## Sm Sf2 U22 a V50

If test data are available, M and V50 can be obtained directly from the results. For example consider the data of Figure 7 in the 8 in. (0.20 m) pipe. In calculating the ratio (im — iw)/(Sm — 1), the clear water gradient iw has been used to approximate if, and Sf is Sw, i.e. 1.0. The value of iw was calculated from the Darcy-Weisbach formula using the friction factor ff = 0.013 measured previously for flows of water in this pipe. The plotted points fall on an essentially straight line on Figure 7. This behavior corresponds to Eq. 22. The slope of the line gives M — 1.7, which is typical for slurries with narrow particle grading. The point on the line where (im — iw)/(Sm — 1) = 0.22 gives V50, which is approximately 9 ft/s (2.8 m/s).

With V50 and M obtained for the 8 in. (0.20 m) pipe, scale-up to a larger pipe diameter can be carried out. The larger diameter of 18 in. (0.44 mm) has been selected because data are available with the same sand in this larger pipe (Clift et al., 1982) and thus the scaled-up results can be verified directly. In fact, as seen on Figure 7, the fit line for the larger pipe coincides with that for the smaller pipe in this instance. In this case the clear-water friction factor fw was found to be the same for both pipes and in both pipes the particle size d was a small fraction of the pipe diameter. It has been found that V50 should vary with (8/fw)1'2; it should also depend on the diameter ratio d/D (Wilson & Watt, 1974; Wilson et al., 1997).

These factors can be incorporated in the scale-up procedure, which involves preparing curves of im versus Vm for various values of Cvd in the larger pipe, the relation for each line of constant Cvd being expressed as ## Survival Treasure

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