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

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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}

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