Example

A laminar flow occurs between two horizontal parallel plates under a pressure gradient $d\frac{p}{d}s(p$ decreases in the positive $s$ direction$).$ The upper plate moves left at velocity $u_t.$ The expression for local velocity $u$ is given as

$u=-\frac{1}{2}\frac{dp}{ds}(Hy-y^2)+u_t\frac{y}{H}$

Estimate the shear stress at the two plates.

$($A$)$ Use Excel to draw the velocity distribution at $d\frac{p}{d}x=0\mathrm{.}6P\frac{a}{m}$;$=0\mathrm{.}001$ Pa$.$s ;$H=0\mathrm{.}15m$; and $U_t=0\mathrm{.}5\frac{m}{s}.$

$($B$)$ From the graph, can you estimate where the location $??)$ with zero velocity?

The deadline is Tuesday, $6$ Feb., $4$:$00$ PM on the BB$.$

Please submit the excel sheet having the graph with your name only.