A liquid of density \(600 \mathrm{~kg} / \mathrm{m}^{3}\) flowing steadily in a tube of varying cross-section. The cross-section at a point A is \(1.0 \mathrm{~cm}^{2}\) and that at B is \(20 \mathrm{~mm}^{2}\). Both the points A and B are in same horizontal plane, the speed of the liquid at A is \(10 \mathrm{~cm} / \mathrm{s}\). The difference is pressures at A and B points is \_\_\_\_ Pa.

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Fluid Mechanics

A liquid of density

600 kg / m^{3}

flowing steadily in a tube of varying cross-section. The cross-section at a point A is

1.0 cm^{2}

and that at B is

20 mm^{2}

. Both the points A and B are in same horizontal plane, the speed of the liquid at A is

10 cm / s

. The difference is pressures at A and B points is
____ Pa.

Answer: (D)

By continuity, the volume flow rate is the same at both sections, so

A_{A} v_{A} = A_{B} v_{B}

. With

A_{A} = 1.0 cm^{2}

A_{B} = 0.2 cm^{2}

and

v_{A} = 10 cm/s

, the speed at B is

v_{B} = \frac{A _{A} v _{A}}{A _{B}} = \frac{1.0 \times 10}{0.2} = 50 cm/s

. Both points lie in the same horizontal plane, so Bernoulli's equation gives

P_{A} - P_{B} = \frac{1}{2} ρ (v_{B}^{2} - v_{A}^{2})

. Substituting

ρ = 600 kg/m^{3}

v_{B} = 0.5 m/s

and

v_{A} = 0.1 m/s

P_{A} - P_{B} = \frac{1}{2} \times 600 \times (0. 5^{2} - 0. 1^{2}) = 300 \times 0.24 = 72 Pa

. The difference of pressures between A and B is

72 Pa

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option