Buoyant Unit Weight

Written by Jerry Ratzlaff on . Posted in Geotechnical Engineering

completely dry soil 1Buoyant 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 \(\large{dimensionless}\)

 

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Tags: Equations for Weight Equations for Soil Equations for Geotechnical