Question

A flat plate of width L = 1 m  is pushed down with a velocity U = 0.01 m/s 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, Uavg of the fluid (in m/s) draining out at the instant shows in the figure is ___________ (correct to three decimal places).

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Answer :

0.05

Assuming length of plate as B

Let in infinitely small time ‘dt’ the plate is displaced with ‘dh’

So, dh/dt = U

As per continuity,

Rate of mass displaced through plate= Rate of mass displaced between plates and wall

LBdh = 2*Uavg*d*Bdt

Ldh/dt = 2Uavgd

Uavg = LU/2d = 1*0.01 / 2*0.1 = 0.05 m/s

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