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# calculating N2 flow through a flexible hose

## calculating N2 flow through a flexible hose

(OP)
I am trying to determine the flowrate of nitrogen (90 psig) through a flexible rubber utility hose.  I found some online calculators, but want to do some hand calculations to validate.  I guess I am looking for friction factor for 3/4" id rubber hose and any other tips.  The hose lengths would be 25 feet and 50 feet lengths.  Thanks

### RE: calculating N2 flow through a flexible hose

Are you going to atmosphere?  How many bends and curls for pressure drop, or will you hold it straight?

### RE: calculating N2 flow through a flexible hose

(OP)
I wanted to calculate both the max flow going to atmosphere, and also with an outlet pressure of 15 psig.  (75 psi differential).  I was going to probably assume 3 or 4 90 degree bends as a minimum, and the rest of the hose straight.  I am trying to determine what relief capacity would be required on equipment rated for 15 psig in the event someone hooked up a 90 psig utility hose to the system.  There is currently a relief installed on the equipment, but don't belief it has sufficient capacity to handle the volume from a N2 utility hose added to the system.

### RE: calculating N2 flow through a flexible hose

When checking relief capacity, keep it conservative and simple.  In this scenario, that means the short 25' hose with no bends.  If the relief is big enough, great!  If it's not, then start adding reality and complexity.

I recommend Crane's Technical Paper 410.  Google it and buy it on the net.  I suspect the flow will be close to fully turbulent and there's a couple graphs and a table in TP410 you can get the friction factor from.

Good luck,
Latexman

### RE: calculating N2 flow through a flexible hose

Is it not a choked flow problem?
With an supply pressure of 90 psig to 1 atmosphere.
I think  you will get critical flow through the hose....

### RE: calculating N2 flow through a flexible hose

My calculations show that it would be a choked flow situation for 25' and 50' hoses going to atmosphere.  Using a roughness of 0.0004" gives a flow of around 1300 lb/hour for the 50' hose and close to 1700 lb/hour for the 25' hose. It is difficult to know what to use for the roughness because "rubber hose" can describe a wide variety of items.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

### RE: calculating N2 flow through a flexible hose

(OP)
Is it still choked flow if the discharge of the hose is 15 psig instead of atmospheric?  The rubber hose I am referring two is a standard utility/industrial hose that is utilized for air, nitrogen, process water within the chemical industry.  3/4" id.  Thank you.

### RE: calculating N2 flow through a flexible hose

Compressible flow thru pipe to a larger flow area, use Crane TP410, page A-22 for k = 1.4 and 25':

K = fL/D = (0.245)(25*12)/0.75 ~ 100
dP/P1' = (90-15)/104.7 = 0.716
For sonic velocity dP/P1' = 0.926 for K = 100

Therefore, flow is not sonic for 25' and 50' with 15 psig discharge pressure.

Good luck,
Latexman

### RE: calculating N2 flow through a flexible hose

Wouldn't that be K = 0.025*25*12/0.075 = 10?

3/4" = 0.75"

Good luck,
Latexman

### RE: calculating N2 flow through a flexible hose

It's so easy to slip the decimal isn't it.  Yes, it's K = 0.0245*25*12/0.75 ~ 10.  Thanks for noticing.

For sonic velocity dP/P1' = 0.784 for K = 10

Therefore, flow is still not sonic for 25' and 50' with 15 psig discharge pressure.

Good luck,
Latexman

### RE: calculating N2 flow through a flexible hose

I agree that the 50' pipe with 15 psig at the end is not sonic flow.  But the 25' pipe is borderline and it depends very much as what you assume for the roughness of the rubber.

In order to get a friction factor of 0.0245 (as used by Latexman) you need a roughness of about 0.002", which would be typical of commercial steel pipe.  The roughness I would use for smooth PVC pipe would be 0.0002" and this would give a friction factor of 0.015 and would predict supersonic flow.  In my earlier calc I took the roughness as 0.0004" (twice that for PVC).  Fortunately, as you get close to supersonic flow the actual flowrate does not vary much with end pressure so it is not too important.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

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