I already derived for velocity profile, can you derive the equation for average velocity.

$2\mathrm{.}9-2.$ Shell Momentum Balance for Flow Between Parallel Plates. A fluid of constan density is flowing in laminar flow at steady state in the horizontal $x$ direction between two flat and parallel plates. The distance between the two plates in the vertical $y$ direction is $2y_0.$ Using a shell momentum balance, derive the equation

CS

for the velocity profile within this fluid and the maximum velocity for a distane,

Chap. $2$ Problems

$Lm$ in the $x$ direction. $[$Hint: See the method used in Section $2\mathrm{.}9B$ to derive Eq$.(2\mathrm{.}9-9).$ One boundary condition used is $d\frac{v_x}{d}y=0$ at $y=0.]$

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Ans. $,v_x=\frac{p_0-p_L}{2L}{y}_0^2[1-(\frac{y}{y_0}{)}^2]$