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# How to Predict Darcy and Forchheimer Coefficients for Perforated Plates Using Experimental Data?

## Objective

The objective of this practice is to explain how to predict Darcy and Forchheimer coefficients for perforated plates through curve-fitting, using experimental data.

### Curve Fitting Approach

Pressure loss through the porous media is calculated by the following equation:

$\Delta&space;P&space;=&space;\mu&space;\cdot&space;d&space;\cdot&space;L&space;\cdot&space;u&space;+&space;\frac{\rho&space;}{2}&space;\cdot&space;f&space;\cdot&space;L&space;\cdot&space;u^{2}$

Using the experimental data (Pressure loss vs. velocity) one can use curve fitting method to extract d and f coefficients.

To create a curve, minimum three data points are needed. Using the curve-fitting method, A and B coefficients (then d and f) will be predicted. The more data points you have, the more accurate the predictions can be.

 u [m/s] dP [Pa] 1 9.88 2 33.62 4 123.33 8 478.56 16 1852.84

One can use spreadsheet solvers or online curve fitting tools or any other curve fitting software. Just type the pressure versus velocity values from experimental data and let the solver predict A and B coefficients. In the following picture, an online tool (MyCurveFit) is used to predict A and B by user defined equation (Y=A*x+B*x^2). While Y values represent pressure drop, X values represent velocity. In this example, A and B coefficients are predicted as 7.4 and 6.4 respectively.
Once A and B coefficients are found, extract Darcy (d) and Forchheimer (f) coefficients from the following equations:$\mathbf{d}&space;=&space;\frac{A}{\mu&space;\cdot&space;L}$
$\mathbf{f}&space;=&space;\frac{2B}{\rho&space;\cdot&space;L}$

You can use this spreadsheet to calculate d and f. Please use the page “Curve-fitting Method”.

Last updated: July 7th, 2020