GATE ME 2018 Set 1 — Question 32
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
A flat plate of width is pushed down with a velocity towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity, of the fluid (in m/s) draining out at the instant shown in the figure is _____________(correct to three decimal places).
Correct answer
0.045 to 0.055
Solution
By the principle of conservation of mass for an incompressible fluid, the volume flow rate displaced by the plate must equal the volume flow rate of the fluid draining out from both sides.Volume flow rate displaced by the plate: , where is the width into the page (unit width for 2D flow).Volume flow rate draining out from both sides: .Equating the two: Given: , , .
.The average velocity is .
.The average velocity is .
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