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CTC 450 ReviewCTC 450 Review

Energy Equation Energy Equation Pressure headPressure head Velocity headVelocity head Potential energyPotential energy Pumps, turbinesPumps, turbines Head losses due to frictionHead losses due to friction

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ObjectivesObjectives

Know how to calculate friction loss Know how to calculate friction loss using the Darcy-Weisbach equationusing the Darcy-Weisbach equation

Know how to calculate other head Know how to calculate other head losses losses

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Studies have found that Studies have found that resistance to flow in a pipe isresistance to flow in a pipe is

Independent of pressureIndependent of pressure Linearly proportional to pipe lengthLinearly proportional to pipe length Inversely proportional to some power of the Inversely proportional to some power of the

pipe’s diameterpipe’s diameter Proportional to some power of the mean Proportional to some power of the mean

velocityvelocity If turbulent flow, related to pipe roughnessIf turbulent flow, related to pipe roughness If laminar flow, related to the Reynold’s If laminar flow, related to the Reynold’s

numbernumber

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Head Loss EquationsHead Loss Equations Darcy-WeisbachDarcy-Weisbach

Theoretically basedTheoretically based Hazen WilliamsHazen Williams

Frequently used-pressure pipe systemsFrequently used-pressure pipe systems Experimentally basedExperimentally based

Chezy’s (Kutter’s) EquationChezy’s (Kutter’s) Equation Frequently used-sanitary sewer designFrequently used-sanitary sewer design

Manning’s EquationManning’s Equation

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Darcy-WeisbachDarcy-Weisbach

hhff=f*(L/D)*(V=f*(L/D)*(V22/2g)/2g)

Where:Where:

f is friction factor (dimensionless) and f is friction factor (dimensionless) and determined by Moody’s diagram (PDF determined by Moody’s diagram (PDF available on Angel)available on Angel)

L/D is pipe length divided by pipe diameterL/D is pipe length divided by pipe diameter

V is velocityV is velocity

g is gravitational constantg is gravitational constant

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For Class Use Only: Origin Not Verified!!!

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For Class Use Only: Origin Not Verified!!!

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Problem TypesProblem Types

Determine friction lossDetermine friction loss Determine flowDetermine flow Determine pipe sizeDetermine pipe size

Some problems require iteration Some problems require iteration (guess f, solve for v, check for (guess f, solve for v, check for correct f)correct f)

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Example Problems Example Problems

PDF’s are available on Angel:PDF’s are available on Angel:

Determine head loss given Q Determine head loss given Q (ex 10.4)(ex 10.4)

Find Q given head loss Find Q given head loss (ex 10.5)(ex 10.5)

Find Q (iteration required) Find Q (iteration required) (ex 10.6)(ex 10.6)

Find Head Loss Per Length Find Head Loss Per Length of Pipeof Pipe

Water at a temperature of 20-deg C Water at a temperature of 20-deg C flows at a rate of 0.05 cms in a 20-cm flows at a rate of 0.05 cms in a 20-cm diameter asphalted cast-iron pipe. diameter asphalted cast-iron pipe. What is the head loss per km of pipe?What is the head loss per km of pipe? Calculate Velocity Calculate Velocity (1.59 m/sec)(1.59 m/sec)

Compute Reynolds’ # and ks/D Compute Reynolds’ # and ks/D (3.2E5; 6E-4)(3.2E5; 6E-4)

Find f using the Moody’s diagram Find f using the Moody’s diagram (.019)(.019)

Use Darcy-Weisbach Use Darcy-Weisbach (head loss=12.2m per km of (head loss=12.2m per km of pipe)pipe)

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For Class Use Only: Origin Not Verified!!!

Find Q given Head LossFind Q given Head Loss

The head loss per km of 20-cm asphalted The head loss per km of 20-cm asphalted cast-iron pipe is 12.2 m. What is Q?cast-iron pipe is 12.2 m. What is Q? Can’t compute Reynold’s # so calculate Can’t compute Reynold’s # so calculate

Re*fRe*f1/2 1/2 (4.4E4)(4.4E4)

Compute ks/D Compute ks/D (6E-4)(6E-4)

Find f using the Moody’s diagram Find f using the Moody’s diagram (.019)(.019)

Use Darcy-Weisbach & solve for V Use Darcy-Weisbach & solve for V (v=1.59 (v=1.59 m/sec)m/sec)

Solve Q=V*A (Q=.05 cms)Solve Q=V*A (Q=.05 cms)

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For Class Use Only: Origin Not Verified!!!

Find Q: Iteration RequiredFind Q: Iteration Required

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Similar to another problem we did previously; however, in this case we are accounting for friction in the outlet pipe

IterationIteration Compute ks/D Compute ks/D (9.2E-5)(9.2E-5)

Apply Energy Equation to get the Apply Energy Equation to get the Relationship between velocity and fRelationship between velocity and f

Iterate (guess f, calculate Re and find f on Iterate (guess f, calculate Re and find f on Moody’s diagram. Stop if solution matches Moody’s diagram. Stop if solution matches assumption. If not, assume your new f and assumption. If not, assume your new f and repeat steps). repeat steps).

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IterateIterate

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Other head lossesOther head losses

Inlets, outlets, fittings, entrances, Inlets, outlets, fittings, entrances, exitsexits

General equation is hGeneral equation is hLL=kV=kV22/2g /2g

where k is a fitting loss coefficient (see where k is a fitting loss coefficient (see Table 4-1, page 76 of your book)Table 4-1, page 76 of your book)

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Head Loss of Abrupt Head Loss of Abrupt ExpansionExpansion

(v(v11-v-v22))22 / 2g / 2g

Not vNot v1122-v-v22

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If vIf v22 =0 =0 (pipe entrance into tank or reservoir) (pipe entrance into tank or reservoir)

then the fitting loss coefficient is 1then the fitting loss coefficient is 1

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Hazen-WilliamsHazen-Williams

Q=0.283CDQ=0.283CD2.632.63SS0.540.54

Q is discharge in gpmQ is discharge in gpm C is coefficient, see Table 4-2 ,page C is coefficient, see Table 4-2 ,page

7676 D is pipe diameter in inchesD is pipe diameter in inches S is hydraulic gradientS is hydraulic gradient

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Manning’s Equation-EnglishManning’s Equation-English

Q=AV=(1.486/n)(A)(RQ=AV=(1.486/n)(A)(Rhh))2/32/3SS1/21/2

Where:Where:

Q=flow rate (cfs)Q=flow rate (cfs)

A=wetted cross-sectional area (ftA=wetted cross-sectional area (ft22))

RRhh=Hydraulic Radius=A/WP (ft)=Hydraulic Radius=A/WP (ft)

WP=Wetter Perimeter (ft)WP=Wetter Perimeter (ft)

S=slope (ft/ft)S=slope (ft/ft)

n=friction coefficient (dimensionless)n=friction coefficient (dimensionless)

Manning’sManning’s

How would you estimate friction How would you estimate friction loss?loss?

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Hardy-Cross method for determining Hardy-Cross method for determining flow in pipe networksflow in pipe networks