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# Relationship Between Flow Rate, Pressure, and Nozzle Size

04/09/2017 9:52 PM

Can somebody better explain how these three concepts are related in practice? I'm trying to pressurize a bag-like contraption with holes on one of its face. The goal is to maximize the force the bag can impart as a result of air flowing through those holes where we can vary the positioning and the size of them. I was told that the valve that feeds this bag will have a set pressure, so how could I maximize the force?

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#1

### Re: Relationship between flow rate, pressure and nozzle size

04/09/2017 10:50 PM

You maximize the force by allowing the outflow to match the inflow when it reaches set pressure....

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#3

### Re: Relationship between flow rate, pressure and nozzle size

04/09/2017 10:56 PM

I'm sorry but I'm not following. So let the outflow from the outlet equal the flow from the inlet?

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#2

### Re: Relationship between flow rate, pressure and nozzle size

04/09/2017 10:53 PM

Use just one hole as large as it can be until the valve no longer can supply the assumed pressure.

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#4

### Re: Relationship between flow rate, pressure and nozzle size

04/09/2017 10:58 PM

If I'm also aiming for stability, can I have multiple outflows that equal the one inlet flow rate? Is there a mathematical way to solve for this if I already know the inlet flow rate so we can model it on CAD rather than trial and error?

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#5

### Re: Relationship between flow rate, pressure and nozzle size

04/09/2017 11:51 PM

What sort of CAD package are you using? I know ANSYS can do computational fluid dynamics. This could be overkill - or not; we know nothing of your application and its requirements.

Does the inflated bag have a fixed volume or does it expand and contract with changes in internal pressure? If so, does the exit-hole-size change? What is the bag venting into? Atmosphere? A larger fixed or variable volume? If atmosphere, how sensitive to ambient pressure? What of temperature dependencies? Is the inlet air diffused or is it a jet? If it's a jet, what are the chances of it exiting directly through the hole? And so on.

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#6

### Re: Relationship between flow rate, pressure and nozzle size

04/10/2017 12:23 AM

We can definitely do ANSYS so I'll get to that.

The bag has a maximum volume but other than that expands and contracts with internal pressure. The exit holes do not change size and they vent into the atmosphere. From my understanding this is no temperature dependency and I am not aware of its sensitivity to ambient pressure, although I don't think its highly sensitive. I don't know the difference between diffused inlet air or a jet. What I can say is that it is pressurized air from a compressed tank.

My hope was some kind of mathematical relationship or previous literature/notions on the relationship between force and the outlet holes (their size, shapes, placement etc).

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#7

### Re: Relationship between flow rate, pressure and nozzle size

04/10/2017 1:08 AM

Roughly speaking, every time you half the size of the orifice you divide the flow by 4...

 Ta : Air Temperature (°F) p1 : Primary Pressure (psia) p2 : Secondary Pressure (psia) do : Diameter of Orifice (in) C : Discharge Coefficient Qa : Air Flow Rate (Normal) (SCFM) Fγ : Specific heat ratio factor xT : Pressure differential ratio factor (=0.72)

http://www.tlv.com/global/TI/calculator/air-flow-rate-through-orifice.html

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#8

### Re: Relationship between flow rate, pressure and nozzle size

04/10/2017 1:22 AM

Ok. How does the flow rate relate to say the force you get from the contraption as a whole?

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#9

### Re: Relationship between flow rate, pressure and nozzle size

04/10/2017 1:34 AM

Well if you are supplying 40 scfm of air at 100 psi, and your bag is capable of 20 psi, then your orifice totals should max at total 40 scfm@20 psi...= .17" or 4 orifices half that size...

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#16

### Re: Relationship between flow rate, pressure and nozzle size

04/11/2017 1:55 AM

If I wasn't so lazy that was pretty much what I would have said/suggested because with so many unknowns, such as input source, output "atmoshpere", the mechanical s of the "bag" and so on that's pretty much as far as you can take it.

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#10

### Re: Relationship between flow rate, pressure and nozzle size

04/10/2017 7:06 AM

Why not use a sealed bag with inlet only (or possibly a valved outlet for venting), and control the force by controlling the inlet pressure with a pressure regulator?

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#11

### Re: Relationship between flow rate, pressure and nozzle size

04/10/2017 7:39 AM

Vehicle airbag using compressed air instead of a gas generator? Just curious. Not many applications where you'd want to use a perforated bag (in a manner of speaking) to exert a force unless you'd also want it to deflate quickly.

Even if this isn't your application, look at some of the studies covering vehicular airbag design.

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#12

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/10/2017 9:56 AM

Wouldn't the pressure be maximum if there were no holes?

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#13

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/10/2017 10:08 AM

What force? The force of the air flowing out of the bag? The force of the bag banging into something? IS this a collision arrest bag?

Is it a shopping bag to cushion eggs?

What are you trying to accomplish, and why?

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#14

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/10/2017 10:35 AM

P=F/A, obviusly, you need to decrease the area cross section of whatever mechanism is pushing.

It's obvious if you try to experiment your garden hose. When you reduce the nozzle area of water discharge, you have a fast discharge of water and its moving something with greater force than having the nozzle open wide.

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#15

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/10/2017 12:17 PM

Just as a matter of curiosity,

- of what material is the bag to be made?,

- of what operating-volume is the bag to be? and

- how big are the holes to be?, and

- how many holes are there to be?, and

- what is the diameter of the supply line?, and

- how long is the bag to last?, before exploding, or to have the inflation ceased?...

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#17

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 6:11 AM

Given that pressure is constant, and force is pressure multiplied by area, the solution is to increase the area.

The nozzles are a red herring.

Google "lifting bags", and "recovery of the Costa Concordia", perhaps?

