitrrigation system. Pressure is the force per unitarea exerted on the walls of a container. Therea exerted on the walls of a container. Thepressure may be expressed as:ressure may be expressed as:

P == h or h = P /or h = P / Equation 2quation 2where:here: P = pressure (lb per square inch)= pressure (lb per square inch)

= weight of a unit volume of fluidweight of a unit volume of fluid(specific weight), lb per ftspecific weight), lb per ft3.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsIn general, the maximum recommended averagen general, the maximum recommended averagevelocity in an enclosed pipeline is 5 ft/sec.elocity in an enclosed pipeline is 5 ft/sec.When the velocity in a pipeline exceeds 5 ft/sec,hen the velocity in a pipeline exceeds 5 ft/sec,there is a potential to develop very highhere is a potential to develop very highpressure surgesressure surges which may damage pipelines.hich may damage pipelines.Pressure surges are due to flow being stoppedressure surges are due to flow being stoppedsuddenly while the upstream water has a largeuddenly while the upstream water has a largeamount ofmount of momentumomentum. When the flow isWhen the flow isstopped too quickly, the rapid change intopped too quickly, the rapid change inmomentum results in impulsive force calledomentum results in impulsive force calledwater hammerater hammer.

HYDRAULICSYDRAULICSBasic Hydraulicsasic Hydraulics

P == h or h = P /or h = P / Eqq 2where:here: P = pressure (lb per square= pressure (lb per squareinch)nch)

= weight of a unit volume ofweight of a unit volume offluid (specific weight), lbluid (specific weight), lbper fter ft3h = pressure head, ft.= pressure head, ft.

HYDRAULICSHYDRAULICS


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HYDRAULICSYDRAULICSEXAMPLE 1XAMPLE 1Two columns of water are filled to a height of 10wo columns of water are filled to a height of 10feet with water. One column has a crosseet with water. One column has a cross-sectional area of 1 inectional area of 1 in2, the other 10 inthe other 10 in2. Find theFind thepressure at the bottom of each column.ressure at the bottom of each column.Given:iven: h = 10 ft, and= 10 ft, and

= 62.4 lb/ft62.4 lb/ft3Find:ind: Pressure, Pressure, P

HYDRAULICSYDRAULICSEXAMPLE 1XAMPLE 1Given:iven: h = 10 ft, and= 10 ft, and

= 62.4 lb/ft62.4 lb/ft3Find:ind: Pressure, Pressure, PSolution:olution:P == h or h = P /or h = P / Equation 2quation 2P = 62.4 lb/ft= 62.4 lb/ft3 (10 ft) (ft10 ft) (ft2 / 144 in144 in2) = 4.33 lb/in= 4.33 lb/in2P = 4.33 psi= 4.33 psi

HYDRAULICSYDRAULICSEXAMPLE 1XAMPLE 1Given:iven: h = 10 ft, and= 10 ft, and

= 62.4 lb/ft62.4 lb/ft3Find:ind: Pressure, Pressure, PSolution:olution:P = 4.33 psi= 4.33 psiNOTE: THE PRESSURE ISOTE: THE PRESSURE ISINDEPENDENT OF THE SURFACE AREANDEPENDENT OF THE SURFACE AREAOF THE COLUMN.F THE COLUMN.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsThe PRESSURE IS INDEPENDENT OF THEhe PRESSURE IS INDEPENDENT OF THESURFACE AREA!URFACE AREA!In English units, it is convenient to express:n English units, it is convenient to express:

= 0.433 psi / ft0.433 psi / ft Equation 3quation 3Orr1// = 2.31 ft / psi2.31 ft / psi ONLY FORNLY FORWATERATER


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HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsKinetic energy is the result of the movement ofinetic energy is the result of the movement ofthe fluid and the termhe fluid and the term VELOCITY HEADELOCITY HEAD is givens givenby:y:

Velocity Head = V2 / (2g) Equation 1quation 1where:here: V = average velocity at a point in a= average velocity at a point in apipe or channel, ft/sec,ipe or channel, ft/sec,

g = gravitational constant, 32.2= gravitational constant, 32.2ft/sect/sec2.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsThe sum of the energy forms the total energyhe sum of the energy forms the total energyper unit weight called HYDRAULIC HEAD (H). Iter unit weight called HYDRAULIC HEAD (H). Itis:s:H = + elevation head + pressure head + velocity= + elevation head + pressure head + velocityheadead

H = Z + h += Z + h + VV22/(2g)/(2g) Equation 4quation 4

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsAnother important concept of water flow isnother important concept of water flow iscontinuityontinuity. In a hydraulic system, mass mustIn a hydraulic system, mass mustbe conserved. For incompressible fluid flow,e conserved. For incompressible fluid flow,such as water, the continuity equation isuch as water, the continuity equation isexpressed as:xpressed as:

Q = V A= V A Equation 5quation 5where:here: Q = volumetric flow rate or= volumetric flow rate or

discharge,ischarge,V = average flow velocity= average flow velocityA = cross= cross-sectional area of flow.ectional area of flow.


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HYDRAULICSYDRAULICSEXAMPLE 2XAMPLE 2In the pipeline system shown on the nextn the pipeline system shown on the nextpage, find the hydraulic head at the inlet intoage, find the hydraulic head at the inlet intothe 4he 4-inch diameter pipeline.nch diameter pipeline.Given:iven: Z = 15 feet= 15 feetP = 60 psi= 60 psiQ = 400 gpm= 400 gpmd = 4 inch (internal diameter)= 4 inch (internal diameter)Find:ind: h, V = Q/A, Velocity Head, and, V = Q/A, Velocity Head, andTotal Headotal Head


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HYDRAULICSYDRAULICSEXAMPLE 2XAMPLE 2Solution:olution:h = 60 psi (2.31 ft/psi) = 139 feet= 60 psi (2.31 ft/psi) = 139 feetA == /4 (4 in)4 (4 in)2 = 12.57 in12.57 in2 (ftft2/144 in144 in2) = 0.087 ft= 0.087 ft2Q = 400 gpm/ (450 gpm/cfs) = 0.89 cfs (ft= 400 gpm/ (450 gpm/cfs) = 0.89 cfs (ft3/sec)sec)V = Q/A = 0.89 ft= Q/A = 0.89 ft3/sec / 0.087 ftsec / 0.087 ft2 = 10.23 ft/sec10.23 ft/sec

