First slide

Fluid dynamics

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 (g = 10 m/s²)

Moderate

A

$50 m^{2} / s^{2}$
B

$50.5 m^{2} / s^{2}$
C

$51 m^{2} / s^{2}$
D

$52 m^{2} / s^{2}$

Solution

Let A = cross-section 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 Bernoulli's theorem energy per unit volume Energy per unit volume at point A : Energy per unit volume at point B
$P + ρ g h + \frac{1}{2} ρ V^{2} = P + 0 + \frac{1}{2} ρ v^{2}$
$\Rightarrow v^{2} = \frac{2 g h}{1 - {(\frac{a}{A})}^{2}} = \frac{2 \times 10 \times (3 - 0.525)}{1 - (0.1)^{2}} = 50 (m / s)^{2}$

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