# 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 R_{1}, and R_{0}, (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 P_{1} and P_{2} 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 = R_{1}/R_{0} . 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.)