HYDRAULICSYDRAULICSEXAMPLE 2XAMPLE 2Solution:olution:V = Q/A = 0.89 ft= Q/A = 0.89 ft3/sec / 0.087 ftsec / 0.087 ft2 = 10.23 ft/sec10.23 ft/secVelocity Head = Velocity Head = V2/2g =2g =

(10.23 ft/sec)10.23 ft/sec)2 / {2 (32.2 ft/sec{2 (32.2 ft/sec2)} = 1.6 ft} = 1.6 ftTotal Head (H) = 15 ft + 139 ft + 1.6 ft = 156 ftotal Head (H) = 15 ft + 139 ft + 1.6 ft = 156 ft

HYDRAULICSYDRAULICSEXAMPLE 3XAMPLE 3What is the velocity head at point 2 inhat is the velocity head at point 2 inEXAMPLE 2?XAMPLE 2?Given:iven: Q2 = QQ1 = 400 gpm400 gpmd2 = 10 inch10 inch

Find:ind: A2 = /4 d4 d22Velocity, Velocity, VVelocity Head at point 2elocity Head at point 2

HYDRAULICSYDRAULICSEXAMPLE 3XAMPLE 3Solution:olution:A2 = /4 (10 in)4 (10 in)2 = 78.5 in78.5 in2 (ftft2/144 in144 in2) = 0.526= 0.526ftt2Q2 = QQ1 = 400 gpm/ (450 gpm/cfs) = 0.89 cfs400 gpm/ (450 gpm/cfs) = 0.89 cfs(ftft3/sec)sec)V = Q/A = 0.89 ft= Q/A = 0.89 ft3/sec / 0.526 ftsec / 0.526 ft2 = 1.69 ft/sec1.69 ft/sec


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HYDRAULICSYDRAULICSEXAMPLE 3XAMPLE 3Solution:olution:V = Q/A = 0.89 ft= Q/A = 0.89 ft3/sec / 0.526 ftsec / 0.526 ft2 = 1.69 ft/sec1.69 ft/secVelocity Head = Velocity Head = V2/2g =2g =

(1.69 ft/sec)1.69 ft/sec)2 / {2 (32.2 ft/sec{2 (32.2 ft/sec2)} = 0.04 ft} = 0.04 ftTHUS, the velocity head in the 10HUS, the velocity head in the 10-inch pipe isnch pipe isonly 0.025 times the velocity head in the 4nly 0.025 times the velocity head in the 4-inchnchpipe.ipe.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsAn important law of fluid mechanics isn important law of fluid mechanics isconservation of energyonservation of energy. Conservation of energyConservation of energyfor irrigation systems is described by theor irrigation systems is described by theBernoulli Equationernoulli Equation, which is given by:which is given by:

H2 = HH1 - hL Equation 6quation 6where:here: H1 = hydraulic head at point 1 in ahydraulic head at point 1 in asystemystem (upstream)upstream)H2 = hydraulic head at point 2 in ahydraulic head at point 2 in asystemystem (down stream)down stream)

hL = head loss during flow from point 1head loss during flow from point 1to point 2.o point 2.

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsThe head loss from point 1 to point 2 ishe head loss from point 1 to point 2 isdue to friction loss from the resistanceue to friction loss from the resistanceto flow along a pipeline and to minoro flow along a pipeline and to minorpressure losses of energy through piperessure losses of energy through pipefittings, etc.ittings, etc.


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HYDRAULICSYDRAULICSFriction Loss in Pipesriction Loss in PipesDarcyarcy-Weisbacheisbach Formulaormula

).(L/Tgravityofonacceleratitheis

(L/T),pipetheinvelocityfluidmeantheis

(L)diameterpipeinternaltheis

(L),lengthpipetheis

less),(dimensionnumberReynoldsandpropertiesfluid

roughness,pipeoffunctionaiswhichfactor,frictionWeisbach-Darcytheis

(L),lossfrictiontheis

:where

2

2

2

g

V

D

L

f

h

g

V

D

Lfh

f

f

HYDRAULICSYDRAULICSFriction Loss in Pipesriction Loss in Pipes

constant.conversion

where

2

:madebecanonssubstitutifollowingthepipes,circularforFurther,

2

5

2

2

2

k

D

QLfk

g

V

D

Lfh

f

HYDRAULICSYDRAULICS HYDRAULICSYDRAULICS


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HYDRAULICSYDRAULICSFriction Loss in Pipesriction Loss in PipesThe friction factor is a function of Reynoldshe friction factor is a function of ReynoldsNumber and relative roughness of the pipeumber and relative roughness of the pipeinternal material. Generally, the solution ofnternal material. Generally, the solution ofthis equation is often a trial and error as thehis equation is often a trial and error as theflow is not known and thus the Reynoldslow is not known and thus the Reynoldsnumber (and thus the friction factor) is notumber (and thus the friction factor) is notknown.nown.

Hazenazen-Williams Formulailliams Formula

/T),(Lvelocityfluidmeantheis


(L),lengthpipetheis

material.pipeoffunctionaiswhich

factorfrictionWilliams-Hazentheis

units,thehandlefactor toconversionais


:where

2

852.1

852.1

167.1

V

D

L

C

K

h

C

V

D

LKh

f

f

HYDRAULICSYDRAULICSFriction Loss in Pipesriction Loss in Pipes

/T),(Lrateflowtheis


(L),lengthpipetheis

material.pipeoffunctionaiswhichfactor,frictionWilliams-Hazentheis



:where

:madebecantionsimplificafollowingtheconduits,circularforFurther,

3

1

852.1

852.1

871.41

Q

D

L

C

k

h

C

Q

D

Lkh

f

f

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction Losshf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D 4.866.866] Equation 8aquation 8aPf = 456 [Q/C]456 [Q/C] 1.852.852 [1/D1/D4.866.866] Equation 8bquation 8bwhere: hhere: hf = friction loss, ft of head per 100 ftfriction loss, ft of head per 100 ftof pipef pipePf = friction loss, psi per 100 ft of pipefriction loss, psi per 100 ft of pipeQ = flow rate, gpm= flow rate, gpmD = inside pipe diameter, inches= inside pipe diameter, inchesC = roughness coefficient= roughness coefficient


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HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction LossRepresentative values of C for different pipeepresentative values of C for different pipematerials are given inaterials are given in TABLE 1ABLE 1. The value of CThe value of Cdecreases as the roughness of the pipe wallecreases as the roughness of the pipe walldecreases. Accordingly, of the materials listedecreases. Accordingly, of the materials listedinn TABLE 1ABLE 1, steel pipe is the roughest material (Csteel pipe is the roughest material (C= 100) while PVC is the smoothest (C = 150).100) while PVC is the smoothest (C = 150).Table 2able 2 illustrates the friction loss for PVC pipellustrates the friction loss for PVC pipeas a function of pipe size and flow rate. Note thes a function of pipe size and flow rate. Note thefriction losses in Table 2 are in ft per 100 ft andriction losses in Table 2 are in ft per 100 ft andare for PVC pipe of an SDR of 21.re for PVC pipe of an SDR of 21.

