We can look at flow between flat plates in the same way. Many layered materials can be modeled in this way and a particular experimental set-up for studying fluid dynamics, the Hele-Shaw cell, is made in this configuration to make it easy to visualize the flow. The situation is shown in Figure P2.4. The two plates are stationary and so the velocity takes on a profile that is defined by:

\[v_{x}(y)=\frac{P_{\text {in }}-P_{\text {out }}}{2 \mu L}\left(y^{2}-h y\right)=\frac{\Delta P}{2 \mu L}\left(y^{2}-h y\right)\]

Darcy's Law basically posits a relationship between the average velocity through the medium and the pressure drop, $\Delta P / L$. Calculate the average velocity between $y=0, h$ and compare that with Darcy's law for the velocity to determine the permeability of the medium.

Transcribed Image Text:

FIGURE P2.4 P. LD L vx(y) P h y Z out S X