Correlations Describing Laminar Hydrodynamic Development in a Circular Pipe

Computational fluid dynamics (CFD) is employed to study incompressible and steady laminar flow in the hydrodynamic entrance region of circular pipes for a wide range of Reynolds numbers. Dimensionless analytic expressions for streamwise variations of the centerline velocity, skin friction coefficient, and pressure drop are derived by applying a two-stage nonlinear regression analysis to computational solutions of the Navier–Stokes equations for various Reynolds numbers between 1 and 2000. Similar expressions are also presented for the correction factors for the momentum and kinetic energy fluxes. First, the correlation parameters for a flow variable are obtained for each Reynolds number considered. Subsequently, a second nonlinear regression analysis is conducted to obtain another set of equations for the variation of fitting parameters with the Reynolds number. Constant parameter correlations are also given for the Reynolds number range between 200 and 2000, which are less accurate than the expressions containing Reynolds number-dependent terms. The correlations presented here are also valid for flows with heat transfer, under the assumptions of constant property and zero buoyancy.