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction LossTABLE 1. HAZENABLE 1. HAZEN-WILLIAMS C VALUESILLIAMS C VALUESMATERIALATERIAL CAluminum pipe with couplersluminum pipe with couplers 12020Aluminum pipe with gatesluminum pipe with gates 11010Cement asbestos pipeement asbestos pipe 14040Galvanized steel pipealvanized steel pipe 14040Standard steel pipetandard steel pipe 10000PVC Class 160 irrigation pipeVC Class 160 irrigation pipe 15050PVC pipe with gatesVC pipe with gates 13030

HYDRAULICSYDRAULICSTable 2 Friction loss for IPS PVC pipe.

Q

(gal/min) 1-in 11/4-in 11/2-in 2-in 21/2-in

- - - - - - - Friction head loss in ft/100 ft - - - - - - -

2

4

6

8

10

.15

.54

1.15

2.98

.04

.17

.37

.63

.95

.02

.09

.19

.32

.49

.03

.06

.11

.16

.01

.02

.04

.06

15

20

25

30

35

40

45

50

6.32

10.79

16.30

22.86

2.03

3.46

5.22

7.32

9.75

12.46

15.51

18.87

1.04

1.78

2.70

3.78

5.03

6.46

8.02

9.75

.35

.60

.91

1.27

1.70

2.18

2.71

3.30

.14

.23

.36

.50

.67

.86

1.07

1.30

Q(gal/min) 4-in 5-in 6-in 8-in 10-in 12-in

- - - - - - - Friction head loss in ft/100 ft - - - - - - -

150

160170180190200

1.11

1.261.411.571.731.90

220

240260280300320

340360380400420440460

480500550

600650700

750800850900950

2.28

2.673.103.564.044.56

5.105.676.266.90

.81

.951.101.261.431.62

1.822.022.222.452.692.923.18

3.443.70

.34

.40

.46

.54

.61

.69

.77

.86

.951.041.141.251.35

1.461.581.89

2.222.582.96

3.363.784.244.715.21

.09

.10

.12

.14

.17

.19

.21

.24

.26

.28

.31

.34

.37

.41

.43

.52

.61

.71

.81

.931.041.171.301.44

.10

.10

.11

.12

.14

.15

.18

.21

.24

.28

.32

.36

.40

.44

.49

.060

.083

.096

.110

.125

.141

.158

.175

.194

.213


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HYDRAULICSYDRAULICSPipe Sizesipe SizesBoth the internal and external pipe diametersoth the internal and external pipe diametersare determined by the material used tore determined by the material used tomanufacture the pipe and theanufacture the pipe and the nominalominal pipeipediameter. These values are available iniameter. These values are available inmany different locations and standards.any different locations and standards.Several are included here for reference.everal are included here for reference.

HYDRAULICSYDRAULICSSHOW EXAMPLES OF PVC PIPEHOW EXAMPLES OF PVC PIPE

HYDRAULICSYDRAULICSPipelinesipelinesDiscuss pipe sizesiscuss pipe sizesPVCVC ------- OD controlled (fittings are externalD controlled (fittings are externalto pipe). Thus, pipe thickness reduceso pipe). Thus, pipe thickness reducespipeipe ID.D.ALUMINUMLUMINUM ----- OD controlled (fittings areD controlled (fittings areexternal to pipe). Thus, pipe thicknessxternal to pipe). Thus, pipe thicknessreduces pipe ID.educes pipe ID.BLACK POLYLACK POLY ----- ID controlled (fittings areD controlled (fittings areinternal to pipe). Thus, pipe thicknessnternal to pipe). Thus, pipe thicknessdoes not impact pipe ID.oes not impact pipe ID.

HYDRAULICSYDRAULICSAluminum Pipe Sizesluminum Pipe Sizes

NOTE: Aluminum Pipe with Couplers, C = 130OTE: Aluminum Pipe with Couplers, C = 1309.818.8180.000.00007.856.856.00.006.872.872.00.005.884.884.00.004.896.896.00.003.906.906.00.002.914.914.00.001.902.902.00.00

PIPE I.D. (in)IPE I.D. (in)IPE O.D. (in)IPE O.D. (in)OMINAL PIPE SIZEOMINAL PIPE SIZE(in)in)


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220 ft head433.5

250001.0300034.0400301.0

310030001.04003000252.550400025606.0640002560001.0

63000256000505.07.01600050151.53.5

1002560.01.01256000.01600050.3

psisisisisisisi.D.BasedPipeO.D.BasedPipe

PE 2305E 3406PE 3306PE 2306PE 3408VC 2110VC 2112VC 2116VC 1120PVC 1220PVC 2120

SDRDR

HYDRAULICSYDRAULICSPVC Pipe SizesVC Pipe Sizes Table 1. Pressure ratings (PR) for nonthreaded thermoplastic pipe. HYDRAULICSHYDRAULICS

5.8405.906.000PIP6.140156.00

5.7616.0655.8455.9936.1156.3016.417IPS6.625168.286150

4.8135.0474.9095.0335.1355.2915.389IPS5.563141.305125

3.9323.9724.004PIP4.134105.00

3.8264.0263.9704.0724.1544.2804.36IPS4.500114.304100

3.3643.5483.5303.623.6923.804IPS4.000101.603 90

2.9003.0683.0883.1663.2303.330IPS3.50088.90380

2.3232.4692.5372.6012.655IPS2.87573.022 65

1.9392.0672.0952.1492.193IPS2.37560.32250

1.5001.6101.6761.7201.754IPS1.90048.261 40

1.2181.3801.4641.5021.532IPS1.66042.161 32

0.9571.0491.1611.1891.212IPS1.31533.40125

0.7420.8340.9260.930IPS1.05026.6720

0.5460.622IPS0.84021.3415

0.4230.493IPS0.67517.143/810

0.3020.364IPS0.54013.728

0.2150.279IPS0.40510.291/84

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

inmmInmm

Schedule

80

Schedule

40

SDR 17SDR 21SDR 26SDR 41SDR 51SDR 6450 ft

head

Pipe

Class

Average

O.D.

