Buoyant Unit Weight

Buoyant unit weight, abbreviated as \( \gamma ' \), also called effective unit weight or submerged unit weight, is the unit weight of a submerged object minus saturated weight of the object.

 

Buoyant Unit Weight formulas

\(\large{ \gamma ' =  \gamma_{sat} - \gamma_w   }\)
\(\large{ \gamma ' =  m \;  \left( 1 - \frac{ \rho_o }{ \rho_f }   \right)   }\)
\(\large{ \gamma ' =  \frac{ SG_s \; \gamma_w \;-\; \gamma_w }{ 1 \;+\; e }   }\)
\(\large{ \gamma ' =  \frac{ \left( SG_s \;-\; 1 \right) \; \gamma_w  }{ 1 \;+\; e }   }\)
\(\large{ \gamma ' =  \frac{ \left( SG_s \;+\; e \right)  \; \gamma_w  }{ 1 \;+\; e } \;-\; \gamma_w  }\)
\(\large{ \gamma ' =  \frac{ \left( SG_s \;+\; e \right)  \; \gamma_w \;-\; \left( 1 \;+\; e \right)  \; \gamma_w  }{ 1 \;+\; e }  }\)
\(\large{ \gamma ' =  \frac{ SG_s \; \gamma_w \;+\; e \; \gamma_w \;-\;  \gamma_w  \;-\; e \; \gamma_w    }{ 1 \;+\; e }  }\)

Where:

Units	English	Metric
\(\large{ \gamma ' } \)  (Greek symbol gamma) = buoyant unit weight	\(\large{ \frac{lbm}{ft^3} }\)	\(\large{ \frac{N}{m^3} }\)
\(\large{  \rho_f } \)  (Greek symbol rho) = density of fluid	\(\large{ \frac{lbm}{ft^3} }\)	\(\large{ \frac{kg}{m^3} }\)
\(\large{  \rho_o } \)  (Greek symbol rho) = density of object	\(\large{ \frac{lbm}{ft^3} }\)	\(\large{ \frac{kg}{m^3} }\)
\(\large{ m } \) = mass of object	\(\large{lbm}\)	\(\large{kg}\)
\(\large{ \gamma_{sat} } \)  (Greek symbol gamma) = saturated unit weight	\(\large{ \frac{lbm}{ft^3} }\)	\(\large{ \frac{N}{m^3} }\)
\(\large{ SG_s }\) = specific gravity of soil	\(\large{dimensionless}\)
\(\large{ \gamma_w }\)  (Greek symbol gamma) = unit weight of water	\(\large{ \frac{lbm}{ft^3} }\)	\(\large{ \frac{N}{m^3} }\)
\(\large{ e }\) = void ratio	\(\large{dimensionless}\)