Question

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

• A. $50 \,m ^2 / s ^2$
• B. $50.5\, m ^2 / s ^2$
• C. $51 \,m ^2 / s ^2$
• D. $52\, m ^2 / s ^2$

Answer 1

Answer: (A)

let $A=$ cross-sectional of tank
$a=$ cross-section hole
$V=$ velocity with which level decreases
$v=$ velocity of efflux

From equation of continuity, $a v=A V$
$\Rightarrow V=\frac{a v}{A}$
By using Bernoullis theorem for energy per unit volume.
Energy per unit volume at point $A=$ energy per unit volume at point $B$
$p +\rho g h+\frac{1}{2} \rho v^2=p+0+\frac{1}{2} \rho v^2 $
$\Rightarrow v^2 =\frac{2 g h}{1-\left(\frac{a}{A}\right)^2}=\frac{2 \times 10 \times(3-0.525)}{1-(0.1)^2}$
$ =50( m / s )^2$