Average

O.D.

Nominal

Pipe Size

Nominal

Pipe Size

HYDRAULICSYDRAULICSPVC Pipe SizesVC Pipe Sizes


31.76432.57233.23034.244IPS36.000914.4036900

26.4727.14427.69228.536IPS30.000762.0030750

25.80326.58926.857PIP27.953710.0027700

22.89523.59323.83124.271PIP24.803629.99

21.17621.71422.15422.83023.05823.486IPS24.000609.6024600

20.35120.97121.18321.575PIP22.047559.9921550

17.64818.09618.46219.02419.20019.564IPS20.000508.0020500

17.26317.78917.96918.310PIP18.701475.00

15.88216.28616.61617.12217.28017.606IPS18.000457.2018450

14.11814.47614.77015.220IPS16.000406.4016400

13.84414.12414.55414.70014.97215.000PIP15.300388.6215380

12.35412.66812.92413.318IPS14.000355.6014350

11.64211.76011.97812.000PIP12.240311.00

11.93811.25011.53811.77012.128IPS12.750323.8512300

9.7209.8009.98210.000PIP10.200259.00

10.029.4869.7289.92410.226IPS10.750273.0510250

7.7627.8407.9868.000PIP8.160207.00

7.9817.6097.8057.9618.205IPS8.625219.088200

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

Pipe

I.D.(in)

inmmInmm

Schedule

40

SDR 17SDR 21SDR 26SDR 41SDR 51100 ft

head

50 ft

head

Pipe

Class

Average

O.D.

Average

O.D.

Nominal

Pipe Size

Nominal

Pipe Size

HYDRAULICSYDRAULICSPVC Pipe SizesVC Pipe Sizes HYDRAULICSYDRAULICSTable 3. Pipe dimensions for PE pipe, I.D. Controlled.

6.6257.1196.8736.7036.065154.056154

4.0004.7264.5624.4504.026102.264102

3.5003.6023.4783.3903.06877.93378

2.8752.8992.7992.7292.46962.712 63

2.3752.8472.6572.5272.4272.3432.2852.06752.50252

1.9002.2182.0701.9681.8901.8241.7801.61040.891 41

1.6601.9001.7741.6861.6201.5641.5261.38035.051 35

1.3151.4451.3491.2831.2311.1891.1691.04926.64127

1.0501.1341.0601.0080.9680.9440.9440.82420.9321

0.8400.8560.8000.7600.7420.7420.7420.62215.8016

Pipe

O.D.(in)

Pipe

O.D.(in)

Pipe

O.D.(in)

Pipe

O.D.(in)

Pipe

O.D.(in)

Pipe

O.D.(in)

Pipe

O.D.(in)

inmmInmm

Schedule

40

SDR

5.3

SDR

7

SDR

9

SDR

11.5

SDR

15

SDR

19

Average

I.D.

Average

I.D.

Nominal

Pipe Size

Nominal

Pipe Size


15/29

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsBernoulli Equationernoulli Equation

H2 = HH1 - hL Equation 6quation 6h2 + ZZ2 + VV22/2g =2g = hh11 + Z+ Z11 + V+ V1122/2g/2g - lossesossesZ1 = 110 feet, Z110 feet, Z2 = 100 feet100 feetP1 = 50 psi, P50 psi, P2 = ????Pipe is 6 inch IPS PVC, SDR = 21 (200 psi)ipe is 6 inch IPS PVC, SDR = 21 (200 psi)Length is 1,000 feetength is 1,000 feet

HYDRAULICSYDRAULICSBasic Hydraulicsasic HydraulicsZ1 = 110 feet, Z110 feet, Z2 = 100 feet100 feetP1 = 50 psi, P50 psi, P2 = ??; h??; h1 = 50 (2.31) = 115.5 feet50 (2.31) = 115.5 feetIn this case, Vn this case, V1 = VV2, thus velocity heads cancelthus velocity heads cancelh2 + 100 = h100 = h1 + 110110 lossesossesh2 = 115.5 + 110115.5 + 110 - 10000 - lossesosses

HYDRAULICSYDRAULICSBasic Hydraulicsasic Hydraulicsh2 = 115.5 + 10115.5 + 10 lossesossesQ lossesosses lossesosses h2 P2gpmpm ft/100 ftt/100 ft 1,000 ft,000 ft ftt psisi60000 2.22.22 22.22.2 103.303.3 44.74.730000 0.61.61 6.10.10 119.419.4 51.71.7

HYDRAULICSYDRAULICS

EXAMPLE OF PIPEXAMPLE OF PIPEMATERIAL ONATERIAL ON

FRICTION LOSSRICTION LOSS


16/29

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction Losshf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D 4.866.866] Equation 8aquation 8awhere: hhere: hf = friction loss, ft of head per 100 ft offriction loss, ft of head per 100 ft ofpipeipe Q = flow rate, gpm= flow rate, gpmD = inside pipe diameter, inches= inside pipe diameter, inchesC = roughness coefficient,= roughness coefficient,

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction LossPipeipe PipeipeSizeize Materialaterial I.D..D. O.D..D. C1 inin Sch 40 PVCch 40 PVC 1.049.049 1.315.315 150501 inin Sch 40 Steelch 40 Steel 1.049.049 1.315.315 10000 inn Sch 40 PVCch 40 PVC 0.622.622 0.848.848 15050Q = 10 gpm= 10 gpm

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction Losshf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D 4.866.866] inch SCH 40 PVCnch SCH 40 PVC

hf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D 4.866.866]hf = 1054 [10/150]1054 [10/150] 1.852.852 [1/0.6221/0.622 4.866.866]hf = 70.5 ft/100ft70.5 ft/100fthf = 130.5 psi/100ft130.5 psi/100ft

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction Losshf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D 4.866.866]1 inch SCH 40 PVCinch SCH 40 PVC

hf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D 4.866.866]hf = 1054 [10/150]1054 [10/150] 1.852.852 [1/1.0491/1.049 4.866.866]hf = 5.541 ft/100ft5.541 ft/100fthf = 2.4 psi/100ft2.4 psi/100ft


