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.