The steady turbulent-flow equations for continuity, momentum, and energy were derived for certain finite systems. It was found that for an incompressible fluid the continuity relation contained neither nonuniform velocity-distribution correction terms nor turbulence terms, that the momentum equation involved velocity-distribution corrections and mean-square velocity fluctuations, and that the energy relation contained not only velocity-distribution corrections and mean-square terms but in addition mean-cube and double- and triple-correlation terms. The correction factors for nonuniform velocity distribution were evaluated for fully developed open channel and pipe flow. Through the momentum law the effect of turbulence was shown quantitatively in the case of the hydraulic jump in open channels and the sudden expansion in closed conduits.

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