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CTC 261CTC 261

►Energy EquationEnergy Equation

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ReviewReview

►Bernoulli’s EquationBernoulli’s Equation Kinetic Energy-velocity headKinetic Energy-velocity head Pressure energy-pressure headPressure energy-pressure head Potential EnergyPotential Energy

►EGL/HGL graphsEGL/HGL graphs Energy grade lineEnergy grade line Hydraulic grade lineHydraulic grade line

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ObjectivesObjectives

►Know how to apply the energy Know how to apply the energy equation equation

►Know how to incorporate head Know how to incorporate head (friction) losses into EGL/HGL graphs(friction) losses into EGL/HGL graphs

►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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Energy EquationEnergy Equation

► Incorporates energy supplied by a Incorporates energy supplied by a pump, energy lost to a turbine, and pump, energy lost to a turbine, and energy lost due to friction energy lost due to friction and other and other head losses (bends, valves, head losses (bends, valves, contractions, entrances, exits, etc)contractions, entrances, exits, etc)

Pumps, turbines, friction lossPumps, turbines, friction loss

►Pump adds energy Pump adds energy ►Turbine takes energy out of the Turbine takes energy out of the

systemsystem►Friction loss-loss out of the system as Friction loss-loss out of the system as

heatheat

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Energy Equation

PE+Pressure+KE+Pump Energy=

PE+Pressure+KE+Turbine Losses+Head Losses

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Energy/Work/PowerEnergy/Work/Power

►Work = force*distance (in same Work = force*distance (in same direction)direction)

►Power = work/timePower = work/time►Power=pressure head*specific Power=pressure head*specific

weight*Qweight*Q►Watt=Joule/second=1 N-m/secWatt=Joule/second=1 N-m/sec►1 HP=550 ft-lb/sec1 HP=550 ft-lb/sec►1 HP=746 Watts1 HP=746 Watts

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Hints for drawing EGL/HGL Hints for drawing EGL/HGL graphsgraphs

► EGL=HGL+Velocity HeadEGL=HGL+Velocity Head► Friction in pipe: EGL/HGL lines slope downwards in Friction in pipe: EGL/HGL lines slope downwards in

direction of flowdirection of flow► A pump supplies energy; abrupt rise in EGL/HGLA pump supplies energy; abrupt rise in EGL/HGL► A turbine decreases energy; abrupt drop in A turbine decreases energy; abrupt drop in

EGL/HGLEGL/HGL► When pressure=0, the HGL=EGL=water surface When pressure=0, the HGL=EGL=water surface

elevationelevation► Steady, uniform flow: EGL/HGL are parallel to each Steady, uniform flow: EGL/HGL are parallel to each

otherother► Velocity changes when the pipe dia. ChangesVelocity changes when the pipe dia. Changes► If HGL<pipe elev., then pressure head is negative If HGL<pipe elev., then pressure head is negative

(vacuum-cavitation)(vacuum-cavitation)

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Transition ExampleTransition Example

►On boardOn board

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Reservoir ExampleReservoir Example

►On boardOn board

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Pumped StoragePumped Storage

► Energy use is not steadyEnergy use is not steady► Coal/gas/nuclear plants operate best at a Coal/gas/nuclear plants operate best at a

steady ratesteady rate►Hydropower can be turned on/off more Hydropower can be turned on/off more

easily, and can accommodate peakseasily, and can accommodate peaks► Pumping water to an upper reservoir at Pumping water to an upper reservoir at

night when there is excess energy available night when there is excess energy available “stores” that water for hydropower “stores” that water for hydropower production during peak periodsproduction during peak periods

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Head (Friction) LossesHead (Friction) Losses

►Flow through pipeFlow through pipe►Other head lossesOther head 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 determined by Moody’s diagram (handout)(handout)

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 correct (guess f, solve for v, check for correct f)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 of Find Head Loss Per Length of PipePipe

►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=12.2 per km of (head loss=12.2 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 The head loss per km of 20-cm asphalted cast-iron pipe is 12.2 m. asphalted cast-iron pipe is 12.2 m. What is Q?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, exitsInlets, outlets, fittings, entrances, exits

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

Not covered in your book. Will cover in Not covered in your book. Will cover in CTC 450CTC 450

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Next classNext class

►Orifices, Weirs and Sluice GatesOrifices, Weirs and Sluice Gates