Flow equations based on temp changes
Flow equations based on temp changes
(OP)
I am not a fluids person, so I want to make sure this is right. I want to measure the flow of a fluid through an orifice by means of differential pressure. I also want to take temperature changes into consideration for density.
So if
Q = Cf Ao sqrt(2(p2-p1)/rho)
where Q = volumeteric flow, Cf = flow coefficeint of the orifice, Ao = orifice diameter, and rho = density
And
rho1 = rho0/(1+B(t1-t0))
where rho0, t0, and B are speced by the fluids manufacture and T1 is measureable,
Then
Q = Cf Ao sqrt(2(p2-p1)/(rho0/(1+B(t1-t0))))
Is this correct?
So if
Q = Cf Ao sqrt(2(p2-p1)/rho)
where Q = volumeteric flow, Cf = flow coefficeint of the orifice, Ao = orifice diameter, and rho = density
And
rho1 = rho0/(1+B(t1-t0))
where rho0, t0, and B are speced by the fluids manufacture and T1 is measureable,
Then
Q = Cf Ao sqrt(2(p2-p1)/(rho0/(1+B(t1-t0))))
Is this correct?





RE: Flow equations based on temp changes
As for your handling of the density, you lost me. Density is a temperature dependent variable but I'm hard pressed to recognize your equation which I imagine (?) is specific to the fluid in question. Sorry, I can't help you on that part.
RE: Flow equations based on temp changes
RE: Flow equations based on temp changes
Density_1 = Density_0 / (Thermal_coefficient_of_volumetric_expansion * (T1-T0))
Each oil will have their own value for B, which usually follows pretty closely as a function of either specific gravity or specific density of the oil.
As you will find out, oil at high pressure is not incompressible.
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Flow equations based on temp changes
RE: Flow equations based on temp changes
Let me know if you have a hard time finding the expansion coefficient value.
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Flow equations based on temp changes
Good luck,
Latexman
RE: Flow equations based on temp changes
For accurate equations, get yourself a copy of Spinks or Miller. The equation (in metric units) are:
W = 0.01251 * K * d^2 * Fa * (rho * hw)^0.5
K = C / (1 - Beta^4)^0.5.
W = Mass flow in kg/h
d = Bore in mm
Fa = thermal expansion correction factor
hw = dP in mm H2O
rho = Actual flowing density in kg/m3
K is different depending on whether you have flange taps or pipe taps (permanent dP).
So, temperature has several effect:
1) It changes Fa, as the bore changes.
2) It changes density (rho), as does a change in pressure. Not a lot for liquids, but can be significant.
3) Liquid flow is often expressed in Standard Conditions. Which means: Q_std = W / rho_std. If this is what you are doing, then only rho should be compensated for temperature changes.
Also note that I excluded some other correction factors (Fc, F weep hole, etc).
RE: Flow equations based on temp changes
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Flow equations based on temp changes
These equations assume the effect of orifice geometry (square, quadrant edge, thick plate, etc) is included in the K or C value. Thus, C is different for a thin plate (beveled if necessary), than a thick plate orifice.
Some people put a weep hole at the top for liquids, and bottom for gases. Think one can argue how effective it is, especially in fouling services.
RE: Flow equations based on temp changes
Fluid temperatures range from ambient to 150 F. I cannot accurately define ambient, because what is ambient in Alaska is not ambient in Texas.
CJ, I will look into Spinks/Miller, thank you.
RE: Flow equations based on temp changes
I've put vents and drains there though as you have the taps anyway. Never felt I had to use weep holes. Weep hole and bubble hole then, huh? Well... why not? The techs gotta get it installed with the right allignment though.
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Flow equations based on temp changes
Liquid flows are normally considered incompressible, except for certain calculations in hydraulic transient analysis where compressibility effects are important even for nearly incompressible liquids with extremely small density variations.
Since you said you are measuring flow through an orifice meter, I'd recommend using Y = 1, which is the normal practice for liquids.
Good luck,
Latexman
RE: Flow equations based on temp changes