Please provide clear eplanation on each step and solve completely mentionining the symbols and abbreviation used and what they mean. Thanks

Question $4$

Water flows vertically and at a constant rate in a pipe of length $L,$ as shown in Figure $4.$

The pipe consists of a circular outer pipe of radius $R$ and a central rod of radius $=$

$\frac{R}{4}.$ The walls of the outer pipe are coated with Teflon so that the water does not wet

the surface $($negligible shear$).$ The inner rod is not coated, so that the water does wet

the surface. The walls are non$-$porous. The inlet and outlet of the pipe are exposed to

atmosphere, such that the inlet and outlet static pressures are the same. Assuming that

$\frac{L}{R}10$ and that the flow is laminar and axisymmetric, determine the following.

Figure $4$: Schematic of vertical pipe with central rod.

$($a$)$ A formula for the radial distribution of the radial velocity component $v_r.$

$($b$)$ A formula for the radial distribution of the vertical velocity component $v_z.$

$($c$)$ The force per unit length $($magnitude and direction$)$ acting on the inner rod.

Plr