Water steadily enters a tank of diameter D T at a flow rate Q. A small hole
Question:
Water steadily enters a tank of diameter D T at a flow rate Q. A small hole in the bottom of the tank (with diameter D 0 ) allows water to escape. We will show in class that the water velocity through the hole is given by?2gH , where H is the depth of water in the tank.
(a) If the tank is initially empty, derive an expression for the maximum height (H max ) that the water will reach in the tank. Check your answer using your intuition: is H max proportional to, inversely proportional to, or independent of D T , D 0 and Q? Does this make sense?
(b) Once this maximum height is reached, the flow coming into the tank (i.e. Q) is turned off. If the hole diameter is one-fifth of the tank diameter, and the maximum height is 50 cm, how quickly will the water surface fall as soon as the incoming flow is turned off?
Fundamentals of Thermal-Fluid Sciences
ISBN: 978-0078027680
5th edition
Authors: Yunus A. Cengel, Robert H. Turner, John M. Cimbala