Solution to Exercise 8

William W. Woessner; Eileen P. Poeter

Solution to Exercise 8

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

Using Equation 45 in this book

S_s = ρg (α + n_eβ)

where:

S_s	=	specific storage (1/L)
α	=	compressibility of the aquifer solid structure (T²L/M)
n_e	=	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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