FLUID DYNAMICS:

There is flow between two infinitely long parallel plates. The top plate is moving to the left at $-2$Vo$,$ and the bottom plate is stationary. dP$/$dx does not equal zero. The coordinate system is located at the centerline between the $2$ plates $($x positive is to the right, y positive is upwards$).$ w $=$ unit width

$1.$ Draw the diagram with all pertinent information $($velocity profile, dimensions, coord system, etc.$)$

$2.$ Solve the following:

a$.$ Simplify the x$-$direction Navier$-$Stokes and continuity equations using a numbered assumption approach $($such as: $1.$ steady state$->$ d$/$dt$=0,$

$2.$ density$=$constant, $3.$ v$=0,4.$ w$=0,$ etc.$)$

b$.$ Develop the u$($y$)$ velocity profile using the correct boundary conditions

c$.$ Check that your boundary conditions are correct

d$.$ Develop an equation for the Qnet. Do not substitute any values; keep the equation as all variables

e$.$ Determine the dp$/$dx required for a Qnet $=3$ cm$^3/$s$,$ h $=1$ cm$,$ and viscosity $=10^-3$ N$-$s$/$m$^2.$

f$.$ Using excel or MATLAB develop the following graphs: Substitute all known values so the u$($y$)$ equation is made up of y$$s and numbers. Plot u$($y$)$ on x$-$axis and gap distance on y$-$axis.

i$.$ Vo $=-1$ cm$/$s$,$ dp$/$dx $=0\mathrm{.}2($pressure decreases to the right$),$ h $=1$ cm and

viscosity $=10-3$ N$-$s$/$m$2.$ Indicate the direction of Qnet

ii$.$ Vo $=0$ cm$/$s$,$ dp$/$dx $=0\mathrm{.}2($pressure decreases to the right$),$ h $=1$ cm and viscosity

$=10-3$ N$-$s$/$m$2.$ Indicate the direction of Qnet

iii. Vo $=-1$ cm$/$s$,$ dp$/$dx $=0,$ h $=1$ cm and viscosity $=10-3$ N$-$s$/$m$2.$ Indicate the

direction of Qnet

iv$.$ Vo $=-1$ cm$/$s$,$ dp$/$dx $=0\mathrm{.}2($pressure decreases to the left$),$ h $=1$ cm and viscosity

$=10-3$ N$-$s$/$m$2.$ Indicate the direction of Qnet

thank you!