First slide

Fluid dynamics

Question

A light cylindrical vessel is kept on a horizontal surface. It’s base area is A. A hole of cross sectional area a is made just at its bottom side. The minimum coefficient of friction necessary to stop sliding of the vessel due to impact force of the emerging liquid is (a << A).

Easy

A

varying
B

a / A
C

2a / A
D

None of these

Solution

Velocity of efflux = $\sqrt{2 g h}$
Force $= a v^{2} ρ = a 2 g h ρ$
i.e., equal to frictional force $a 2 g h ρ = μ m g = μ A h ρ g$
$μ = \frac{2 a}{A}$

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