# Derive expressions for the velocity in outer and inner regions of flow in long tube.

Assume blood flow down a long tube may be thought of as the flow of two immiscible fluids, one in the core of the tube (modeled as normal whole blood) and the other as a cell-free layer near the wall (modeled as plasma). Assume the cell-free layer has a thickness x, the tube has a radius R, the blood viscosity is u_b and the plasma viscosity is u_p. For the steady uniform flow of a Newtonian fluid in a long straight tube, what do the Navier-Stokes equations in cylindrical coordinates reduce to? Derive expressions for the velocity in the plasma layer and the core region. These expressions should be functions of deltaP/deltax (assume this to be a constant), R, x, u_b, u_p and r.

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#### Solution Preview

In this problem, both fluids behave like Newtonian fluids. Therefore, it can be state that:

d(Vb)/dr = -1/Mb *r ( considering the origin the longitudinal

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#### Solution Summary

Full solution where both fluids behave like Newtonian fluids, and it is stated that d(Vb)/dr = -1/Mb *r (considering the origin the longitudinal axe of the conduction). 100 words.