A flat channel of depth 1 m has a fully developed laminar flow of air at P₀, T₀ with a velocity profile of V = 4V_cx(H − x)/H₂, where V_c is the velocity on the centerline and x is the distance across the channel, as shown in Fig. P4.15. Find the total mass flow rate and the average velocity both as functions of V_c and H.

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H Ve V(x) FIGURE P4.15