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Specific Gravity for a Solids Slurry Formulae and Calculator

Civil Engineering Application & Design Resources

Specific Gravity for a Solids Slurry Formula and Calculator

Eq.1
${\displaystyle S=\frac{W_w+W_s}{(W_w/1.00)+(W_s/S_s)}}$

where

S = specific gravity of wet sludge
W_w = weight of water (lb)
W_s = weight of dry solids (lb)
S_s = specific gravity of dry solids

The volume of waste sludge for a given amount of dry matter and concentration of solids is given by

Eq. 2
${\displaystyle V=\frac{W_s}{(s/100)\cdot <!--\; \cdot \; -->\mathrm{\gamma <!--\; \gamma \; -->}\cdot <!--\; \cdot \; -->S}=\frac{W_s}{[(100-<!--\; -\; -->p)/100]\cdot <!--\; \cdot \; -->\mathrm{\gamma <!--\; \gamma \; -->}\cdot <!--\; \cdot \; -->S}}$

Where

V = volume of sludge, ft³ (gal) [m³]
W_s = weight of dry solids (lb or kg)
s = solids content (%)
γ = unit weight of water, 62.4 lb/ft³ (8.34 lb/gal) [1,000 kg/m³]
S = specific gravity of wet sludge
p = water content (%)

Reference
NCEEA Fundamentals of Engineering (FE) exam Handbook 2020

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