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Fluid is in laminar motion between two parallel plates separated by distance b under the action of motion of one of the plates and also under the presence of a pressure

gradient in such a way that the net forward discharge across any section is zero. Consider ‘U’ be the velocity of the moving plate.

(i) Find out the point where minimum velocity occurs and its magnitude

(ii) Draw rough sketch of velocity distribution across any section

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In the given case of flow, the velocity distribution is given by

u=$\frac{U}{b} y-\frac{1}{2μ} \frac{∂p}{∂x} (by-y^2 )$………(1)

And the discharge per unit width,

q=$\frac{Ub}{2}-\frac{b^3}{12μ} \frac{∂p}{∂x}$………(2)

Net forward discharge,

q=0…………(given)

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