Chapter 8, Problem 12P

The Ergun equation, shown below, is used to describe the flow of a fluid through a packed bed. $\Delta P$ is the pressure drop, $\rho$ is the density of the fluid, $G_0$ is the mass velocity (mass flow rate divided by cross-sectional area), $D_p$ is the diameter of the particles within the bed, $\mu$ is the fluid viscosity, L is the length of the bed, and $\epsilon$ is the void fraction of the bed.

$\frac{\Delta P\rho }{G_o^2}\frac{D_p}{L}\frac{{\epsilon }^3}{1-\epsilon }=150\frac{1-\epsilon }{\left(D_p{G}_o/\mu \right)+1.75}$

Given the parameter values listed below, find the void fraction $\epsilon$ of the bed.

$\begin{array}{l}\frac{D_p{G}_o}{\mu }=1000\\ \frac{\Delta P\rho D_p}{G_o^{2}L}=10\end{array}$