EXAMPLE 4.6 For steady incompressible laminar flow through a long tube, the velocity distribution is given by v = U (1-7) V₁ = V = 0 where U is the maximum, or centerline, velocity and R is the tube radius. If the wall tem- perature is constant at Tw, and the temperature T = T(r) only, find T(r) for this flow. Solution With T = T(r), Eq. (4.75) reduces for steady flow to pcpvr dT dr k d dT == r r dr dr dv ( stant Flow with constant p, p, and k is a basic simplification that will be used, for example, throughout Chap. 6. The basic equations of motion (4.56) to (4.58) reduce to (4.73) V.V=0 Continuity: dv Momentum: ρ dt =pg - Vp+μVV (4.74) dT Energy: pcp dt = kV2T+0 (4.75)