17/29

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction Losshf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D 4.866.866]1 inch SCH 40 STEELinch SCH 40 STEEL

hf = 1054 [Q/C]1054 [Q/C] 1.852.852 [1/D1/D4.866.866]hf = 1054 [10/100]1054 [10/100] 1.852.852 [1/1.0491/1.049 4.866.866]hf = 11.74 ft/100ft11.74 ft/100fthf = 5.08 psi/100ft5.08 psi/100ft

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction LossCOMPARISONS BETWEEN PIPESOMPARISONS BETWEEN PIPES INCH PVCNCH PVC ------- 30.5 PSI/100 FT0.5 PSI/100 FT1 INCH PVCINCH PVC ------------- 2.4 PSI/100FT.4 PSI/100FT1 INCH STEELINCH STEEL ----------- 5.08 PSI/100FT.08 PSI/100FTSTEEL HAS TWICE THE LOSS OF PVCTEEL HAS TWICE THE LOSS OF PVCDOUBLE SIZE HAS APPROXIMATELY 1/6OUBLE SIZE HAS APPROXIMATELY 1/6LOSSOS S

HYDRAULICSYDRAULICSHead Lossead LossMinor or Fitting Lossesinor or Fitting LossesHead losses also occur in the fittings used inead losses also occur in the fittings used inconstruction of a system. These head lossesonstruction of a system. These head lossesare due to the friction in the fitting, plus lossesre due to the friction in the fitting, plus lossesresulting from the turbulence and changes inesulting from the turbulence and changes inthe direction of flow. Head losses in fittings,he direction of flow. Head losses in fittings,valves, etc., can be described by:alves, etc., can be described by:

HYDRAULICSYDRAULICSHead Lossead LossMinor or Fitting Lossesinor or Fitting LossesHead losses in fittings, valves, etc., can beead losses in fittings, valves, etc., can bedescribed by:escribed by:

hm = K {VK {V2/2g}2g} Equation 9quation 9where:here: hm = head loss in fitting, fthead loss in fitting, ft

K = resistance coefficient for fitting,= resistance coefficient for fitting,V = velocity of flow, ft/sec= velocity of flow, ft/sec


18/29

HYDRAULICSYDRAULICSHead Lossead LossMinor or Fitting Lossesinor or Fitting LossesResistance coefficients for various types ofesistance coefficients for various types offittings and valves are given inittings and valves are given in TABLE 4.ABLE 4.

Table 4 Resis tance coefficient K for use determining head losses in fittings and valves.

Standard pipe

Nominal diameter

Fitting or valve

3 in

(76.2 mm)

4 in

(101.6 mm)

5 in

(127.0 mm)

6 in

(152.4 mm)

7 in

(177.8 mm)

8 in

(203.2 mm)

10 in

(254 mm)

Bends:

Return flanged

Return screwed

Elbows:

Regular flanged 90

Long radius flanged 90

Long radius flanged 45

Regular screwed 90

Long radius screwed 90

Regular screwed 45

Tees:

Flanged line flow

Flanged branch flow

Screwed line flow

Screwed branch flow

Valves:

Globe flangedGlobe screwed

Gate flanged

Gatescrewed

0.33

.80

0.34

.25

.19

.80

.30

.30

.16

.73

.90

1.20

7.06.0

.21

14

0.30

.70

0.31

.22

.18

.70

.23

.28

.14

.68

.90

1.10

6.35.7

.16

12

0.29

0.30

.20

.18

.13

.65

6.0

.13

0.28

0.28

.18

.17

.12

.60

5.8

.11

0.27

0.27

.17

.17

.11

.58

5.7

.09

0.25

0.26

.15

.17

.10

.56

5.6

.075

0.24

0.25

.14

.16

.09

.52

5.5

.06

HYDRAULICSYDRAULICSHead Lossead LossVELOCITY HEAD (practical guide)ELOCITY HEAD (practical guide)V2/(2g) = 2.594 * 10(2g) = 2.594 * 10-3 (gpmgpm2)/I.D./I.D.4EXAMPLEXAMPLEQ = 40 GPM, ID = 1.5 INCH= 40 GPM, ID = 1.5 INCHV2/(2g) = 2.594*10(2g) = 2.594*10-3 (40402)/1.5/1.54 = 0.82 ft0.82 ft

HYDRAULICSYDRAULICSPipelinesipelinesIrrigation pipelines are made of manyrrigation pipelines are made of manymaterials. Currently, the most commonaterials. Currently, the most commonmaterials used for above ground sprinkleraterials used for above ground sprinklersystems and gatedystems and gated-pipe surface irrigationipe surface irrigationsystems are aluminum and ultravioletystems are aluminum and ultravioletradiation protected PVC (polyvinyl chlorideadiation protected PVC (polyvinyl chlorideplastic). Centerlastic). Center-pivot and lateral systemsivot and lateral systemscommonly use galvanized steel as theommonly use galvanized steel as thepipeline material.ipeline material.


19/29

HYDRAULICSYDRAULICSPipelinesipelinesFor pipelines that are buried below theor pipelines that are buried below theground, the most common material inround, the most common material inagricultural applications is PVC and ingricultural applications is PVC and inlandscape and turf application it is eitherandscape and turf application it is eitherPVC or PE (polyethylene plastic). PE is alsoVC or PE (polyethylene plastic). PE is alsocommonly used for aboveommonly used for above-ground microround micro-irrigation systems.rrigation systems.

HYDRAULICSYDRAULICSPipelinesipelinesSizing mainlines is usually based on aizing mainlines is usually based on amaximum of 5 to 6 ft/sec average velocity.aximum of 5 to 6 ft/sec average velocity.The typical flow ranges for aluminum pipehe typical flow ranges for aluminum pipeand class 160 PVC pipe at various nominalnd class 160 PVC pipe at various nominalsizes and reasonable flow velocities areizes and reasonable flow velocities areshown below.hown below.

