7 2 v subject to no slip at the walls and known inlet

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Unformatted text preview: rface solutions for Chap. 10.) Both laminar and turbulent flows satisfy Eqs. (6.7). For laminar flow, where there are no random fluctuations, we go right to the attack and solve them for a variety of geometries [2, 3], leaving many more, of course, for the problems. Reynolds’ Time-Averaging Concept For turbulent flow, because of the fluctuations, every velocity and pressure term in Eqs. (6.7) is a rapidly varying random function of time and space. At present our mathematics cannot handle such instantaneous fluctuating variables. No single pair of random functions V(x, y, z, t) and p(x, y, z, t) is known to be a solution to Eqs. (6.7). Moreover, our attention as engineers is toward the average or mean values of velocity, pressure, shear stress, etc., in a high-Reynolds-number (turbulent) flow. This approach led Osborne Reynolds in 1895 to rewrite Eqs. (6.7) in terms of mean or time-averaged turbulent variables. The time mean u of a turbulent function u(x, y, z, t) is defined by 1 T u T u dt (6.8) 0 where T is an...
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