Flow equations based on temp changes

[MarkChan]

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?

 

[dtn6770]

Your initial flow rate equation is missing a gravity term...sqrt(2g(p2-p1)/rho). Do a unit analysis to make sure you end up with what you want. If you're dealing with compressible fluids (gases or vapors) you'll need a net expansion factor (Y) multiplier.

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.

 

[MarkChan]

The fluid is incompressible. And as for as the density, I am lost too. I was hoping to find more information from forum members on this because I was unsure of the equation I found. Is it fluid specific? I am not sure if hydraulic oil fits into a general equation, or if each oil has its own specific equation.

 

[BigInch]

The equation you're wondering about looks like a rough method of approximating the fluid density with temperature change based on the coefficient of volumetric thermal expansion of the fluid.

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

 

[MarkChan]

Thanks for the info BigInch. Pressures range from 2000 to 2500 psi, so should I be taking Y into account at this range?

 

[BigInch]

Might not hurt. Its in the range where it could matter. I forgot you only seem to be sizing an orifice, so I quess it really only depends on how accurately you must measure the flow (I guess that's the ultimate objective). Start with a bulk modulus of around 225,000 psi and see if it looks like it will make any difference to your measurement requirements.

Let me know if you have a hard time finding the expansion coefficient value.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[Latexman]

What's the temperature range of the hydraulic oil?

Good luck,
Latexman

 

[CJKruger]

MarkChan,

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).

 

[BigInch]

Is one of those the beveled or square edge shape factor? Weep hole would only be for gas, right, or is that something else?

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[CJKruger]

BigInch,

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.

 

[MarkChan]

Latexman:

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.

 

[BigInch]

Thought so, just that you mentioned the tap effect but didn't mention the edge effect.

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

 

[Latexman]

In practice, Y, the expansion factor, corrects for the change in gas density as it expands adiabatically from p1 (upstream tap pressure) to p2 (downstream tap pressure).

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

 

[dcasto]

Have the orifice plate Flow Calc'd from the vendor if you are worried about C