HYDRAULICSYDRAULICSPipeline flow rates. VELOCITY = 5 ft/secipeline flow rates. VELOCITY = 5 ft/secNominalominal Aluminumluminum Class 160 PVClass 160 PVCSizeize IDD Q IDD Qinn inn gpmpm inn gpmpm

1 1.4.4 244 1.754.754 3882 1.9.9 444 2.193.193 5994 3.9.9 18686 4.154.154 211116 5.9.9 42626 6.115.115 458588 7.9.9 76464 7.961.961 77676100 9.9.9 1199199 9.924.924 1205205122 11/91/9 1733733 11.7701.770 1695695


Table 8.2 Friction loss for IPS PV C pipe.Q( gal/min) 1-in 111/44-in 111/22-in 2-in 211/22-in 3 -in 311/22-in

- - - - - - - Fr iction head loss in ft/100 ft - - - - - - -246810

. 15. 541.152.98

.0 4.1 7.3 7.6 3.9 5

.02.09.19.32.49

.0 3.0 6.1 1.1 6

.0 1.0 2.0 4.0 6 .01.02 .011520253035404550

6.3210.7916.3022.86

2.033.465.227.329.7512.4615.5118.87

1.041.782.703.785.036.468.029.75

.3 5.6 0.9 11.271.702.182.713.30

.1 4.2 3.3 6.5 0.6 7

.8 61.071.30

.05.09.13.19.25

.32.40.49

.0 2.0 4.0 7.1 0.1 3

.1 7.2 1.2 5


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VA = Vacuum, Air Vent Valve

C = Check Valve or Backflow Preventer

G = Shutoff Valve

PR = Pressure Relief

D = Automatic Drain Valve

Lateral Designateral DesignThe irrigation planner and designer ishe irrigation planner and designer isinterested in two basic problems related tonterested in two basic problems related topipeline hydraulics. The first is concernedipeline hydraulics. The first is concernedwith the flow of water in pipes with multipleith the flow of water in pipes with multipleoutlets (sprinkler laterals or drip irrigationutlets (sprinkler laterals or drip irrigationlaterals) and flow of water in pipelinesaterals) and flow of water in pipelineswithout multiple outlets, such as main linesithout multiple outlets, such as main linesand subnd sub-mains.ains.

HYDRAULICSYDRAULICSComputing Friction Lossomputing Friction LossA pipeline with outlets has a lower friction losspipeline with outlets has a lower friction lossthan a conveyance pipe because the velocityhan a conveyance pipe because the velocitydecreases with distance along the pipe. Toecreases with distance along the pipe. Tocorrect for the effect of outlets, a multipleorrect for the effect of outlets, a multipleoutlet factor, F is used. The value of F is one,utlet factor, F is used. The value of F is one,for pipelines without outlets.or pipelines without outlets.

ess).dimensionl(exponentdiameterpipetheisandless),(dimensionexponent,velocitytheis

(L/T),velocityfluidmeantheis

(L),diameterpipeinternaltheis

(L),lengthpipetheis

chosen,formulalossfrictiontheand



:where

:followingtheasexpressedbecanpipesinlossfrictionthegeneral,In

nm

V

D

L

K

h

V

D

LKh

f

m

nf


21/292

m

nmf

m

m

n

m

nf

m

nf

Q

D

LkhThus

D

Q

D

LK

V

D

LKh

D

QV

A

QV

V

D

LKh

23

2

2

general,in

4

Thus,

4

orand

:madebecantionsimplificafollowingtheFurther,

Assume the sprinkler spacings (S) are all equalssume the sprinkler spacings (S) are all equaland that the total number of sprinklers is N, thend that the total number of sprinklers is N, thetotal flow into the lateral is Q and each sprinklerotal flow into the lateral is Q and each sprinklerflow (q) is equal to Q/N. Further, the sprinklerlow (q) is equal to Q/N. Further, the sprinklerlateral length (L) is given as SN. The head loss inateral length (L) is given as SN. The head loss insection one of the above figure is calculated as:ection one of the above figure is calculated as:

m

nmf

q

D

Skh

231

Likewise, the head loss in section two and theLikewise, the head loss in section two and the

next sections are calculated as:next sections are calculated as:

m

nmf

q

D

Skh

)2(232

m

nmf

q

D

Skh

)3(233

m

nmfiiq

DSkh )(23

The total head loss in the entire lateral in now theThe total head loss in the entire lateral in now the

sum of the head loss from each section of thesum of the head loss from each section of the

lateral, orlateral, or

N

i

m

nm

N

i

fiT

iq

D

Skhh

123

1

)(

NLS /

N

i

m

nm

N

i

m

nm

N

i

fiT

iqNL

D

kiq

D

NLkhh

12

3

123

1

)(/)(/


22/292

NQq /

N

i

m

m

m

nm

N

i

m

nmT

i

N

Q

N

L

D

kNiQNL

D

kh

12

3

12

3 )()/(/

N

i

m

m

m

nmTi

N

QL

D

kh

112

3 )(

NOW, finally recall that for the entire lateral, if itOW, finally recall that for the entire lateral, if itwere a mainline, the friction loss isere a mainline, the friction loss ism

nmf

Q

D

Lkh

23

1

1

11

112

3 )(1

)(

m

N

i

m

f

N

i

m

mf

N

i

m

m

m

nmTN

i

hiN

hiN

QL

D

kh

Factor F.*linemainawerelateraltheiflossHead

outlets.multipleforaccountFactor to*linemainawerelateraltheiflossHead

T

T

h

h

21

1

6

1

2

1

1

1Factor F

N

m

NmN

i

m

N

i

m

If the first sprinkler outlet is locatedf the first sprinkler outlet is located spacing from the inlet to the lateral, then thepacing from the inlet to the lateral, then thefactor F must be adjusted. These are givenactor F must be adjusted. These are givenin the attached tables.n the attached tables.


23/292

Computing Friction Lossomputing Friction LossFor lateral pipelines with constant spacedor lateral pipelines with constant spacedoutlets and nearly the same discharge perutlets and nearly the same discharge peroutlet, useutlet, use TABLE 3.ABLE 3. With centerith center-pivots, theivots, thesprinkler discharge increases with distanceprinkler discharge increases with distancefrom the pivot point. These factors are givenrom the pivot point. These factors are givenat the bottom.t the bottom.

Table 3 Multiple outlet factors for laterals with equallyspread outlets of the same discharge. For centerpivots, see footnote**.No. ofoutlets F No. ofout lets F123456789101112131415

1. 00.6340.5280.4800.4510.4330.4190.4100.4020.3960.3920.3880.3840.3810.379

16171819202224262830354050100More than100

0.3770.3760.3730.3720.3700.3680.3660.3640.3630.3620.3590.3570.3550.3500.345**F = 0.54 for center pivots without end g uns.F = 0.56 for center pivots with end guns.

