# Relation Between Submerged Unit Weight, Specific Gravity, Void Ratio and Unit Weight of Water

## Relation Between Submerged Unit Weight, Specific Gravity, Void Ratio and Unit Weight of Water

In this article, we shall make a formula or relation between the submerged unit weight(${\gamma }'$), specific gravity(G), void ratio(e) and unit weight of water/ density of water($\gamma_{w}$).

We know,

$\gamma _{sat} = \frac{W_{sat}}{V_{sat}}$
Or, $\gamma _{sat} = \frac{W_{s} + W_{w}}{V_{s}+V_{v}}$

Or, $\gamma _{sat} = \frac{G \gamma_{w} + e\gamma_{w} }{1+e}$

Or, $\gamma _{sat} = \left (\frac{G + e}{1 + e} \right )\gamma_{w}$

From the definition of submerged unit weight, we have,

${\gamma }' = \gamma_{sat} - \gamma_{w}$

Or, ${\gamma }' = \left (\frac{G + e}{1 + e} \right )\gamma_{w} - \gamma _{w}$

Or, ${\gamma }' = \left (\frac{G - 1}{1 + e} \right )\gamma_{w}$