GATE ME 2023 Set 1 — Question 64
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Fluid Mechanics → Fluid Properties & Statics → Centre of Pressure
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Question
The figure shows two fluids held by a hinged gate. The atmospheric pressure is . The moment per unit width about the base of the hinge is ________ . (Rounded off to one decimal place)Take the acceleration due to gravity to be .
Correct answer
55.9 to 58.5
Solution
To find the moment per unit width about the base of the hinge, we integrate the gauge pressure distribution over the gate. The atmospheric pressure acts on both sides and cancels out.Let be the depth from the top of the first fluid.
For (Fluid 1: ):
For (Fluid 2: ):
The moment per unit width about the hinge (at ) is given by:
Substituting , , and :
Let , then . When ; when . Also .
Total moment .
For (Fluid 1: ):
For (Fluid 2: ):
The moment per unit width about the hinge (at ) is given by:
Substituting , , and :
Let , then . When ; when . Also .
Total moment .
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