Solution to Exercise 8

8) Show that the units of Ss are 1/L.

Using Equation 45 in this book

Ss = ρg (α + neβ)

where:

Ss = specific storage (1/L)
α = compressibility of the aquifer solid structure (T2L/M)
ne = effective porosity (dimensionless)
β = compressibility of water (T2L/M)

checking units:

\displaystyle S_{s}: \frac{\textup{M}}{\textup{L}^3}\frac{\textup{L}}{\textup{T}^2}\left(\frac{\textup{T}^2\textup{L}}{\textup{M}}+\frac{\textup{L}^3}{\textup{L}^3}\frac{\textup{T}^2\textup{L}}{\textup{M}}\right)
\displaystyle S_{s}: \frac{\textup{M}}{\textup{L}^{2}}\frac{1}{\textup{T}^2}\left(\frac{\textup{T}^2\textup{L}}{\textup{M}}+\frac{\textup{T}^2\textup{L}}{\textup{M}}\right)
\displaystyle S_{s}: \frac{\textup{M}}{\textup{L}^2\textup{\textup{T}}^2}\left(\frac{\textup{T}^2\textup{L}}{\textup{M}}\right)
\displaystyle S_{s}: \frac{1}{\textup{L}}

Return to Exercise 8

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