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PhyMedMain 2026 • 8th Apr - Shift 2

Pressure Difference in Horizontal Tube of Varying Cross Section

A liquid of density 600 kg/m3600\text{ kg/m}^3 flowing steadily in a tube of varying cross-section. The cross-section at a point AA is 1.0 cm21.0\text{ cm}^2 and that at BB is 20 mm220\text{ mm}^2. Both the points AA and BB are in same horizontal plane, the speed of the liquid at AA is 10 cm/s10\text{ cm/s}. The difference in pressures at AA and BB points is _______ Pa.

Options

A

18

B

144

C

36

D

72

Correct

Topics & Concepts

Mechanical Properties of FluidsBernoulli's PrincipleFluid Dynamics

Step-by-Step Solution

To find the pressure difference between points AA and BB, we apply the equation of continuity and Bernoulli's principle for a horizontal streamline.

First, using the equation of continuity AAvA=ABvBA_A v_A = A_B v_B: vB=AAABvA=1.0×10−4 m220×10−6 m2×0.1 m/s=0.5 m/sv_B = \frac{A_A}{A_B} v_A = \frac{1.0 \times 10^{-4} \text{ m}^2}{20 \times 10^{-6} \text{ m}^2} \times 0.1 \text{ m/s} = 0.5 \text{ m/s}

Next, applying Bernoulli's equation for points at the same horizontal level: PA−PB=12ρ(vB2−vA2)P_A - P_B = \frac{1}{2} \rho (v_B^2 - v_A^2)

Substituting the given density ρ=600 kg/m3\rho = 600 \text{ kg/m}^3 and the respective speeds: PA−PB=12×600×(0.52−0.12)=300×0.24=72 PaP_A - P_B = \frac{1}{2} \times 600 \times (0.5^2 - 0.1^2) = 300 \times 0.24 = 72 \text{ Pa}

Thus, the pressure difference between points AA and BB is 72 Pa72 \text{ Pa}, which corresponds to Option D.

Pressure Difference in Horizontal Tube of Varying Cross Section | Physics PYQ Solution - JEE Challenger