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