Turbulent Flow Of Newtonian Fluids Research Articles

On the theoretical calculation of friction factors for laminar, transitional, and turbulent flow of newtonian fluids in pipes and between parallel plane walls

AbstractVarious modifications of the Prandtl mixing‐length model for turbulent momentum transport in pipes and between parallel plane walls are discussed. The most complete modification, due to Gill and Scher, is improved by replacing one of their two empirical constants by a theoretically calculable parameter. The new theory is compared with experimental data from the literature and found to reproduce frictional resistance data accurately for all values of the Reynolds number. It is somewhat in error for velocity profiles at high Reynolds numbers, but accurately reproduces velocity profile data in the transition region. The new theory represents the first accurate semi‐theoretical calculation of frictional resistance coefficients for all regimes of flow (laminar, transitional, and turbulent) for both pipes and parallel plane ducts, and of velocity profiles in the transitional flow regime in either geometry.

Application of a Simplified Velocity Profile to the Prediction of Pipe-Flow Heat Transfer

The temperature profiles and heat-transfer coefficients are predicted for fully developed turbulent pipe flow with constant wall heat flux for a wide range of Prandtl and Reynolds numbers. The basis for integrating the energy equation comes from a continuously differentiable velocity profile which fits the physical boundary conditions and is a rigorous (though not necessarily unique) solution of the Reynolds equations. This velocity profile is the semiempirical relation proposed by S. I. Pai, reference [12]. The assumptions are those of steady, incompressible, constant-property, fully developed, turbulent flow of Newtonian fluids in smooth, circular pipes with constant heat flux at the wall. The ratio of the turbulent thermal diffusivity to the turbulent momentum diffusivity is taken to be unity. The thermal quantities are obtained by numerical integration of the energy equation, and they are presented as curves and tables. A compact formula for the Nusselt number is given for a wide range of Reynolds and Prandtl numbers. The results degenerate identically to the case of laminar flow. The heat-transfer calculation requires neither adjustable factors nor data-fitting beyond the empirical constants in the momentum equation; thus this analysis constitutes a heat-transfer prediction to be tested against heat-transfer data.