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JEE Main 2025 · Physics · Fluid Mechanics, Elasticity and Surface Tension · medium

Water of density 1000 kg m^-3 flows steadily through a horizontal pipe of radius 4 cm which narrows smoothly to a radius of 2 cm. The pressure in the…

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Water of density 1000 kg m−31000\ \mathrm{kg\,m^{-3}} flows steadily through a horizontal pipe of radius 4 cm4\ \mathrm{cm} which narrows smoothly to a radius of 2 cm2\ \mathrm{cm}. The pressure in the wide section exceeds that in the narrow section by 7.5 kPa7.5\ \mathrm{kPa}. The volume flow rate through the pipe is nearly
  1. A. 1.3 L s−11.3\ \mathrm{L\,s^{-1}}
  2. B. 2.5 L s−12.5\ \mathrm{L\,s^{-1}}
  3. C. 5.0 L s−15.0\ \mathrm{L\,s^{-1}}
  4. D. 10 L s−110\ \mathrm{L\,s^{-1}}
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Answer: (C) 5.0 L s−15.0\ \mathrm{L\,s^{-1}}

The area ratio is 4:14:1, so continuity gives v2=4v1v_2 = 4v_1. Bernoulli's equation for the horizontal pipe: ΔP=12ρ (v22−v12)=12(1000)(15 v12)=7500 v12\Delta P = \tfrac12\rho\,(v_2^2 - v_1^2) = \tfrac12(1000)(15\,v_1^2) = 7500\,v_1^2. Setting this equal to 7500 Pa7500\ \mathrm{Pa} gives v1=1 m s−1v_1 = 1\ \mathrm{m\,s^{-1}}. The flow rate is Q=A1v1=π(0.04)2(1)=5.03×10−3 m3 s−1≈5.0 L s−1Q = A_1 v_1 = \pi(0.04)^2(1) = 5.03\times10^{-3}\ \mathrm{m^3\,s^{-1}} \approx 5.0\ \mathrm{L\,s^{-1}}.
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