Does an orifice control mass or volume flow? 5

[jennyrabbit]

I am trying to understand the effect of ambient pressure on venting a gas from a pressurized vessel. I understand that conductance of an orifice has units of torr-litre/sec. Does this mean that if there is a pressure difference of 1 psi, regardless of the absolute value of the input/output pressures, the same mass will flow? That is, if I hypothetically pressurized a vessel to 14 psia and vented it through a 1/16 inch diameter hole into a 13 psia ambient, the mass flow rate would be the same as if I vented that same vessel from an initial internal pressure of 4 psi into a 3 psi ambient? If this is the case, then an orifice controls mass flow. I'm having a hard time visualizing this as I am not a fluids person. I'm assuming that the gas is incompressible in this case, and flow is viscous. Any insight much appreciated.

 

[BigInch]

Here....play around with this until Monday.

http://www.theleeco.com/LEEWEB2.NSF/airlohms.htm!OpenPage

http://virtualpipeline.spaces.msn.com

 

[zdas04]

No, you don't quite have it right. For a fixed upstream pressure there is a corresponding downstream pressure that represents the start of maximium (or "choked") flow. Lowering the downstream pressure below this point with a constant upstream pressure will not change mass flow.

If you know the upstream density then you can calculate sonic velocity (choked flow is at 1.0 Mach) and determine volume flow rate from the orifice area.

In your example of 14 psia upstream and 13 psia downstream you would have flow, but determining the exact flow rate is a difficult exercise with questionable accuracy and poor repeatibility.

On the other hand, if your vessel was above about 25 psia (depending on your atmospheric pressure and the gas makeup) then the flow out your 1/16" hole (provided the material was suffeciently thin) would be very well known. A hole that small my not actually be an "orifice", it may be a "pipe" and subject to friction losses.

David

 

[mbeychok]

Click on ==> faq798-1196 and read it. It may help you understand choked flow.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[jennyrabbit]

Thank you very much for your replies. I took a look at the links and they don't quite fit my question. I don't think that the gas flow in my case is necessarily choked, although I could be wrong. I think it would be helpful to explain my application a bit more. I am studying the venting behavior of space telescopes on launch. The initial condition is that the telescope interior is at atmospheric pressure. On launch, the ambient pressure drops to approximately 0 in 100-200 seconds. I want to understand the flow through the orifices, which may be vents of complicated shapes. I have made mock up vents and have tested their flow characteristics with ambient pressure being 1 atm. I end up with a relationship of mass flow vs delta P (upstream - downstream pressure). The question is whether I can apply that same relationship to the same delta P, but different ambient pressure. e.g. I measure 10 g/sec at 1 psi from 14.7 psi to 13.7 psi. Will 10 g/sec also flow between 3 psi to 2 psi (assuming subsonic flow...unchoked). That's what I had meant by my original question of whether an orifice/vent controls mass flow or volume flow...Thanks again for any insights.

 

[Zapster]

For an incompressible liquid flow through an orifice remains the same for a constant differential pressure across an orifice. No difference in flow (either mass or volumetric) between 14psia let down to 13 psia and 4 psia let down to 3 psia because a given mass of the liquid will always have the same volume.

Your original post states that, “I'm assuming that the gas is incompressible in this case, and flow is viscous.” This is not a valid assumption for any gas when there are significant changes in pressure. Do not make that assumption.

Does this mean that if there is a pressure difference of 1 psi, regardless of the absolute value of the input/output pressures, the same mass will flow? No, not for a gas. You have a transient analysis where the density of the gas changes with time.

 

[mbeychok]

jennyrabbit:

Read this website page:

http://www.air-dispersion.com/source.html

which leads you to either the metric or USA versions of an article entitled Source Terms For Accidental Discharge Flow Rates.

It discusses and explains the gas discharge mass flow rate for non-choked flow as well as for choked flow of gases.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[25362]

Beside some factors which depend on the prevailing T,P conditions, and the orifice geometry, the mass flow rate is proportional to [√]([ρ][×][Δ]P).

For the same orifice and the same [Δ]P it would be proportional to [√][ρ], where [ρ] is the upstream density.

The volumetric flow rate, would, of course, be proportional to [√](1/[ρ]).

