JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Fluid Mechanics

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Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of

5 \times 1 0^{5} N

is applied an the top surface of water using a piston. The speed of efflux from the hole will be :
(given atmospheric pressure

P_{A} = 1.01 \times 1 0^{5} Pa

, density of water

ρ_{w} = 1000 kg / m^{3}

and gravitational acceleration

g = 10 m / s^{2}

)

(A) $11.6 m / s$
(B) $10.8 m / s$
(C) $17.8 m / s$ ✓ Correct
(D) $14.4 m / s$

Answer: (C)

Solution

Apply Bernoulli's theorem between the piston and the hole. The pressure at the piston is

P_{p i s t o n} = F / A = 5 \times 1 0^{5} / (π \times 1^{2})

Pa. At the hole (height difference 10 m from piston):

P_{p i s t o n} + ρ g h = P_{A} + \frac{1}{2} ρ v_{e}^{2}

. Substituting values:

\frac{5 \times 1 0 ^{5}}{π} + 1 0^{3} \times 10 \times 10 = 1.01 \times 1 0^{5} + \frac{1}{2} \times 1 0^{3} \times v_{e}^{2}

. Solving gives

v_{e} \approx 17.8

m/s.

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Fluid Mechanics

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