INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

October 17, 2017

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.


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 $$ h=\frac{x^2}{2gA^2}$$ $$=\frac{70^2}{2\times 980\times(0.25)^2}$$ $$=40cm$$

One comment on “Maximum Height of Water in A Tank With A Hole”

  1. Um could you explain why the height is Maximum when the volume flow rates become equal. If the speed of outflow is lesser then wouldn't the height increase more?

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.