Project ForgeA 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 (gap d=0.1 m). Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity, u_avg, of the fluid (in m/s) draining out at the instant shown is ______ (correct to three decimal places).
Explanation
By continuity, the volume swept out by the plate up to a distance x from the centreline equals the volume exiting through the gap there: U·x = u(x)·d, so u(x) = Ux/d. At the edge x=L/2: u_avg = U(L/2)/d = 0.01×0.5/0.1 = 0.05 m/s.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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