JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Fluid Mechanics

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area

0.5 m^{2}

. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is :

(g = 10 m / s^{2})

(A) $3 m / s$
(B) $5 m / s$
(C) $2 m / s$
(D) $4 m / s$ ✓ Correct

Answer: (D)

Solution

Apply Bernoulli's equation between the top water surface and the hole. The load adds a pressure

\frac{m g}{A} = \frac{50 \times 10}{0.5} = 1000 Pa

at the surface, which stands a height

h = 1.6 - 0.9 = 0.7 m

above the hole. Taking the surface speed as negligible,

\frac{m g}{A} + ρ g h = \frac{1}{2} ρ v^{2},

1000 + (1000) (10) (0.7) = \frac{1}{2} (1000) v^{2},

8000 = 500 v^{2} \Rightarrow v^{2} = 16.

The water emerges with a speed of

4 m/s

JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Fluid Mechanics

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