 

[jennyrabbit]

Thanks again to all of you. I read more of Milton's link, and it looks like mass flow depends on the square root of the product of density and upstream pressure, not square root of product of density and delta P...This isn't what 25362 posted. The full equation in Milton's post does have additional factors in the square root which are ratios of upstream/downstream pressures, but not delta P's. The point was made earlier that if I have a very small hole in a plate, it is probably more reasonably modeled was a tube. I agree with this, but am trying to get the fundamentals figured out first. I have a much better gut understanding if molecular flow than viscous flow. With molecular flow, I can visualize the impingement of individual molecules at an orifice zipping through. With viscous flow, I understand there is a boundary layer, but I don't understand under what conditions I must consider compressibility. In my application, I will never have more than 1 psi difference between upstream and downstream pressures. Do I have to consider compressibility? it seems the equations are more complicated!

 

[jennyrabbit]

Also, is the discharge coefficient of an orifice or vent independent of pressure or flow rate? Is it just a geometric thing?

 

[Latexman]

You may never have more than 1 psi [Δ]P, but as the telescopes approach 0 psia won't the mechanism change to molecular flow?

Good luck,
Latexman

 

[jennyrabbit]

You are correct, Latexman. But at that point, I'm not worried about the telescope blowing up. ; )

 

[25362]

Visit:

http://www.flowmeterdirectory.com/flowmeter_orifice_calc.html

or

http://www.efunda.com/formulae/smc_fluids/calc_orifice_flowmeter.cfm

 

[sterl]

Fundamental Answer: Orifice as Choked Orifice, Volume Flow. Orifice at ratio of pressures less than critical ratio: Not Choked, still Volume Flow device. Area constant to a third order approximation; Integral of Velocity over Area is Volume Flow.

Orifice bleeding down a fixed volume to a varying pressure O/S is a Fixed Volume analysis, solve according to velocity as profiled across area. Boundary layer effects can then be incorporated if length and diameter, viscoisty and density indicate boundary layer actually developed. Solving as decay of starting mass contained is going to complicate the topic.

Develop equation as model for dV/dt and integrate toward V total....

 

[Latexman]

Based on the telescope construction, how many "resistances" does the air have to pass thru to get outside? One? Several? Or, does it depend on which internal volume (compartment) the air originates from? I.e., some have one resistance and some have several?

We've been putting telescopes and other satellites in space for several decades. Have you searched NASA (1958 - present) and the old NACA (1917 - 1958) collections? They are public records and are at:

http://ntrs.nasa.gov/search.jsp

Why struggle over "complicated shapes"? Just assume all the compartments are air tight and add vent holes (circular) where they are needed.

Good luck,
Latexman

 

[Latexman]

As for the subject question, an orifice is simply a restriction to flow. Mass flow and volumetric flow are related by the continuity equation and PVT relationship.

Have you considered CFD?

Good luck,
Latexman

 

[GregLamberson]

I've been reading this thread with interest and have learned allot, but have a question (related to the thread - no hijacking) - is mass measurement not a better alternative to volume measurement in many cases, custody transfer? Am i correct that mass measurement does not require the correlation of temperature, pressure, and empirical data as would volume measurement?

Greg Lamberson, BS, MBA
Consultant - Upstream Energy
Website:

http://www.oil-gas-consulting.com

 

[BigInch]

Mass measurement correlates a signal to density and, since products are not sold by density, correlation of the product's density at the measured temperature to volume and/or weight is still necessary.

http://virtualpipeline.spaces.msn.com

 

[jennyrabbit]

I am also enjoying this thread. More comments. Amazingly, there is only one article in the literature that I have found on flow through orifices at reduced pressures, and the famous rule of thumb of venting 1 cubic foot through a 1/4 inch diameter vent. The whole aerospace industry uses that. Unfortunately, to your point, Latexman, we don't want to use circular orifices because we want to block light and particulates. We also use various types of filters which inhibit flow. I would love it if orifices were mass flow devices independent of upstream pressure because then I would just measure mass flow into atmospheric pressure and use that mass flow in my models. I know that is not the case, but I'm not convinced an orifice is only a volume control device either. I'm not sure on that one yet, and have not followed all the links provided to me so far. Being an experimentalist by heart, I believe that experimental results are essential in this case, but I still want to understand flow a bit better. The continuity equation doesn't really satisfy my more molecular based thinking. I'm a condensed matter physicist.

 

[BigInch]

Jenny, I'm not sure what you mean with this "mass or volume controled" question. An orifice, like a control valve, does not control either flow or pressure. Both allow a certain passage of mass based on the pressure differential... nothing else. A control valve's controls may be configured to change the orifice properties such that it attempts to maintain a certain pressure, upstream, downstream or differential across two points, or a set flowrate at some measurement point, if its configured for flowrate control. How they are configured is simply a matter of what signal they read.

http://virtualpipeline.spaces.msn.com