Problem #$4.[$Governing equations$]($Poirier and Geiger problem $2\mathrm{.}7)$ Water $($viscosity ${10}^{-3}$

$N*\frac{s}{m^2})$ flows parallel to a flat horizontal surface. The velocity profile at $x_1=a$ is given by

$v_1=6sin(\frac{}{2}{x}_2)$

with $v_1$ in $\frac{m}{s}$ and $x_2$ as distance from the surface in mm $.$

a$)$ Find the shear stress at the wall at $x_1=a.$ Express results in $Pa=\frac{N}{m^2}.$

b$)$ Further downstream, at $x_1=b,$ the velocity profile is given by

$v_1=4sin(\frac{}{2}{x}_2)$

Is the flow "fully developed"? Explain.

c$)$ Is there a $x_2$ component to the flow $($i$.$e$.,v_2)?$ Explain with the aid of the continuity

equation.$($Poirier and Geiger problem $2\mathrm{.}7)$ Water $($viscosity ${10}^{-3}N*\frac{s}{m^2})$ flows parallel to a flat horizontal surface. The velocity profile at $x_1=a$ is given by $v_1=6sin(\frac{}{2}{x}_2)$ with $v_1$ in $\frac{m}{s}$ and $x_2$ as distance from the surface in mm $.$

a$)$ Find the shear stress at the wall at $x_1=a.$ Express results in $Pa=\frac{N}{m^2}.$

b$)$ Further downstream, at $x_1=b,$ the velocity profile is given by

$v_1=4sin(\frac{}{2}{x}_2)$

Is the flow "fully developed"? Explain.

c$)$ Is there a $x_2$ component to the flow $($i$.$e$.,v_2)?$ Explain with the aid of the continuity equation.