Chemical Engineering > GATE 2024 > Momentum Transfer
Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity μ) between two infinitely long horizontal plates separated by a distance 2H as shown in the figure. The flow is driven by the combined action of a pressure gradient and the motion of the bottom plate at y = −H in the negative x direction. Given that ΔPL = (P1 − P2) / L > 0, where P1 and P2 are the pressures at two x locations separated by a distance L. The bottom plate has a velocity of magnitude V with respect to the stationary top plate at y = H. Which one of the following represents the x-component of the fluid velocity vector?
A
(ΔP/L)(H2/2μ)(1-y2/H2)+V/2(y/H-1)
B
(ΔP/L)(H2/2μ)(y2/H2-1)+V/2(y/H-1)
C
(ΔP/L)(H2/2μ)(1-y2/H2)-V/2(y/H-1)
D
(ΔP/L)(H2/2μ)(y2/H2-1)-V/2(y/H-1)

Correct : c

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