8 replies to this topic

[mbeychok]

Guest:

Visit this website by clicking on this link ==> www.air-dispersion.com/source.html and then select whether you want SI metric units or the customary USA units. That will take you to the page that uses the selected units.

Then click on "Gas Discharge From a Pressure Source" and you will find a detailed explanation of choked flow for gases ... as well as the equations to be used for calculating the mass flow rate when the gas flow is choked.

Please note that the above referenced web site applies only to choked flow for a gas.

[mbeychok]

Guest:

[ It is important to note that although the gas velocity reaches a maximum and becomed choked, the mass flow rate is not choked. The mass flow rate can still be increased if the source pressure is increased. ]Could you please explain to me why the mass flow can still go up?

Look at the equation for the choked velocity of a gas ... you will see that increasing the upstream (source) pressure increases the mass flow rate of a gas even at choked flow conditions. Why? Because increasing the pressure increases the gas density and therefore the mass flow increases even though the velocity is at a maximum (i.e., sonic velocity).

Does this apply to liqud fluid too? If so, I don't really have to worry about sonic flow as long as it can pass through all the mass I want it, right?

I don't know the answer to these questions. The equations I referenced you to are strictly for gases. Sonic flow of a liquid is a different story. I suggest you read a good textbook on fluid flow ... or perhaps someone else partcipating on this forum can help you with that.

[mbeychok]

Guest:

You are much too focused on your specific application of a recycle line from your pump discharge to your pump suction.

(1) Again, the equation to which I referred you applies only to gas flows and it applies to many different situations other than the one upon which you are focused.

(2) Assume that we had two identical vessels filled with gas and each vessel had identically sized holes from which gas could escape to the ambient atmosphere. Let us also assume that the gas absolute pressure in vessel A was 3 atmospheres and the gas absolute pressure in vessel B was 6 atmospheres.

Since the pressure in each vessel is more than twice the downstream pressure of the ambient atmosphere, then the velocity of the gas escaping from each vessel would be choked ... and the escaping gas velocity from each vessel's leaking hole would be identical (i.e,. the sonic velocity of that particular gas).

However, the mass flow rate from vessel B would be twice the mass flow rate from vessel A because the upstream pressure in vessel B is is twice the pressure in vessel A.

Also, if we raised the gas pressure in vessel A to 6 atmospheres then the leak mass flow rate would increase by a factor of two.

In other words, for a gas, the mass flow rate even at choked velocity conditions can be increased by raising the upstream pressure ... but cannot be increased by lowering the downstream pressure.

Please keep in mind that velocity (i.e., feet per second or meter per second) is not the same as mass flow rate (i.e., pounds per second or kilograms per second):

mass flow rate = (gas velocity)(cross-sectional flow area)(gas density).

I am sorry for being so long-winded, but I hope this helps you.

[sskumar]

Milton:
In a very nice way you have explained regarding choked flow. I have a doubt regarding sonic velocity.
I read somewhere that flare stacks are normally designed for 30% of sonic velocity. In our plant we have got a 126 M tall flare stack to burn Hydrogen Sulfide gas in case of any uncontrollable abnormality. In its data sheet stack velocity is given as 110M/Sec. It is approx. 30% of sonic velocity. ( with k~1.4,T=405K, Mol wt=34 for H2S).

(a) Why do they design flares for 30% sonic velocity.

(b) Does it mean that at any time, gas velocity remains less than 110M/sec. How can it be possible? When I connect a vessel at 20 Kg/sqcm pressure to flare header, gas velocity reaches sonic as flare top is open to atmosphere and hence it should be more than 110M/Sec.

Could you please educate me on this

Regards
sskumar

[mbeychok]

sskumar:

My email address is: mbeychok@xxx.net (replace the xxx with cox)

If you will send me your email, I will continue our discourse ... but I don't think we should subject all of the other readers of this forum to our discussion.

Regards,

[djack77494]

sskumar:
Let me expand a bit on Milton's explanations. I would emphasize gas density in the equation Milton provided. If you consider a particular orifice and a velocity (fixed at sonic), then you can pass a certain number of cubic feet (or meters) of fluid through the orifice, the VOLUMETRIC flowrate. If we can neglect changes in the sonic velociity as the pressure changes, then the volumetric flowrate passing through the orifice would be unchanging as the pressure changes. (Please note that the volumetric flowrate refers to the UPSTREAM conditions.) The MASS flowrate would not be unchanged, however. If the upstream pressure doubled, then the gas density and therefore the mass flowrate would double. (Note however that this example is really overly simplified. The speed of sound is affected by density, and it is not realistic to assume it will not change with pressure.)

Let me now address your last two questions.
1)Why design flares for 30% of sonic velocity? I suspect this is a compromise between the desire for higher velocities (to reduce the size of the flare and piping) versus lower velocity (to keep excessive backpressure from developing and to limit noise). [I'd like to hear other opinions.]
2)How can it be possible? The relieving gases from high pressure sources typically reach sonic velocity in the throat of the relief valve...at least for a well designed system. The velocity is well under sonic at the flare tip. It appears your flare tip is designed and should operate at 110 m/sec or 30% of sonic, which is quite reasonable. The flare tip must not be a restriction to the flow of gases being relieved from your pressure equipment, and must therefore not operate near sonic flow.

Concerning liquids, the fluid density is relatively unaffected by pressure since liquids are nearly incompressible. Thus the sonic velocity is not affected by pressure either. If your system involves continuous flows, then a modulating backpressure control valve might be a good choice for ensuring that the liquid filled system is not overpressurized.

Doug