Question

A tank has a small hole at its bottom of area of cross-section a. Liquid is being poured in the tank at the rate $V{m}^3/s$, the maximum level of liquid in the container will be(Area of tank A):

• A. $\frac{V}{gaA}$
• B. $\frac{V^2}{2g{a}^2}$
• C. $\frac{V^2}{gAa}$
• D. $\frac{V^2}{2gaA}$

Answer 1

Answer: (B)

$\frac{V^2}{2g{a}^2}$

At maximum level the discharge due to small hole will be equal pouring rate

$V=va$ , let the maximum height be H , assuming a<<A

$V=a\sqrt{2gH}$

$H=\frac{V^2}{2g{a}^2}$