Consider a flow between two plates as shown:

$($a$)$ Knowing that the velocity profile is parabolic, how many boundary

conditions are needed? What are those boundary conditions?

Note: the velocity profile has its maximum value on the mid$-$line.

$($b$)$ The velocity profile is given as

$\frac{u}{U_{\text{m}\text{a}\text{x}}}=1-(\frac{2y}{h}{)}^2$

Find the shear stress. What type of distribution does the shear stress have?

$($c$)$ Consider water at $15C,$ with $U_{\text{m}\text{a}\text{x}}=0\mathrm{.}05\frac{m}{s}$ and $h=0\mathrm{.}2mm.$ Calculate

shear stress on the upper plate.

Consider a flow between two plates as shown:

$($a$)$ Knowing that the velocity profile is parabolic, how many boundary

conditions are needed? What are those boundary conditions?

Note: the velocity profile has its maximum value on the mid$-$line.

$($b$)$ The velocity profile is given as

$\frac{u}{U_{\text{m}\text{a}\text{x}}}=1-(\frac{2y}{h}{)}^2$

Find the shear stress. What type of distribution does the shear stress have?

$($c$)$ Consider water at $15C,$ with $U_{\text{m}\text{a}\text{x}}=0\mathrm{.}05\frac{m}{s}$ and $h=0\mathrm{.}2mm.$ Calculate

shear stress on the upper plate.