Consider pressure-driven flow in an annular channel. The inner and outer radii are as in Fig. P7.1, but now both cylinders are stationary and there is a mean fluid velocity U in the z direction. The conduit length is L.

(a) Solve for v_z(r) in terms of the pressure drop. It is convenient to lump the viscosity and pressure drop together as 

and write the final result in terms of a dimensionless radial coordinate η = r/R.

(b) Relate U to B and the two radii.

(c) Derive the result for the friction factor that is given by Eq. (2.4-5).

Transcribed Image Text:

B = |Δg\/(μL)