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FIGURE 8 Variation of v50 with viscosity

FIGURE 8 Variation of v50 with viscosity

Projection to the central axis gives Vsm = 8.7 ft/s (2.65 m/s) for sand-weight material. This number is joined to the relative density S (i.e. Ss) of 4.4 on the sloping axis and projected to the right-hand axis to give Vsm = 13 ft/s (4.0 m/s) for the magnetite.

b. Find the hydraulic gradient im for a volumetric solids concentration of 0.10 and a throughput velocity Vm = 16.4 ft/s (5.0 m/s). Assume rather angular material with B' = 0.9. The first step is to calculate the clear-water friction gradient of iw. Using fw = 0.013, iw is given by 0.013Vm/2gD or 0.033 (height of water per length of pipe). To this must be added (im — iw), which Eq. 20 gives as (Sm — 1)B'(Vm/0.55Vsm)—025. The quantity (Sm — 1) equals Cv(Ss — 1) i.e. (0.10)(3.4) = 0.34. B' has been taken as

0.9 and the ratio (Vm/0.55Vsm) equals 2.27, giving (im — iw) = 0.250 and im = 0.28,

1.e. 28 ft of water per 100 ft of line or 0.28 m of water per m of line. Very large gradients like this, which have been verified in prototype-scale testing, show why fully-stratified flow is only of interest for short-haul applications.

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