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Motion In Fluid. Help Me Solve This Question?
Water in an enclosed tank is subjected to gauge pressure of 2.0x10^4 Pa, applied by compressed air introduced into the top of the tank. There is a small hole in the side of the tank 5.0m below the level of the water. What is the SPEED with which water escapes from this hole?
1 Answer
- ?Lv 71 decade agoFavorite Answer
Bernouilli's equation says that
p + 1/2 rho v^2 + rho g h = constant along a streamline.
At the top
p = 2.0 x 10^4 Pa + p0 (p0 atmospheric pressure)
v = 0 (approximately if the hole is small relative to the diameter of the tank)
h = 5.0 m
At the bottom:
p = p0
v (to be calculated)
h = 0
p0 + 1/2 rho v^2 + 0 = 2.0 x 10^4 Pa + p0 + 0 + rho g 5.0 m
So
1/2 * 10^3 kg/m^3 * v^2 = 2.0 10^4 N/m^2 + 10^3 kg/m^3 * 9.81 m/s^2 * 5.0 m
v^2 = 138.1 m^2/s^2
v = 11.8 m/s