The velocity u at radius r for fully-developed Poiseuille flow through a concentric annulus of a fluid with constant viscosity μ is given by where R 1 is the radius of the inner cylinder, RO is the...

The velocity u at radius r for fully-developed Poiseuille flow through a concentric annulus of a fluid with constant viscosity μ is given by

where R₁
is the radius of the inner cylinder, RO is the radius of the outer cylinder, and dp/dx is the axial pressure gradient. If the inner cylinder is rotating at angular velocity Ω„ the tangential velocity at radius r is given by

The shear stresses in the axial and tangential directions are given by

respectively. Derive expressions for

(a) the radial distributions of τ_rx
and τ_rθ,

(b) the location of the peak axial velocity, and

(c) the torque exerted on the fluid at the location of peak axial velocity.