Velocity and Volume Flow Rate for Flow in a Pipe

Consider the steady, incompressible flow of a Newtonian fluid through a cylindrical pipe $($circular in cross$-$section$)$ of radius R$.$ Use cylindrical coordinates $($r$,,$ z$),$ where z is the direction along the pipe$$s axis

$($a$)$ Write down the Navier$-$Stokes equations in cylindrical coordinates and simplify them for steady axisymmetric flow in the pipe, noting that the velocity v $=(0,0,$ vz $($r$)).$

$($b$))$ Starting from the simplified Navier$-$Stokes equation in the z direction from $($a$),$ under a constant pressure gradient dp $/$dz $=$G$,$ solve for the velocity profile vz $($r$)$ in terms of G$,$ R$,$ and the fluid viscosity $.$

$($c$))$ Integrate the velocity profile across the pipe cross$-$section to find the volumetric flow rate Q$$ as a function of G$,$ R$,$ and $.$ If Q$$ R$,$ what is the value of $/$eta$?$ HINT:

Volume flow rate Q$=$ dQ$/$dt $=$ Avz $,$ where A is the area of a cross$-$section of the circular

I just need help with b and c$.$ Thank you!

pipe, and vz represents the average velocity of a cross$-$section of the pipe.