is anyone knows how to treat this problem?

Determine velocity distribution and a friction force of a viscous gas moving in a coaxial tube.

thanks

Hi Bublik!

You must first determine if the flow is laminar or turbulent. Empirical criteria determine it, based on Reynolds' number Re.

In a turbulent flow, only empirical formulas give you the speed distribution and force.

In a laminar flow (this is the uncommon case, excepted at school), admitting that the flow is constant over time, there would be analytic solutions. Write the equation on a thin cylinder of gas between r and r+dr telling that the friction forces at r and at r+dr compensate. Do NOT forget that the surface is bigger at r+dr.

Then, put zero speed at the inner and outer radii, solve the differential equation. Deduce the mean velocity from the peak velocity, compute a throughput from it, relate it to the shear number at inner and outer radii, and deduce the force.

thanks, it really helped me