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Maximum Height of Water in A Tank With A Hole

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

October 17, 2017

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