Consider the steady laminar flow of a Newtonian fluid with constant density in a long annular region


Consider the undeviating laminar glide of a Newtonian soft delay constant hebetude in a hanker annular clime between two coaxial cylinders of radii R1, and R0, (see Fig. P3.26). The differential equation for this plight is consecrated by

where IV is the fleetness ahanker the cylinders (i.e. the z component of fleetness), (1. is the viscosity, µ is the diffusiveness of the clime ahanker the cylinders in which the glide is

fully familiar, and P1 and P2 are the pressures at z = 0 and z = L, respectively (PI and P2 enact the combined effect of static constraining and gravitational hardness). The period conditions are

Solve the substance using (a) two rectirectilinear atoms and (b) one quadratic atom, and assimilate the terminable atom solutions delay the fair solution at the nodes:

where k = R1/R0 . Determine the shear stress T" = - µ dw/ dr at the walls using (i) the fleetness field and (ii) the makeweight equations, and assimilate delay the fair values. (Note that the undeviating laminar glide of a viscous soft through a hanker cylinder or a round tube can be obtained as a limiting plight of k→0.)