0008 we can guess f and iterate until the velocity

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Unformatted text preview: ocity or the flow rate. We cannot know both, or else we could immediately compute d 4Q/( V). Let us assume that we know the flow rate Q. Note that this requires us to redefine the Reynolds number in terms of Q: Red Vd 4Q d (6.67) Then, if we choose (Q, , ) as scaling parameters (to eliminate d), we obtain the functional relationship 4Q d Red fcn gh f , L5 Q (6.68) and can thus solve d when the right-hand side is known. Unfortunately, the writer knows of no formula for this relation, nor is he able to rearrange Eq. (6.64) into the explicit form of Eq. (6.68). One could recalculate and plot the relation, and indeed an ingenious “pipe-sizing” plot is given in Ref. 13. Here it seems reasonable to forgo a plot or curve fitted formula and to simply set up the problem as an iteration in terms of the Moody-chart variables. In this case we also have to set up the friction factor in terms of the flow rate: f hf gh f d 5 8 LQ2 2 d 2g L V2 (6.69) The following two examples illustrate the iteration. EXAMPLE 6.11 0.342 m3/s and 950 kg/m3, Work Example 6.9 backward, as...
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