Maximum Height of Water in A Tank With A Hole

Let's discuss a problem based on the maximum height of water in a tank with a hole. Try the problem yourself first and then read the solution.

The Problem: Maximum Height of Water

A large tank is filled with water of (70 cm^3/s). A hole of cross-section (0.25cm^2) is punched at the bottom of the tank. Find the maximum height to which the tank can be filled.

Solution:

For the water level to remain stationary volume efflux= rate of filling = (x)
The velocity $$ v=\sqrt{2gh}$$ where (g) is the acceleration due to gravity.
Hence,$$ vA=\sqrt{2gh}A$$ $$ =x$$ $$=70cm^3//s$$
The maximum height $$ h=\frac{x^2}{2gA^2}$$ $$=\frac{70^2}{2\times 980\times(0.25)^2}$$ $$=40cm$$