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October 23, 2017

Velocity of Efflux at The Bottom of A Tank

Let's discuss a problem based on the velocity of efflux at the bottom of a tank. Try the problem yourself and read the solution here.

The Problem:

A large tank is filled with water. The total pressure at the bottom is (3.0atm). If a small hole is punched at the bottom, what is the velocity of efflux?

Solution:

A large tank is filled with water. The total pressure at the bottom is (3.0atm). A small hole is punched at the bottom.
Pressure at the bottom due to water coloumn $$ (3-1)atm$$ $$=2atm$$ $$ =2\times 10^5 Pa$$

The equation for pressure is $$ P=h\rho g$$
Hence, $$ h=\frac{P}{\rho g}$$ $$=\frac{2\times 10^5}{1000g}$$ $$=\frac{200}{g}$$
Hence, velocity $$ v=\sqrt{2gh}$$ $$=\sqrt{\frac{200}{2g}}$$ $$=20m/s$$

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