Linear vs. non-linear air flow

[dingpud]

Lets us a potato gun for an example.

Having a source tank filled with air, and when a trigger is activated, the air is dumped straight threw the valve and out the tube.

--> --> --> -->

What would happen if the flow of air had to go out of the pressurized source (~160 psi ~40 cu. in volume) through a 90 degree fitting, then through another 90 degree fitting, then out the end of the tube?

-->-->-->
^
|
^
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<--<--<--

I am looking for some sort of relationship or calculation set that would explain the kind of losses that I am going to experince in changing the air flow from being linear to non-linear, any help would be great, and no, it isn't a spud gun.

Scott

 

[FredGarvin]

What kind of fluids background do you have? If we start talking about equivilent lengths, friction factors and compressibility factor will you know what that refers to?

Not to take short cuts here, but the addition of bends, corners and fittings all add up to give you a frictional effect that would be the same as if you used a much longer straight tube.

 

[RainmanAero]

Hi Fred & dingpud,

Not to take short cuts here, but the addition of bends, corners and fittings all add up to give you a frictional effect that would be the same as if you used a much longer straight tube.

In my view, it gets a bit more complex than that. Clearly with the long, straight tube you can assume irrotational flow (no vorticity). Thus, if one is really looking for analytical differences between the two configurations, I think you need to take into account (and model) the 2-D flow, rather than trying to retain 1-D flow assumptions and compensate for them.

I am looking for some sort of relationship or calculation set that would explain the kind of losses that I am going to experince in changing the air flow from being linear to non-linear

As I note above, you are purposely introducing vorticity into the flow with the bends. Even if we assume continuous, non-surging flow (m-dot=constant throughout the control volume) we can no longer assume 1-dimensional flow. I'm afraid there is no "simple" set of calculations if you want to model this situation accurately. You would need to use the http://www.navier-stokes.net/" with frictional loss terms. The good news is that you would not necessarily have to model the equations in all 3 dimensions (but your solution would be that much more accurate if you did). The bad news is that these equations cannot be solved in closed-form, only numerically via simulation and numerical integration with boundary conditions specified.

Now maybe what I am proposing here is overkill. It is easy to see that the losses will be greater with the two 90 deg elbows, and as Fred mentioned you could estimate this as just another loss term in the 1-D model. But if you really want an accurate comparison, the better your model the better your answers!
Rainman

 

[Q_Goest]

Hi Rainman. What Fred eludes to regards the well established and standard practice used throughout industry for the past (roughly) one hundred years of reducing the restriction of a series of piping components to a single equivalent restriction. The fact that vortices are created in an elbow is well known, though it need not be over analyzed by using 2 or 3 dimensional NS equations.

 

[dingpud]

Well this gives me a starting point. I have a degree in Physics, but not much of a background in fluids. The links that have been posted appear to be useful in guiding me to the proper equations. I might be able to get some of the equations to work for my system.

Thanks for all of the posts. I'll post again if I get stumped trying to work out the equations. I am going to be shooting for an estimated loss through the system. Fortunatley, I have the luxury of not needing this to be an exact measurement.

I am 98% sure that I am correct on this, but wanted to check...(2) 90 degree fittings with a pipe between them allows less flow than a straight pipe with 90 degree bends at either end...correct?

 

[FredGarvin]

I am 98% sure that I am correct on this, but wanted to check...(2) 90 degree fittings with a pipe between them allows less flow than a straight pipe with 90 degree bends at either end...correct?

It allows the same mass flow (to a point). What will happen is that the flow will require more pressure drops across each new component to get the same flow through the additional components. Depending on what pressures and flows you are talking about, you may not even notice any difference. That will be something you will find out with the numbers. As always, if you can use two 45° elbows in stead of one 90°, the frictional effects are less.