It doesn't want to come out

Water up-to height \(h\) is filled in a very wide cylindrical tank of height \(H\). Now the tank is sealed from the top and a small hole is made near the bottom so that the water can freely flow out. It is observed that after some time water stops coming out of the hole.

If the fraction of water left in the tank (compared to the original level) can be represented by \(\frac{a}{b}\), for coprime positive integers \(a,b\). Find \(a+b\).

With \(H=10 \text{ m},h=7.5 \text{ m}, { P }_{ \text{atm} }={ 10 }^{ 5 } \text{ Pa}, \rho ={ 10 }^{ 3 } \text{ kg/m}^3 ,g=10 \text{ m/s}^{ 2 }\)

Details and Assumptions:

  • Assume process above the water to be isothermal.

  • Neglect surface tension and viscous effects.

This problem is originally part of set Mechanics problems by Abhishek Sharma.
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