Finding an expression for velocity

Question

Consider an annulus formed by two circular cylinders, with one cylinder inside the other. The inner cylinder has radius $a$ and the outer cylinder has radius $b$. The cylinders have a common axis, and both can be considered infinitely long. Between the two cylinders is an incompressible liquid with kinematic viscosity $ν$ and density $ρ$. The inner cylinder moves with constant speed $U$ in the direction of the common axis. The outer cylinder is stationary. The pressure of the fluid is constant and the flow is steady.

Using cylindrical polar coordinates $(r,θ,z)$ (where $z$ is the distance along the common axis (from some origin), $r$ is the radial distance from the axis and $θ$ is the angle), determine an expression for the velocity $w(r)$, the flow in the direction of the axis.

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I am very new to these types of questions. Is there a general method to work these out? I have drawn a diagram but I don't know which equations to use to derive the velocity $w(r)$

Answer 1

incompressible liquid with kinematic viscosity $ν$ and density $\rho$.
(..)
The pressure of the fluid is constant and the flow is steady.

You need physics here to come up with a (partial) differential equation for the velocity field $w$.

The other information seems to favour some symmetry argument and give boundary conditions.