- #1
OldStudent0382
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Homework Statement
Derive an analytical expression for the permeability (k) of the structured porous medium (which is a size selective filter) constituted by a periodic array of cylinders of diamter d separated by a distance h = 1.8d
Homework Equations
Q=k*(μ/A)*(Δp/L)
Q = volumetric flow rate
k= media permeability
μ=fluid viscosity
A=cross sectional area
L=length between inlet and outlet
Δp=pi-po
Please note that h should be 1.8d and not 0.8d
The Attempt at a Solution
I'm not sure where to start with this, since I can't even seem to get the units to work out given the equation for the volumetric flow rate.
My first attempt was to take the cross sectional area of 1 cylinder (since 1 array consists of 1 quarter of 4 cylinders and divide by the cross section of the array (1.8^2 * d^2), then multiply by the average velocity of the flow through 1 of the cylinders (which I found to be 31.25 m/s)
I am at a complete loss as to how to approach this problem. I know I'm overlooking something very basic.
THANK YOU!