Answer to Question #196508 in Physics for Aprile Anne Lupac

Question

Water in an enclosed tank is subjected to a gauge pressure of 2x10^4 Pa, applied by a compressed air introduced into the top of the tank. There is a small hole (diameter = 4 cm) in the side of the tank 5 m below the level of the water. Calculate the discharge rate.

Answer 1

According to the Bernoulli equation

$(p_A+p_M)+\rho gh\approx p_A+\rho v^2/2 \to$

$p_M+\rho gh\approx \rho v^2/2 \to v=\sqrt{2(p_M+\rho gh)/\rho}=$

$=\sqrt{2\cdot(20000+1000\cdot9.8\cdot5)/1000}=11.75\ (m/s)$ . Answer