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GATE ME 2016 Set 1 — Question 51

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NAT+2 / -0HardControl Volume AnalysisFluid Kinematics & DynamicsFluid MechanicsBoundary Layer TheoryViscous & Pipe Flow

Fluid Mechanics → Fluid Kinematics & Dynamics → Boundary Layer Theory

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Question

A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is UoU_o. The velocity profile at the inlet a−ba-b is uniform, while that at a downstream location c−dc-d is given by u=Uo[2(yδ)−(yδ)2]u = U_o \left[ 2 \left( \frac{y}{\delta} \right) - \left( \frac{y}{\delta} \right)^2 \right].
Boundary layer flow over a flat plate showing inlet section a-b and downstream section c-d with velocity profiles
The ratio of the mass flow rate, m˙bd\dot{m}_{bd}, leaving through the horizontal section b−db-d to that entering through the vertical section a−ba-b is ___________
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