Specific Gravity of Sludge

Sludge density is not a weighted average of the components, it is a weighted average of their reciprocals — because volumes add, not densities. Split a kilogram of sludge into its dry solids and its water, work out the volume each occupies, add them, and you get this reciprocal form. Five percent solids of specific gravity 2.5 gives 1/S = 0.05/2.5 + 0.95 = 0.97, so the sludge is only 1.031 times as dense as water despite containing solids two and a half times as dense.

That result is the point: at ordinary solids contents, sludge is essentially water and any pump, tank or truck calculation that treats it as much heavier will be wrong in an expensive direction. Use $S_s$ ≈ 1.4 for volatile organic solids, 2.5–2.65 for grit and inorganic solids, and something in between for a mixed primary sludge — Metcalf & Eddy's worked examples typically land on 1.25–1.45 for digested biosolids. The relation is worth carrying because it also runs backwards: measure the wet sludge density with a hydrometer or a weighed graduated cylinder, know the solids percent from the drying oven, and this equation tells you the specific gravity of the solids themselves, which is a direct read on how much grit has found its way into a supposedly organic sludge.