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Fluid Mechanics

Water Hammer in Pipes

The velocity ...

Question

The velocity of pressure wave in water of infinite extent is 1414 m/s. The velocity of propagation of water hammer pressure in a pipe carrying water and having diameter = 40 cm, pipe thickness = 4 mm, with E (Modulus of elasticity) of the pipe material $= 2.1 \times 10^{11} P a$ , and K (Bulk modulus of water) $= 2.1 \times 10^{9} P a,$ is

1410 m/s

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2000 m/s

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1000 m/s

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700 m/s

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Solution

The correct option is C 1000 m/s
$K = 2.1 \times 10^{9} P a; E = 2.1 \times 10^{11} P a$

$ρ = 1000 k g / m^{3}, D = 400 m m$

Velocity propagation of water hammer pressure

$= \sqrt{\frac{K / ρ}{1 + \frac{K D}{E t}}} = \sqrt{\frac{2.1 \times \frac{10^{9}}{1000}}{1 + 1}} = 1024.7 m / s$

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The correct option is C 1000 m/sK=2.1×109 Pa; E=2.1×1011 Pa ρ=1000 kg/m3, D=400mm Velocity propagation of water hammer pressure =  ⎷K/ρ1+KDEt=  ⎷2.1×10910001+1=1024.7 m/s

The correct option is C 1000 m/s
$K = 2.1 \times 10^{9} P a; E = 2.1 \times 10^{11} P a$

$ρ = 1000 k g / m^{3}, D = 400 m m$

Velocity propagation of water hammer pressure

$= \sqrt{\frac{K / ρ}{1 + \frac{K D}{E t}}} = \sqrt{\frac{2.1 \times \frac{10^{9}}{1000}}{1 + 1}} = 1024.7 m / s$