Question

Water is filled in a cylindrical container to a height of $3m.$ The ratio of the cross-sectional area of the orifice and the beaker is $\mathrm{0.1.}$ The square of the speed of the liquid coming out from the orifice is $\left(g=10m/s^2\right)\dots \dots m^2/s^2.$

Answer 1

Answer: 50

Let $v$ be velocity of efflux and $v^{\prime }$ be the velocity of fall of liquid level in tank. Using equation of continuity for tube of flow formed between level of tank and orifice is
$A{v}^{\prime }=av...\left(i\right)$

Applying Bernoulli's theorem, we have
$\frac{p}{\rho }+\frac{1}{2}{\left(v^{{}^{\prime }}\right)}^2+gh=\frac{p}{\rho }+\frac{1}{2}{v}^2+0$
From equation $v^2=\frac{2gh}{1-\frac{a^2}{A}}=\frac{2\times 10\times (3-0.525)}{1-(0.1{)}^2}$ $\Rightarrow v^2=50m^2{s}^{-2}$