Answer:
The maximum depth of water in the tank shall be 22.784 centimeters.
Explanation:
The maximum height will be reached when the rate at which water enters the tank will be equal to the rate at which water will leave the vessel.
Let us assume that the maximum level of water in the tank is 'h' meters
Since the hole is at bottom
According to Torricelli's Law the speed at which the water shall leave the tank equals
[tex]v=\sqrt{2gh}[/tex]
Thus the rate at which water leaves the tank will be equal to
[tex]Q_{out}=Area\times Speed[/tex]
[tex]Q_{out}=7.00\times 10^{-2}\times \sqrt{2\times 981\times h}[/tex]
Thus equating the rate of inlet of water and rate of outlet of water we get:
[tex]14.8cm^{3}/s=7.00\times 10^{-2}\times \sqrt{2\times 981\times h}\\\\\therefore \sqrt{h}=\frac{14.8}{7.00\times 10^{-2}\times \sqrt{2\times 981}}\\\\\therefore \sqrt{h}=4.77\\\\\therefore h=22.784cm[/tex]
