Velocity field its awnsered but what aboutQuestion $1$: fluid flow in an annulus $(50$ pts$)$

Consider the steady, fully developed laminar flow in a horizontal annulus with inside radius

$R_2[m]$ and outside radius $R_1[m]($see figure$).$ The annulus is completely filled with a

Newtonian fluid of constant density $[kg*m^{-3}]$ and absolute $($or dynamic$)$ viscosity $[Pa*s].$

As the tube is horizontal, gravity does not play a role.

Please answer the following three questions, using only symbols from the text or the figure:

a$.$ Find a relation between the pressure gradient $\frac{dp}{(d)x}[(Pa)*m^{-1}],$ the volume flow rate

$Q[m^3*s^{-1}],$ the fluid viscosity $[Pa*s],$ the outside radius $R_1[m]$ and the dimensionless

ratio $\frac{R_2}{R_1}[-].(10$ pts$)$

b$.$ Find the limiting form of the relation in $($a$)$ for a very thin annulus by expressing it in

terms of $R_1[m]$ and $h=R_1-R_2[m]$ and taking the limit $h0.$ Compare the limiting

form with the formula for fully developed laminar flow between flat plates separated by a

distance $h$ and discuss your answer. $(20$ pts$)$

c$.$ In the opposite limit $R_{2}0,$ does the relation of $($a$)$ reduce to the formula for Hagen$-$

Poiseuille flow in a circular pipe of radius $R_1[$m$]?$ Discuss your answer. $(20$ pts$)$