b) Consider the case of steady, isothermal, laminar flow in the gap formed by two long horizontally aligned and infinite

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B Consider The Case Of Steady Isothermal Laminar Flow In The Gap Formed By Two Long Horizontally Aligned And Infinite 1 (64.29 KiB) Viewed 14 times

b) Consider the case of steady, isothermal, laminar flow in the gap formed by two long horizontally aligned and infinitely wide, parallel plates, positioned one above the other a small distance y = h apart, where using a Cartesian frame of reference, y points in a direction perpendicular to the plates such that y = 0 at the surface of the lower of the two plates along which the corresponding x-coordinate lies and points in the direction of flow. The fluid confined between the plates has constant density, p, and constant dynamic viscosity, p. If the upper and lower plates move with velocity V and U, respectively, and there is a constant pressure gradient in the direction of flow, show the velocity u(y) across the plates is given by: 1 dp 2u dx u(y) = Py? V-U h dph + 1 2u dx y +U.