Question: Consider steady, laminar, constant-property flow in a duct formed by two parallel planes. Let the velocity be uniform at the duct entrance. Calculate the development of the velocity profile in the entry length, using the momentum integral equation an assumption that the velocity profile may be approximated by a constant-velocity segment across the center portion of the duct and by simple parabolas in the growing boundary layer adjacent to the walls. Note that the mean velocity, Eq. (7-3), must be a constant, and thus Eq. (7-4) must be satisfied. [Some help in this problem may be obtained from an examination of the development. Evaluate the hydrodynamic entry length and compare with Eq. 7-20).
