Density of air for calculating the mass flow rate from Darcy's law
Density of air for calculating the mass flow rate from Darcy's law
(OP)
Hi,
I use Darcy's law to calculate first the volumetric flow rate of air through a porous material. From this I want to calculate the mass flow rate namely the product of the volumetric flow rate and the density. However the density is function of the pressure. Is it right the use the mean pressure of the input and output pressure in order to calculate the density of air?
I use Darcy's law to calculate first the volumetric flow rate of air through a porous material. From this I want to calculate the mass flow rate namely the product of the volumetric flow rate and the density. However the density is function of the pressure. Is it right the use the mean pressure of the input and output pressure in order to calculate the density of air?





RE: Density of air for calculating the mass flow rate from Darcy's law
Furthermore, the output condition is probably a better indicator of the porous material performance
RE: Density of air for calculating the mass flow rate from Darcy's law
David
RE: Density of air for calculating the mass flow rate from Darcy's law
Pavg = 2/3 * (P1+P2 - P1*P2/(P1+P2))
Assuming that your porous medium has a pressure drop similar to a gas pipeline.
We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer
RE: Density of air for calculating the mass flow rate from Darcy's law
RE: Density of air for calculating the mass flow rate from Darcy's law
Good luck,
Latexman
RE: Density of air for calculating the mass flow rate from Darcy's law
David
RE: Density of air for calculating the mass flow rate from Darcy's law
Read my original question again
I use Darcy's law to calculate first the volumetric flow rate of air through a porous material. From this I want to calculate the mass flow rate namely the product of the volumetric flow rate and the density. However the density is function of the pressure. Is it right the use the mean pressure of the input and output pressure in order to calculate the density of air?
RE: Density of air for calculating the mass flow rate from Darcy's law
Good luck,
Latexman
RE: Density of air for calculating the mass flow rate from Darcy's law
You can't use a pressure difference for calculating the density! Therefore my question which 'absolute' pressure value which I have to use to calculate the density!
RE: Density of air for calculating the mass flow rate from Darcy's law
The equation is only really valid for constant density, which is why you can not find anything to tell you which density to use.
You might get away with using it for slow flow of gas with a small pressure drop.
Matt
RE: Density of air for calculating the mass flow rate from Darcy's law
Good luck,
Latexman
RE: Density of air for calculating the mass flow rate from Darcy's law
Have you determine whether the expansion of the gases is either of the following:
isothermal - p/ρ = constant
isentropic or adiabatic - p /ρ^k = constant
polytropic - pV^n = constant
Is the input area ands the output area the same? If not, what are their areas.
Do you have a manufacturer and catalog number for this porous air bearing?
RE: Density of air for calculating the mass flow rate from Darcy's law
I'm making a numerical model for porous air bearings, so I don't have a manufacturer.
In my model I assume isothermal behaviour of the gas, thus p/rho = cst!
You can assume that the input and output area is the same!
The equation of Darcy I use is like the first equation on Wikipedia:
http://en.wikipedia.org/wiki/Darcy's_law
RE: Density of air for calculating the mass flow rate from Darcy's law
Good luck,
Latexman
RE: Density of air for calculating the mass flow rate from Darcy's law
RE: Density of air for calculating the mass flow rate from Darcy's law
Either pressure, at either end of the pressure drop, presuming you have the temperature value there as well. The mass flow in and out should be the same.
RE: Density of air for calculating the mass flow rate from Darcy's law
What is the Reynold number do you calculate?
Matt
RE: Density of air for calculating the mass flow rate from Darcy's law
Calculating the density at any pressure will give you the mass/unit volume, but it will not give you the mass flow rate. Even if you use the average pressure, you will only get the average density.
The different pressures at various points will all have different respective densities, and instantaneous pressure drops at those points as well, which will integrate into the overall pressure drop across the medium, but he's not interested in finding that. Problem is that density at any point cannot be related to mass flow rate. You need to use a pressure drop to flow rate relationship, one either for dP vs volumetric flow rate, or dP vs mass flow rate and solve for mass flow rate to find out what the mass flowrate is.
To do that, the easiest way would be to use Inlet Pressure and the Outlet Pressure, calculate the differential pressure, relate that to flowrate. If you used a dP to mass flowrate relationship, you're finished, otherwise you'd have to continue by calculating the density (presumedly at the overall average pressure) and relate that density to your volumetric flowrate to get the mass flowrate as the final answer.
