First slide

Fluid dynamics

Question

A cylindrical vessel contains a liquid of density $ρ$ up to height h. The liquid is closed by a piston of mass m and area of cross section A. There is a small hole at the bottom of the vessel. The speed v with which the liquid comes out of the hole is

Moderate

A

$\sqrt{2 g h}$
B

$\sqrt{2 (g h + \frac{m g}{A})}$
C

$\sqrt{2 (g h + \frac{m g}{ρ A})}$
D

$\sqrt{2 g h + \frac{m g}{A}}$

Solution

Pressure due to mass of piston is also taken into account.
Applying Bernoulli's theorem at points 1 and 2,
$P_{0} + ρ h g + \frac{m g}{A} = P_{0} + \frac{1}{2} ρ v^{2}$
$⇒ v = \sqrt{2 g h + \frac{2 m g}{ρ A}} = \sqrt{2 (g h + \frac{m g}{ρ A})}$

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