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A 600-mm-diameter pipe, 720 m long carries water at the rate of 2.5 m/s. Use Ewater= 2.2 × 109Pa and pw= 1000 kg/m3.

A. What is the water hammer pressure due to instantaneous close of the gate near theexit?
B. How long will it takefor the pressure wave to travel round trip of the pipe?
C. What is the water hammer pressure if the valve is closed in 1.2 seconds?

1 Answer

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Final answer:

A. The water hammer pressure due to instantaneous close of the gate near the exit is -3,700,000 Pa. B. The pressure wave will take 2.432 seconds to travel round trip of the pipe. C. The water hammer pressure with a 1.2-second valve closure is -2.083 Pa.

Step-by-step explanation:

A. Water Hammer Pressure:

To calculate the water hammer pressure, we can use the formula:

Water hammer pressure = -ρ * v * c

where:

  • ρ is the density of water
  • v is the velocity of water
  • c is the speed of sound in water

Given that ρ = 1000 kg/m3, v = 2.5 m/s, and c = 1480 m/s, we can substitute these values into the formula and calculate the water hammer pressure:

Water hammer pressure = -1000 * 2.5 * 1480 = -3,700,000 Pa

Since the water hammer pressure is negative, it indicates compression of the water.

B. Travel Time of Pressure Wave:

The time it takes for the pressure wave to travel round trip of the pipe can be calculated using the formula:

Travel time = 2 * L / c

where:

  • L is the length of the pipe
  • c is the speed of sound in water

Given that L = 720 m and c = 1480 m/s, we can substitute these values into the formula and calculate the travel time:

Travel time = 2 * 720 / 1480 = 2.432 seconds

C. Water Hammer Pressure with a 1.2-second Valve Closure:

The water hammer pressure with a 1.2-second valve closure can be calculated using the formula:

Water hammer pressure = -ρ * v * t / L

where:

  • ρ is the density of water
  • v is the initial velocity of water
  • t is the closure time of the valve
  • L is the length of the pipe

Given that ρ = 1000 kg/m3, v = 2.5 m/s, t = 1.2 seconds, and L = 720 m, we can substitute these values into the formula and calculate the water hammer pressure:

Water hammer pressure = -1000 * 2.5 * 1.2 / 720 = -2.083 Pa

Since the water hammer pressure is negative, it indicates compression of the water.

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