0.300.350.400.450.500.550.600.65

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5Number of S prinklers on the Lateral

MultpleOutetFactor(F) Lateral Designateral DesignThe sizing of sprinkler laterals is a fundamentalhe sizing of sprinkler laterals is a fundamentalconsideration for sprinkler systems. Theonsideration for sprinkler systems. Thelateral must be large enough to carry theateral must be large enough to carry theneeded flow rate so that the pressure losseeded flow rate so that the pressure lossalong the lateral is not excessive.long the lateral is not excessive.

A standard has been established by thestandard has been established by theAmerican Society of Agricultural Engineers formerican Society of Agricultural Engineers formaximum variations of discharge along aaximum variations of discharge along asprinkler lateral.prinkler lateral.


24/292

Lateral Designateral DesignTo achieve an acceptable uniformity theo achieve an acceptable uniformity thestandard requires that the discharge variationtandard requires that the discharge variationfrom the sprinkler with the largest flow to therom the sprinkler with the largest flow to thesprinkler with the smallest flow not exceed 10%prinkler with the smallest flow not exceed 10%of the average discharge.f the average discharge.Since the discharge from a nozzle is related toince the discharge from a nozzle is related tothe square root of the pressure, the 10%he square root of the pressure, the 10%discharge variation is equivalent to a maximumischarge variation is equivalent to a maximumpermissible pressure variation of 20%.ermissible pressure variation of 20%.

Lateral Designateral DesignThe variation of pressure along a lateral can behe variation of pressure along a lateral can bedue to elevation changes along the lateral andue to elevation changes along the lateral andfriction loss in the lateral and fittings. Theriction loss in the lateral and fittings. Thepressure distribution along a lateral placed onressure distribution along a lateral placed onlevel ground is illustrated in Figureevel ground is illustrated in Figure (NEXT).NEXT).The pressure at the inlet of the lateral ishe pressure at the inlet of the lateral isdetermined by the pressure available from theetermined by the pressure available from themainline. The pressure loss in the first severalainline. The pressure loss in the first severaljoints of the lateral is nearly the same as for aoints of the lateral is nearly the same as for amainline of the same diameter and pipeainline of the same diameter and pipematerial.aterial.

Lateral Designateral DesignHowever, as water is discharged from theowever, as water is discharged from thesprinklers on the lateral the flow rateprinklers on the lateral the flow ratedecreases with distance along the lateral.ecreases with distance along the lateral.Ultimately, the only flow in the last joint of theltimately, the only flow in the last joint of thelateral is that discharged from the last sprinklerateral is that discharged from the last sprinkleron the lateral.n the lateral.Of course there is very little loss in the lateralf course there is very little loss in the lateralfor such a small flow. The diagram in Figureor such a small flow. The diagram in Figure(NEXT)NEXT) shows that the friction loss for a lateralhows that the friction loss for a lateralis about 35% of the loss encountered in as about 35% of the loss encountered in amainline pipe of the same diameter when flowainline pipe of the same diameter when flowrate into the mainline and lateral are the same.ate into the mainline and lateral are the same.


25/292

Lateral Designateral DesignThe average pressure along the lateral onhe average pressure along the lateral onlevel ground occurs at a location about 1/4 toevel ground occurs at a location about 1/4 to1/3 of the way from the inlet of the lateral./3 of the way from the inlet of the lateral.Obviously since pressure varies along thebviously since pressure varies along thelateral the discharge also varies.ateral the discharge also varies.Sprinkler systems are usually designed toprinkler systems are usually designed toselect the nozzle size for the average pressureelect the nozzle size for the average pressurealong the lateral. Then the pressure at eachlong the lateral. Then the pressure at eachend of the lateral is computed.nd of the lateral is computed.

Lateral Designateral DesignThe diagram in the pressure loss Figurehe diagram in the pressure loss Figureshows that the average pressure is closer tohows that the average pressure is closer tothe pressure at the distal end of the lateralhe pressure at the distal end of the lateralthan to the pressure at the inlet of the lateral.han to the pressure at the inlet of the lateral.For practical purposes the pressure at eachor practical purposes the pressure at eachend of a lateral on level ground can bend of a lateral on level ground can becomputed by:omputed by:

Pi = PPa + Pl Equation 5quation 5

Pd = PPa Pl Equation 6quation 6


26/292

Lateral Designateral DesignPi = PPa + Pl Equation 5quation 5Pd = PPa Pl

where:here: Pi = pressure at the inlet intopressure at the inlet intothe lateral (psi),he lateral (psi),Pa = average pressure along theaverage pressure along thelateralateral (psi),psi),Pd = pressure at the distal end of thepressure at the distal end of thelateral (psi), andateral (psi), andPl = pressure loss along the lateralpressure loss along the lateral(psi).psi).

Lateral Designateral DesignFrom a practical perspective, the maximumrom a practical perspective, the maximumacceptable pressure loss along a lateralcceptable pressure loss along a lateralplaced on level ground equals 23.4% of thelaced on level ground equals 23.4% of theaverage, or design, pressure of the lateral. Inverage, or design, pressure of the lateral. Inother words,ther words,

Maximum Paximum Pl < 0.234 P0.234 Pa Equation 6quation 6

Lateral Designateral DesignWhen a lateral runs up or down hill, the changehen a lateral runs up or down hill, the changein elevation causes changes in pressure. Ann elevation causes changes in pressure. Anelevation change of 10 feet is equal to alevation change of 10 feet is equal to apressure change of 4.3 psi.ressure change of 4.3 psi.Thus, when laterals run downhill there is lesshus, when laterals run downhill there is lesspressure variation from the inlet to the distal endressure variation from the inlet to the distal endthan for laterals on level ground because thehan for laterals on level ground because theslope provides some pressure increase. Whenlope provides some pressure increase. Whenlaterals run uphill the pressure in the lateralaterals run uphill the pressure in the lateraldrops because of friction and because of therops because of friction and because of thechange in elevation.hange in elevation.

Lateral Design (EQUATION 7)ateral Design (EQUATION 7)

P P PE E

i a l

i d

3

4

1

2 2 31.

