JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Fluid Mechanics

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Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at

A

and

B

are

6 cm^{2}

and

3 cm^{2}

respectively.
The rate of flow will be ____

cm^{3} / s

. (take

g = 10 m / s^{2}

)

(A) $\frac{200}{3}$
(B) $2006$
(C) $2003$ ✓ Correct
(D) $1003$

Answer: (C)

Solution

Continuity gives

A_{A} V_{A} = A_{B} V_{B}

, so

6 V_{A} = 3 V_{B}

and

V_{B} = 2 V_{A}

. The

5 cm

height difference measures the pressure difference, so Bernoulli's equation gives

ρ g h = \frac{1}{2} ρ (V_{B}^{2} - V_{A}^{2}) = \frac{1}{2} ρ (3 V_{A}^{2})

. Hence

V_{A} = \frac{2 g h}{3} = \frac{2 \times 10 \times 0.05}{3} = \frac{1}{3} m/s = \frac{100}{3} cm/s

. The volume flow rate is

A_{A} V_{A} = 6 \times \frac{100}{3} = 2003 c m^{3} /s

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Single correct option

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JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Fluid Mechanics

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