Question

Water is poured into a vessel at a constant rate $\varphi m^3/s$. There is a small aperture of the cross-sectional area an at the bottom of the vessel. The maximum level of water in the vessel is proportional to :

• A. $\varphi$
• B. ${\varphi }^2$
• C. $1/a$
• D. $1/a^2$

Answer 1

The correct option is D $1/a^2$

$\text{mass emerging.}$

$m=av$

$m=a\sqrt{2g{h}_{max}}$

$h_{max}=\frac{m^2}{a^2\left(2g\right)}$

$h_{max}\propto \frac{1}{a^2}$

$\text{Answer:-(D)}$