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#18

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 6:51 AM

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#19

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 10:55 AM

Are you using this bag as a thruster?

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#20

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 1:42 PM

Yes we are using this bag as a sort of thruster. It's a silly design class project. And on that note I can't really answer the other questions as I am trying to piece this project together myself. All I know for sure is that the pressure from the inlet is constant (although the flow rate can be changed). The air then pressurizes a bag and air escapes through one face. The goal is to maximize the force (like a thruster) from the escaping air. How that is achieved is entirely up to us.

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#21

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 2:13 PM

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#23

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 2:18 PM

You can race just about anything. We had a product called a PowerBroom, basically a string trimmer with a 40:1 worm gearcase and nylon drum brushes at the bottom. We had people in technical services wearing roller blades and perched on them like the wicked witch of the west racing around the parking lot.

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#25

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 2:36 PM

You guys have altogether too much fun. That is supposed to be a serious facility doing serious work. No smiling during work hours, damit.

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#27

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 2:42 PM

You need to work on your wordiology...It's DAMMIT!

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#29

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 4:17 PM

You are right, dammit. I was all of about 12 years of age when I finally realized my name was not dammit.

In German, damit means "in order to", I think.

Damit is also usually found oddly at the end of a German sentence, there again, Germanic sentence structure is why English is so messed up.

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#42

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/14/2017 4:35 PM

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#22

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 2:14 PM

Then the answer is that you want the geometry that will give the highest exit velocity and highest mass flow rate, force being equal to mv^2. You will get highest velocity by radiusing the exit bag wall into a discharge nozzle to minimize pressure drop at the transition from bag to nozzle. The nozzle should be shaped to get the highest velocity.

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#24

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 2:35 PM

http://www.engapplets.vt.edu/fluids/CDnozzle/cdinfo.html

That might help design the nozzle for them. I forget the name of the nozzle, but it does have a name. If I made one, I would call it the Bud nozzle. I think a green beer rocket is in order, along with a flattulizer to record the voluminous blast of energy derived therefrom.

If, of course, the bag were attached to several well-known partisans in Washington, D.C., and maybe a pundit or two as an extra booster, this kid might go super-sonic.

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#26

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 2:41 PM

Nozzle and an applet...is that some sort of small apple?

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#28

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 4:14 PM

right. Applets are those things in the small apple bins at the store, when you don't wanna take a bite out of the BIG Apple.

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#32

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 10:01 AM

The link shows a de Laval nozzle. Unlikely OP wants to go to that much trouble, and to get supersonic flow the upstream pressure would have to be above about 2 bara, a bit high for his bag.

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#33

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 10:53 AM

Depends on the bag. Say Kevlar reinforced.

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#41

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/13/2017 5:33 AM

I doubt that the OP wants to put a number of de Laval nozzles on his bag. Perhaps he'll let us know if he does!

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#35

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 11:02 AM

As a thought experiment:

3000 psi nitrogen cylinder

Kevlar reinforced TFE/Kevlar mesh/nitrile/Kevlar mesh/nitrile bag with TFE nozzle insert bag.

Delaval nozzle geometry in TFE nozzle

Rough calcs done in 1997 showed a 175 pound man with said 220 scf tank/bag/nozzle could jump over a 550 foot tall cooling tower.

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#36

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 12:25 PM

Yes, but could he land? I suppose that tower is natural draft, correct? Not that it matters to me, or him...

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#37

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 12:28 PM

"Once the rockets go up who cares where they come down. That's not my department says Werner Von Braun."

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#38

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 1:47 PM

True that. I don't know of a single parachute, or parachute deployment system he ever designed. After all, the V2 did not require any landing system.

What I will say, Werner did have the stones to pull off the moon shots, and was really upset he was not allowed to use the Saturn V to launch further out, such as attempted manned missions to Mars. He really did get turned down on that, and it broke his heart.

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#30

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/11/2017 7:38 PM

OK:

- get a bag of an acceptable material of measurable tensile strength

- make a small circular scratch on the outside of the bag in only one spot

- insert a recording pressure gauge along the supply line right behind the nozzle

- set up to monitor the volume of the maximum volume of the bag right before failure (under water in an open-air tank with a measurable water level is one possibility)

- turn on the air supply, and increment pressure in appropriate amounts, until the bag bursts at it's weakest point (which will probably be where the scratch was).

- measure the smallest length, and thickness, of the rupture of the slightly deformed bag

- report the highest pressure recorded before the burst

- calculate the required force

(if done under water, it should be the average of two successful tests, one with the hole on the top of the bag, and the other on the bottom)

In any case good luck with your class project, and get back to us with the results, what ever they are...

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#31

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 9:35 AM

Sounds like you are telling OP that he/she is all wet, or is about to be all wet if they do this test. Really?

Warning: blowing up gas bags under water can result in water on the ear.

Besides, the Senator from Pennsylvania would drown before he blows up, although he would most definitely obstruct the effort to put him under water, there is always the nuclear option.

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#34

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 10:55 AM

At higher pressures it could be water on the brain, or even worse: brain on the water.

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#39

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 6:26 PM

- first, submerge the entire, empty, open, bag in the water tank, in order to measure the volume of the bag, alone, by recording the resulting difference in the water heights in the water tank. The water tank should be only slightly larger in volume than the bag in order to get a better bagvolume measurement.

(i.e.: (waterheight,after) minus (waterheight,before) indicates the (bagvolume,totally-empty) )...

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#40

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/12/2017 6:30 PM

Please tell us exactly what class, in what academic program, is this project for?...

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#43

### Re: Relationship Between Flow Rate, Pressure and Nozzle Size

04/14/2017 4:51 PM

Balloon class 101, at the Clown College....

Next month I start physics...

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