Chapter 2, Problem 2.1P

To determine

Find the porosity of the rock.

Answer to Problem 2.1P

The porosity of the rock is $\underset{\_}{0.054}$.

Explanation of Solution

Given information:

A mass of dry rock (M) is 2,450 kg.

The volume of dry rock (V) is $0.925{\text{m}}^{\text{3}}$.

The specific gravity of the rock mineral $\left(G_s\right)$ is $2.80$.

Consider the density of water $\left({\rho }_w\right)$ is $1,000\text{kg}/{\text{m}}^3$.

Calculation:

Determine the dry density of rock minerals ${\rho }_d$.

$\begin{array}{c}{\rho }_d=\frac{M}{V}\\ =\frac{2,450}{0.925}\\ =2,648.6{\text{kg/m}}^{\text{3}}\end{array}$

Determine the void ratio $\left(e\right)$ using the relation.

$\begin{array}{l}{\rho }_d=\frac{G_s{\rho }_w}{1+e}\\ 2,648.6=\frac{2.80\times 1,000}{1+e}\\ e=\frac{2.80\times 1,000}{2,648.6}-1\\ e=0.0571\end{array}$

Determine the porosity $\left(n\right)$ using the relation.

$\begin{array}{c}n=\frac{e}{1+e}\\ =\frac{0.0571}{1+0.0571}\\ =0.054\end{array}$

Therefore, the porosity of the rock is $\underset{\_}{0.054}$.