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Water Hammer Unsteady flow Rapid change of discharge Chapter 11

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Water Hammer Example penstock 6 km long Elevation =1670 m D= 1m 3 m Elevation =1000 m ?

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Penstock anchmain3.html

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Incompressible Assumption Steel Penstock diameter = 1m 6000 m V =3.7 m/s valve 4 Tension Surge Pressure Static pressure line Hydraulic gradient

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Momentum Equation Mass of liquid in pipeline= Momentum of liquid = δh = 565 m

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pressure Valve Pressure Valve ( R e = 3.7×1/8×10 -7 = 4.63×10 6, k/D = 0.03/1000 = 3×10 -5 Moody diagram f =.011) valve: Pressure head Valve = = 624 m pressure = 9810×624 N/m 2 = 6.12 MPa Water Hammer =?

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Free Body Diagram tension 6.12 MPa 3.06 MN Water Hammer Thickness= 3.06MN/118MPa =0.026 m

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Surge Tank (Fig /museum/hsdam3.jpg

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Surge Tank

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Transients caused by pumps Read Fig

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Control Dievices Roberson Surge tanks (Fig ) Air Chambers Valves Flywheels

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Compressible Assumption cVoPρVoPρ 0 P+δP ρ+δρ Fluid Mechanics K (Bulk 30 o C K= 2.23×10 9 N/m 3

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Frame of Reference c P+δP ρ+δρ V o -c P ρ wave c Conservation of mometum

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Wave speed c Rigid pipe Conservation of mass ( Continuity Equation density ) ρ = 30 o C = 995 Kg/m 3 c = 1497 m/s say 1500 m/s

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Elastic Pipe c E = Bulk Modulus of Elasticity of Pipe = 207 GPa

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Exercise A steel pipe line 1000 mm diameter conveys 2 cumecs (m 3 /s) under a head of 430 m. What must be the thickness of the walls if the pipe is to withstand the pressure rise caused by sudden closure of a valve? Determine also the rise in pressure. The safe stress for the steel is 100 MPa, E = 207 GPa, K= 2.15 GPa.

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Oscillating Pressure Fig 11-6 Roberson T< L/c V=0

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At T= L/c T= L/c

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T<2 L/c

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T =2L/C T=2 L/c = Static Head V

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T= 3 L/c V=0 static head

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T= 4 L/c oscillating cycle

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Fig Roberson Time H Static Line 4 L/c Fig Roberson = Gradual Valve Closure

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