First slide

Fluid dynamics

Question

If A denotes the area of free surface of a liquid and} the depth of an orifice of area of cross-section o below the liquid surface then the velocity r of flow through the orifice is given by

Moderate

A

$v = \sqrt{(2 gh)}$
B

$V = \sqrt{(2 gh)} \sqrt{\{A^{2} / (A^{2} - a^{2})\}}$
C

$V = \sqrt{(2 gh)} \sqrt{{A / (A - a)}}$
D

$v = \sqrt{(2 gh)} \sqrt{\{(A^{2} - a^{2}) / A^{2}\}}$

Solution

Applying Bernoulli's theorem, the rate off low from surface to orifice is given by
$P + \frac{1}{2} ρ {(v^{'})}^{2} + ρgh = P + \frac{1}{2} {ρv}^{2} + 0 wh e re v' = velocity of all surfacses of liquid . If v is velocity of efflux, then {Av}^{'} = av or v^{'} = (av / A) From eqs . (1) and (2), we 8 et \frac{1}{2} ρ {(\frac{av}{A})}^{2} + ρgh = \frac{1}{2} {ρv}^{2} or v^{2} - \frac{a^{2} v^{2}}{A^{2}} = 2 gh V = \sqrt{2 gh} {[\frac{A^{2}}{(A^{2} - a^{2})}]}^{1 / 2}$

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