Momentum and Energy Coefficients Based on Power‐Law Velocity Profile

Abstract

The theoretical momentum coefficient (β) and energy coefficient (α) for turbulent shear flow in circular pipes and wide channels are derived from the power law, then compared with their counterparts on the basis of the logarithmic law. For such unidirectional flows, the exponent (m) of the power‐law velocity distribution is the sole parameter that determines the values of β and α. A comparison of the corresponding expressions for β and α derived using both laws shows that their values differ only slightly within a valid range of small m's. Use of a power‐law‐based β expression along with a power‐law resistance formula in the cross‐section‐averaged equation of momentum cannot only eliminate the theoretical incompatibility that results from mixing logarithmic and power laws in the equation but also remove the inconsistent assumption of