## 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([latex]{\gamma }'[/latex]), specific gravity(G), void ratio(e) and unit weight of water/ density of water([latex]\gamma_{w} [/latex]).

We know,

[latex]\gamma _{sat} = \frac{W_{sat}}{V_{sat}}[/latex]

Or, [latex]\gamma _{sat} = \frac{W_{s} + W_{w}}{V_{s}+V_{v}} [/latex]

Or, [latex]\gamma _{sat} = \frac{G \gamma_{w} + e\gamma_{w} }{1+e}[/latex]

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

From the definition of submerged unit weight, we have,

[latex] {\gamma }’ = \gamma_{sat} – \gamma_{w} [/latex]

Or, [latex] {\gamma }’ = \left (\frac{G + e}{1 + e} \right )\gamma_{w} – \gamma _{w} [/latex]

Or, [latex] {\gamma }’ = \left (\frac{G – 1}{1 + e} \right )\gamma_{w} [/latex]

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