Entrance flow in conduits (a) Estimate the entrance length
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Entrance flow in conduits (a) Estimate the entrance length for laminar flow in a circular tube. Assume that the boundar
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Entrance flow in conduits (a) Estimate the entrance length for laminar flow in a circular tube. Assume that the boundary-layer thickness S is given adequately by Eq. 4.4-17, with v8 of the flat-plate problem corresponding to vmax in the tube-flow problem. Assume further that the entrance length Le can be taken to be the value of x at which S = R. Compare your result with the expression for Le, cited in S2.3 namely, Le, = 0.035D Re. (b) Rewrite the transition Reynolds number xv8/v = 3.5 x 105 (for the flat plate) by inserting d from Eq. 4.4-17 in place of x as the characteristic length. Compare the quantity dv8/v, thus obtained with the corresponding minimum transition Reynolds number for the flow through long smooth tubes. (c) Use the method of (a) to estimate the entrance length in the flat duct shown in Fig. 4C.1. Compare the result with that given in Problem 4C.1 (d).
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