Solution to Exercise 2

2) Show that n = e/(1 + e), where n is porosity and e is the void ratio.

Porosity is defined by Equation 6 of this book. And, when the effective porosity equals the interconnected porosity then VI = Vv.

\displaystyle n_e=\frac{V_I}{V_T}=\frac{V_V}{V_T}=n

Void Ratio is defined by Equation 7 of this book.

\displaystyle e=\frac{V_V}{V_S}

The total volume is the sum of the solid and the void volume.

VT = VV + VS

Using the three relationships we can show:

\displaystyle n=\frac{V_{V}}{V_{V}+V_{S}}
\displaystyle \frac{1}{n}=\frac{V_{V}+V_{S}}{V_{V}}=1+\frac{V_{S}}{V_{V}}=1+\frac{1}{e}
\displaystyle \frac{1}{n}=\frac{e+1}{e}
\displaystyle n=\frac{e}{1+e}

This matches Equation 8 of this book.

\displaystyle n=\frac{e}{1+e}

Return to Exercise 2

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Hydrogeologic Properties of Earth Materials and Principles of Groundwater Flow Copyright © 2020 by The Authors. All Rights Reserved.