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 $0.1$. The square of the speed of the liquid coming out from the orifice is $\left(g=10m/s^2\right)$

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

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