COPY$-$PASTE SOLUTIONS TAKEN FROM THE SOLUTION MANUAL WILL NOT BE ACCEPTED $!!!$

ATTENTION

YOU HAVE TO SHOW ALL THE STEPS

ATTENTION

$2.$ Oil $)=(0\mathrm{.}38(N).\frac{s}{m^2}$ flows between parallel plates spaced $5mm$ apart. The bottom plate is fixed, but the upper plate moves with a velocity of $0\mathrm{.}2\frac{m}{s}$ in the positive $x$ direction. The pressure gradient is $60kP\frac{a}{m}$ and it is negative. Assume laminar flow.

a$.$ List the assumptions $(12$ P$)$

b$.$ Using the Continuity eq$.,$ show that velocity is only a function of $y(8P)$

c$.$ Using only the x$-$component of NSE, find an expression for the u$-$velocity $(20$ P$)$

d$.$ Apply boundary conditions to velocity and find $c_1$ and $c_2(20P)$

e$.$ Using the given values in the problem, obtain the u$-$velocity equation as a function of y only $(10$ P$)$

$!$

ATTENTION

After you solve the above parts, now solve the following parts.

$[$FIRST$,$ you have to solve from a$)$ to e$).$ Otherwise you won't be graded!$]$

f$.$ Plot the velocity profile using $10$ different values of $y($ranging from $0$ to $5mm$

g$.$ Find the location at which velocity is maximum at which u$-$velocity gradient with respect to $y$ is zero $(10P)$

h$.$ Calculate the flow rate, $Q(10P)$