P P PE E

d a l

i d

1

4

1

2 2 31.

where: Ei = the elevation of the inlet to the lateral (ft) and

Ed = the elevation of the distal end of the lateral (ft).


27/292

Example 4xample 4Giveniven: A sprinkler lateral was designed forsprinkler lateral was designed foran average pressure of 50 psi and sprinklern average pressure of 50 psi and sprinklerheads with one 5/32 inch nozzle in eacheads with one 5/32 inch nozzle in eachsprinkler head.prinkler head.The sprinkler lateral is made of 4 inch diameterhe sprinkler lateral is made of 4 inch diameteraluminum pipe with joints 30 feet long. There isluminum pipe with joints 30 feet long. There isone sprinkler outlet at the end of each joint ofne sprinkler outlet at the end of each joint ofpipe. The lateral is 1,320 feet long.ipe. The lateral is 1,320 feet long.

Lateral Designateral DesignExample 4xample 4Findind: a) The pressure at the inlet and) The pressure at the inlet anddistal ends of the lateral if the lateral is on levelistal ends of the lateral if the lateral is on levelground. b) The pressure at each end of theround. b) The pressure at each end of thelateral if the lateral runs down a uniform 2%ateral if the lateral runs down a uniform 2%grade. c) The pressure at each end of therade. c) The pressure at each end of thelateral if the lateral runs up a uniform 2% grade.ateral if the lateral runs up a uniform 2% grade.Which of these systems meet the ASAE criteriahich of these systems meet the ASAE criteriafor pressure variation in lateralsor pressure variation in laterals

Example 4xample 4Solutionolution: There are 44 sprinklers on the lateralhere are 44 sprinklers on the lateral(i.e., 1,320 feet with 30 feet between sprinklers).i.e., 1,320 feet with 30 feet between sprinklers).With 5/32 inch nozzles, the average flow is 5ith 5/32 inch nozzles, the average flow is 5gpm per sprinkler and the total flow for thepm per sprinkler and the total flow for thelateral is 220 gpm (5 x 44 sprinklers).ateral is 220 gpm (5 x 44 sprinklers).Aluminum pipe with couplers has a C value ofluminum pipe with couplers has a C value of120 in the Hazen20 in the Hazen-Williams equation so theilliams equation so thefriction loss for a mainline with a flow rate of 220riction loss for a mainline with a flow rate of 220gpm through a 4 inch aluminum pipe is given by:pm through a 4 inch aluminum pipe is given by:

Example 4xample 4Pm = 4.56 [Q/C]4.56 [Q/C] 1.852.852 [1/D1/D 4.866.866] Equation 8bPm = 4.56 [220/120]4.56 [220/120] 1.852.852 [1/4.01/4.0 4.866.866] = 21.5= 21.5psisiwhere Phere Pm = the pressure loss in a mainline ofthe pressure loss in a mainline ofconstant diameter and flow.onstant diameter and flow.


28/292

Lateral Designateral DesignExample 4xample 4The multiple outlet friction factor (F) for ahe multiple outlet friction factor (F) for alateral with 44 sprinklers is about 0.36 so theateral with 44 sprinklers is about 0.36 so thefriction loss for the lateral is:riction loss for the lateral is:

Pl = F PF Pm = 0.36 x 21.5 psi = 7.7 psi.0.36 x 21.5 psi = 7.7 psi.

Example 4xample 4The pressure at the inlet to the lateral for levelhe pressure at the inlet to the lateral for levelground is:round is:

Pi = PPa + 3/4 P3/4 Pl = 50 + 0.75 x 7.7 = 56 psi.50 + 0.75 x 7.7 = 56 psi.The pressure at the distal end of the lateral forhe pressure at the distal end of the lateral forlevel ground is:evel ground is:

Pd = PPa - 1/4 P/4 Pl = 5050 - 0.25 x 7.7 = 48 psi..25 x 7.7 = 48 psi.

Example 4xample 4The pressure variation along the lateral ishe pressure variation along the lateral is7.7 psi compared to the average pressure of.7 psi compared to the average pressure of50 psi. The variation is 15.4% of the average0 psi. The variation is 15.4% of the averagepressure and is less than the maximumressure and is less than the maximumpermissible pressure variation so the lateralermissible pressure variation so the lateralmeets the ASAE standard.eets the ASAE standard.

Example 4xample 4When the lateral runs down a 2% grade, thehen the lateral runs down a 2% grade, theelevation change along the lateral is:levation change along the lateral is:Ei - Ed = 0.02 x 1320 ft = 26.4 ft. So the inlet is0.02 x 1320 ft = 26.4 ft. So the inlet isabout 26 feet above the distal end.bout 26 feet above the distal end.


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Example 4xample 4The pressures at the inlet and distal ends arehe pressures at the inlet and distal ends arethen:hen:Pi = PPa + 3/4 P3/4 Pl - 0.5 (.5 (Ei - Ed)/2.31P/2.31Pi (Equation 7)Equation 7)= 50 + 0.75 X 7.750 + 0.75 X 7.7 - 0.5 x 26.4/2.31 = 50.1 psi.5 x 26.4/2.31 = 50.1 psiPd = PPa - 1/4 P/4 Pl + 0.5 (0.5 (Ei - Ed)/2.31 (Equation 7)/2.31 (Equation 7)= 5050 - 0.25 X 7.7 + 0.5 X 26.4/2.31 = 53.8 psi.25 X 7.7 + 0.5 X 26.4/2.31 = 53.8 psi

Here the pressure variation is only 3.7 psi,ere the pressure variation is only 3.7 psi,well within the allowable variation. Note thatell within the allowable variation. Note thatthe highest pressure occurs at the distal endhe highest pressure occurs at the distal endof the lateral for this case.f the lateral for this case.When the lateral runs uphill the elevation ofhen the lateral runs uphill the elevation ofthe inlet is now below the distal end so thehe inlet is now below the distal end so thevalue of (alue of (Ei - Ed) == -26.4 feet. Using this value6.4 feet. Using this valueand the method in Part B the pressures at thend the method in Part B the pressures at theends of the lateral are:nds of the lateral are:

Example 11.4xample 11.4Pi = 61.5 psi and P61.5 psi and Pd = 42.4 psi.42.4 psi.

Now the pressure variation is about 19 psi orow the pressure variation is about 19 psi or38% of the average pressure which is8% of the average pressure which isunacceptable according to the standard.nacceptable according to the standard.

Hydraulics Lecture Material

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