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GATE 2018 ME (ME2) – Question 44

Fluid Mechanics · Bernoulli's equation and fluid acceleration · 2 marks · Multiple choice

Air flows at 1.5 m³/s through the shown horizontal pipe whose diameter reduces from 400 mm at section 1 to 200 mm at section 2. Density is 1.2 kg/m³; assume inviscid incompressible flow. Find pressure change P2 − P1 (kPa).

Diagram for GATE 2018 ME (ME2) question 44
  1. −1.28
  2. 2.56
  3. −2.13
  4. 1.28

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Show answer and explanation

Correct answer: (A) −1.28

Explanation

Continuity gives $V_1=1.5/[\pi(0.4)^2/4]=11.9366$ m/s and $V_2=47.7465$ m/s. Horizontal inviscid Bernoulli gives $$P_2-P_1=\tfrac12\rho(V_1^2-V_2^2)=-1282.35\ \mathrm{Pa}.$$ Thus **−1.28 kPa, A**.