B2.1.1 Fundamentals of Hydro power The energy equation: Implications: Flow in pipes: Friction: Moody diagram

B2.1.1 Fundamentals of Hydro power The energy equation: Implications: Flow in pipes: Friction: Equations

Blasius equationFor hydraulically smooth pipe (Re 4,000 100,000)

Swamee-Jain equation10-6 < k/D < 0.01 (5,000 3x108)

B2.1.1 Fundamentals of Hydro power The energy equation: Implications: Flow in pipes: Friction: Nomogram

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B2.2.2 Hydropower system design Penstocks: Multiple penstocks

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B2.2.2 Hydropower system design Penstocks: Losses in bends

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B2.2.2 Hydropower system design Penstocks: Losses in bendsFor 45 use K x 0.75For 2 use K x 0.5rD

r/D

Kb10.620.530.440.3

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B2.2.2 Hydropower system design Penstocks: Other LossesContractions

Valves

D1/d2Kc1.50.2520.352.50.4050.50

TypeKvSpherical0Gate0.1Butterfly0.3

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B2.2.2 Hydropower system design Penstocks: Energy lines

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B2.2.2 Hydropower system design Penstocks: Anatomy of a penstock

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B2.2.2 Hydropower system design Penstocks: Slide blocks

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Fe = Force due to extensionCe = Coefficient of extensionDT= Change in temperatureE = Youngs modulusD = Penstock diametert = Wall thicknessB2.2.2 Hydropower system design Penstocks: Thermal expansionFeFe

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B2.2.2 Hydropower system design Penstocks: Expansion joints

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B2.2.2 Hydropower system design Penstocks: Forces on bendsHydrostaticVelocityFr= fluid densityg = gravityh= total headA = penstock areaQ = dischargev = velocity

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B2.2.2 Hydropower system design Penstocks: Bends

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B2.2.2 Hydropower system design Penstocks: Forces on bends: Thrust blocks

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B2.2.2 Hydropower system design Penstocks: Anatomy of a penstock

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B2.2.2 Hydropower system design Penstocks: Water hammer

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Tc=critical time (s)L=pipe length (m)Cp=speed of sound in the pipeCw = speed of sound in water (1420m s-1)G = bulk density of water (2GPa)E=Youngs modulusD=diameter of the pipe (m)t =wall thickness (m)Dh=additional pressure due to water hammer (m of water)g= gravityDv=Change in flow velocity (m s-1)B2.2.3 Hydropower system design Penstocks: Water hammer

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B2.2.2 Hydropower system design Penstocks: Water hammer: Dealing with it

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B2.2.2 Hydropower system design Penstocks: Water hammer: Dealing with it: Surge tanks

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B2.2.2 Hydropower system design Penstocks: Getting it wrong

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B2.2.3 Hydropower system design Draft tubes Parallel sidedTaperedAllows turbine to be set above water level but uses vacuum pressure on underside to increase effective headRecovers part of the velocity head by diffusion action Limited by the vapour pressure of water

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B2.2.3 Hydropower system design Draft tubes: Exercise Using Bernoulli's equation and mass continuity, show how a tapered turbine regains velocity head and converts it to pressure reduction at the turbinep2 v2p1 v1

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B2.2.3 Hydropower system design Draft tubes: configurations

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B2.2.3 Hydropower system design Draft tubes

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B2.2.3 Hydropower system design Draft tubes

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