Super Sonic Flow in Pipe 1

[Ace12]

Working on finding the mass flow rate of air exiting a vent out of a softner column. The pressure inside the column is 84.696 psia which is then vented through a 3" pipe (about 35 ft in lenth) to a backwash tank which is at atmospheric pressure.

I have tried solving for this using basic equations which are derived from the bernouli equation (considering non constant density). Although my calculations showed on the exiting side of the vent u2=1730 ft/s at 14.696 psia with a mass flow of 8.2 lbm/s.

I don't feel like this is possible because of the restraints of supersonic flow in pipe (choke flow).

I'm hoping somone can help give me a better understanding of choke flow so I can try to recalculate the mass flow of air. There is no converging/diverging nozzle in my line except if you consider the inlet/outlet of the pipe into the tanks. Does choke flow apply to this situation?

 

[zdas04]

Where to start????

Fluid velocity greater than about 0.7 Mach violates the "incompressible" assumption in the Bernoulli equation. Using that equation for this problem is just wrong.

Choked flow is defined as Mach 1.0, and in no way is it supersonic. Choked flow has a unique characteristic that a Mach 1.0 stream flowing into an increasing cross section will increase in velocity (exactly the opposite of what happens in flow below 0.7 Mach). This allows a properly configured nozzle to exhibit supersonic flow (i.e., velocity greater than 1.0 Mach).

Sonic velocity is a function of gas temperature and gas properties. It is easily calculated and there is an FAQ in Piping and Fluid Mechanics Engineering to take you step by step through it.

Mass flow rate is a function of the density of the fluid upstream of the choke and fluid velocity. Both are very straight forward calculations.

The problem comes in when the high velocity fluid enters the 25 ft of 3-inch pipe. It begins slowing and immediately enters the transsonic region of velocities. Just like most transition regions, this one it really tough to analyze with closed-form equations. I work the problem from both ends.

First, I assume that the friction drop in the pipe is inconsequential and that the full vessel pressure is applied at the pipe exit. That is the approach that API and ASME take with PSV calculations. That gives me an upper limit on flow rate.

Second, I assume that the transsonic region ends at about 10 pipe diameters and use closed-form incompressible flow equations between that point and the exhaust to determine friction drop in the pipe. If the pressure at the transsonic transition calculates to "well under" the critical pressure then I accept the first assumption. If it is close or over, then I back up and calculate the pressure at the exit assuming that the flow rate in the pipe is less than transsonic. If that value is high enough to give me choked flow into the tank, then I calculate the mass flow rate based on the pressure after friction in the pipe.

It is complicated, but the flow is very complicated.

Throwing around terms like "Bernoulli's Equation" and "Super Sonic" for flows that have nothing to do with either concept is pretty unprofessional and adds to the confusion that abounds in this topic.


David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[MikeHalloran]

Just do like David says.

Ignore his last paragraph; David occasionally gets impatient with fools like me.


Mike Halloran
Pembroke Pines, FL, USA

 

[TD2K]

Sounds a lot like example 4-21 in Crane. Have you got access to a copy?

 

[zdas04]

TD2K,
It is very similar to that example. I tend to avoid solutions that include look-up values (I even iterate friction factors instead of going to the graph), which is why I developed the method I mentioned above. At the end of the day you reach the same conclusions.

Mike,
I just get tired of Mr. Bernoulli being accused of every sin in fluid mechanics. He developed an amazingly useful relationship through some really clever math, but he didn't develop a closed-form solution to Navier-Stokes. Stuff like trying to do sonic flows in Bernoulli just sets me off since sonic flow is as far from the incompressible assumption that the Bernoulli Equation is based on as you can get.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[Ace12]

Sorry,

I'm a little green on modeling flows for a compressible fluid, and having a hard time grasping it. Basicly I've been assuming the fluid is first incompressible to get the entering velocity of the fluid into the pipe.
Next I iterated all my friction factors with the increasing velocity(due to decreasing density of the fluid). Lastly I assumed that frictional losses caused all the pressure drop which allowed me to solve for velocities.
Although when my calculated velocities of the fluid the last few feet before the exit tank were above sonic flow I had a hunch that the methods I was using to model the fluid were wrong.

I really appriate any help you guys are giving me.

I don't have a copy of Crane.

 

[MikeHalloran]

It's time for you to buy your own copy of the Crane paper.
Guard it; it may develop high mobility.



Mike Halloran
Pembroke Pines, FL, USA

 

[TD2K]

Crane used to get handed out for free by the piping companies but it's well worth the money to buy your own copy. I have a couple of copies in US units and a copy in SI units.

http://www.amazon.com/Fluids-Throug...ULNO/ref=sr_1_2?ie=UTF8&qid=1336104011&sr=8-2

Hmm, I had better watch my copies, I didn't realize they were that much.

 

[btrueblood]

I gave my first copy away years ago to an intern (well, he never returned it, but I sleep better saying it that way). Second copy, purchased with own money, stays at home.

 

[vpl]

You can also buy from Crane:

http://www.flowoffluids.com/

I own both a US and an SI version. I don't loan them out, though I occasionally will let people look at them (and I don't even do engineering anymore (sigh)).

Patricia Lougheed

******

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[hacksaw]

Ace12,

you appear to have assumed an ideal gas in your calculation, since ideal gas laws only describe isentropic expansions you'll get questionable results,

with frictional losses you have an adiabatic expansion more or less, described by the "real gas" laws.

you cannot have sonic velocity inside the pipe unless there is an abrupt change in area, usually at the exit,

so the real issue is describing the expansion at the exit

one tactic is to calculate the length of pipe for sonic flow at an assumed exit condition, this gives you an effective pipe length.

then calculate the pressure in this effective pipe at the location of your actual pipe exit, that gives you the approximate pressure and fluid velocity at the real pipe exit...you go from there

crane is a classic-was free sales literature in the good ole days, believe the new editions offer a cd with a lot of the calculations coded up in some form

 

[davefitz]

This sounds like "fanno flow"- frictionally choked flow in pipes. Refer to thread378-6648 for the equations.

for a small value of sum{fL/d}, the curves are provided in the appendix of B31.1 on the subject of sizing relief valve exhasut pipes, but for larger values of sum{fL/d} you will need to compute the answer yourself.

Only other proviso is that the assumption is for a constant flow area over the length of the pipe-if there is a flow restriction, the point of choked flow will be at that restriction.

 

[Ace12]

Thanks everyone for your posts, helped alot with getting more familiarized with the compressible flow equations. Especially when I should assume adiabatic, isothermal.. and so on.

I used the adiabatic fanno flow equation to solve for mass flow rate of the air.

Kyle