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GATE 2020 CH – Question 48

Fluid Mechanics and Mechanical Operations · Fluid properties, fluid statics and fluid kinematics · 2 marks · Multiple choice

The U-tube has manometric liquids of densities 1000 and 600 kg/m³. Initially both limbs are open to atmosphere and free levels differ by 10 cm as shown. Air density is negligible, g = 9.81 m/s² and atmospheric pressure is 100 kPa. What absolute pressure applied to limb P raises the level in Q by another 20 cm?

Diagram for GATE 2020 CH question 48
  1. 100.175 kPa
  2. 103.924 kPa
  3. 547.231 kPa
  4. 833.206 kPa

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Show answer and explanation

Correct answer: (B) 103.924 kPa

Explanation

The constant-depth light-fluid column creates the initial 10 cm offset at equal atmospheric pressures. When Q rises 0.20 m, conservation of volume in the equal-area U-tube lowers the opposite heavy-fluid interface by 0.20 m. The additional heavy-fluid head difference is 0.40 m. Required gauge pressure is $1000(9.81)(0.40)=3924$ Pa = 3.924 kPa. Adding atmosphere gives absolute pressure 103.924 kPa, B.

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