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Unformatted text preview: le of Contents | Study Guide 6.6 Flow in Noncircular Ducts Flow between Parallel Plates 359 As shown in Fig. 6.14, flow between parallel plates a distance h apart is the limiting case of flow through a very wide rectangular channel. For fully developed flow, u u(y) only, which satisfies continuity identically. The momentum equation in cartesian coordinates reduces to dp dx 0 d dy gx lam du dy (6.77) subject to no-slip conditions: u 0 at y h. The laminar-flow solution was given as an example in Eq. (4.143). Here we also allow for the possibility of a sloping channel, with a pressure gradient due to gravity. The solution is 1 2 u d (p dx gz) (h2 y2) (6.78) If the channel has width b, the volume flow is bh3 3 h Q u(y)b dy h or h2 3 Q bh V d (p dx d (p dx gz) gz) 2 umax 3 (6.79) Note the difference between a parabola [Eq. (6.79)] and a paraboloid [Eq. (6.43)]: the average is two-thirds of the maximum velocity in plane flow and one-half in axisymmetric flow. The wall shear stress in developed channel flow is a constant: du dy w d (p...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.

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