Physics - Fluid Question with Solution | TestHub

Suppose $A$ be the area of cross section of tank, $a$ be the area of hole, $v_e$ be the velocity of efflux, $h$ be the height of liquid above the hole,
Let $v$ be the speed with which the level decreases in the container. Using equation of continuity, we get $a{v}_e=Av$ or $v=\frac{a{v}_e}{A}$ Using Bernoulli's theorem, we have $\begin{array}{rl}& P_0+h\rho g+\frac{1}{2}\rho v^2=P_0+\frac{1}{2}\rho v_e^2\\ & h\rho g+\frac{1}{2}\rho {\left(\frac{a{v}_e}{A}\right)}^2=\frac{1}{2}\rho v_e^2\\ & \text{ or }{v}_e^2=\frac{2hg}{1-\left(a^2/A^2\right)}=\frac{2\times (3-0.525)\times 10}{1-(0.1{)}^2}\\ & =50{\mathrm{m}}^2{\mathrm{s}}^{-2}\end{array}$