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Q#1 Laminar Flow GATE CH 2024 MCQ +2 marks -0.66 marks

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 \(\begin{align*} \frac{\Delta P}{L} = \frac{(P_1 - P_2)}{L} > 0, \end{align*}\)

where\(𝑃_1\) and \(𝑃_2\) 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?

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