Got it?
We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer
RE: Density of air for calculating the mass flow rate from Darcy's law
RE: Density of air for calculating the mass flow rate from Darcy's law
Is the density being calculated within each finite difference? Or, is the density calculated as boundary conditions or limits? The correct answer depends on which one.
So, is this an undergraduate or postgraduate assignment?
Good luck,
Latexman
RE: Density of air for calculating the mass flow rate from Darcy's law
Matt
RE: Density of air for calculating the mass flow rate from Darcy's law
In original form it was for developed for simple incompressible fluids, but as is also stated there, if you didn't know already, is that it is used to describe flow of water, oil and gas through petroleum resevoirs, so it certainly can be made applicable to complex compressible flows. You just have to be able to somehow calculate the density and find the appropriate relationships of density to shear force of your fluid, viscosity. You only need the equation of state for your fluid, relating density to it's state of pressure and temperature, and viscosity to that density and temperature.
We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer
RE: Density of air for calculating the mass flow rate from Darcy's law
S/He doesn't appear to be interested in knowing if s/he's using the right formula or method. S/He also doesn't appear willing to share other information about the problem -- though a lot of exclamation marks appear which gave the impression that drir thought all the people trying to read his/her mind were idiots for not providing him/her with the obviously simple YES answer s/he wanted.
I would suggest that drir go find a Crane Technical Paper 410, "Flow of Fluids Through Valves, Fittings and Pipes." That way s/he can come to a conclusion based on facts rather than wishful thinking or mind reading. Note I recognize that Crane might not be a perfect fit, but it has a lot of information about when Darcy's is applicable and provides other formulae for when it's not. It also provides the answer to the question about whether the mean pressure should be used (by the way, it's not (P1 + P2)/2. Crane also has a different weighted average than that given by BigInch -- but it applies to more situations than gas pipelines.)
Patricia Lougheed
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RE: Density of air for calculating the mass flow rate from Darcy's law
I sensed that too, but I'm practicing self-control this week.
Good luck,
Latexman
RE: Density of air for calculating the mass flow rate from Darcy's law
As we have also found, the arithmatic mean pressure would only apply to his/her situation, if the pressure drop was linear and that average mass rate through the system were to be some known function of the observed pressure drop. Those can be easily related in the context of limited scenarios, such as gas through a pipe, but is actually quite a stretch, if there are no constraints applied, which consequently resulted in some controversy moving along the rocky road to the "answer" we have gotten to so far.
We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer
RE: Density of air for calculating the mass flow rate from Darcy's law
http://
For compressible flow through porous media
h
RE: Density of air for calculating the mass flow rate from Darcy's law
If you wish, and when the fluid is other than water at standard conditions, the conductivity is replaced by the permeability of the media. The two properties are related by,
K = kρ g / μ = kg / ν
ρ = density
http://bioen.okstate.edu/Darcy/LaLoi/basics.htm
Is this really important now?
We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer
RE: Density of air for calculating the mass flow rate from Darcy's law
Katmar Software - Engineering & Risk Analysis Software
http://katmarsoftware.com
"An undefined problem has an infinite number of solutions"
RE: Density of air for calculating the mass flow rate from Darcy's law
We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer
RE: Density of air for calculating the mass flow rate from Darcy's law
Here I'm back with the solution I was looking for. I made the equation independent of the 'unknown' density. The mass flow rate through an porous media for an isothermal fluid is equal to
[itex]\beta\beta[/itex]
RE: Density of air for calculating the mass flow rate from Darcy's law
Here I'm back with the solution I was looking for. I made the equation independent of the 'unknown' density. The mass flow rate through an porous media for an isothermal fluid is equal to
1/2 * rho_s/p_s * k/viscosity * (p_s^2 - p_a^2)/length * surface
k = permeability
p = pressure
rho = density
s = supply
a = ambient
Thanks everyone for the helpful feedback!
RE: Density of air for calculating the mass flow rate from Darcy's law
Good luck,
Latexman
RE: Density of air for calculating the mass flow rate from Darcy's law
RE: Density of air for calculating the mass flow rate from Darcy's law
Good luck,
Latexman