# Buoyant Unit Weight

Written by Jerry Ratzlaff on . Posted in Geotechnical Engineering

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 $$\large{dimensionless}$$