I have an experiment set up where I am measuring the flow rate from a 375 gallon tank (50.13 ft3).  I am trying to calculate the flow rate from the tank, but my results are not matching up.  The flow meter I have on the tank is measuring 360 SCFH (6 SCFM).  

The tank is being filled with nitrogen gas at intervals and once a valve closes it stops being filled.  During this time I record the start pressure and the final pressure before the valve opens and resumes filling the tank.  The start pressure (when the valve closes) is 62 psig and final pressure is 61 psig and this occurs in 23 seconds.  

P1 - 76.7 psia
P2 - 75.7 psia
T - 528 R
V - 50.13 ft3

(76.7 psia - 75.7 psia) / 14.7 psia * 50.13 ft3 = 3.41 ft3
3.41 ft3 / 23 s = 0.148 ft3/s = 533 ft3/hr

Am I doing something wrong or missing something in the calculation?

Is this a school assignment?  If so, you need to talk to your teacher.

Is the concern that the flow element is measuring less than what you calculated?

Is your experiment being done at standard temperature?

Has your flow meter been calibrated?

Patricia Lougheed

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Nothing you can't determine using a stopwatch and good ol' PV = nRT.

No, this is not a school experiment.

The concern is that we are testing a method for our systems as a way to check flow, but our experimental results are not matching up.

The temperature is 68 F, which is close to the standard temperature of 70 F used in our instrumentation.

Our flow meter has been calibrated and we have used several different flow meters with similar results.  We also have several pressure gauges measuring the tank pressure with identical results.   

Perhaps your volume is wrong?  Fill with water and count the buckets.

I originally suspected the tank size might be off and I did change the tank size based on the U1A form and measurements of the tank.  However, the tank size is listed as 400 gallons and we adjusted it to 375 gallons.  In order for the calculation to match up the tank would have to be approximately 250 gallons.

It doesn't seem likely that a tank that was sold as a 400 gallon tank would be in actuality 250 gallons.

I measured the straight side length of the tank to be 73" with a circumference of 114".  The wall thickness is 0.244" from U1A form.  The heads are elliptical.  

If I plug this information into http://www.northlandstainless.com/volume_calculator.cfm I get 375 gallons.  

Is the tank standing vertically or laying on its side horizontally?  With elliptical heads, and the tank standing vertically you will have fairly linear relationships btwn. liquid volume, liquid head (pressure) and gas volume, as long as you are not operating right up in the elliptical end with the liquid level.  These relationships will not be nearly a cleanly defined for a tank laying on its side because of the elliptical ends, and the constant/variable volume changes vs. liquid level.  How does this figure into the equation?
 

Is the tank discharging to atmosphere?  Maybe the volumetric flowrate past the flowmeter is correct because the gas passing by the flowmeter is not at atmospheric pressure.

dhengr - The tank is standing verically

dvd - The flowmeter is a Dwyer variable area flowmeter with the exhaust open to atmosphere

http://www.dwyer-inst.com/Product/Flow/Flowmeters/VariableArea/SeriesRM-RMA-RMB-RMC-  

We are using the RMC type with a scale reading from 40 to 400 SCFH.  We have no piping attached to the exhaust of the meter, so this should be at atmospheric pressure.

"Also, for pressure-fed flowmeters on air or gas service, the discharge piping should be as short and open as possible. This will allow operation of the flow tube at near atmospheric pressure and insure the accuracy of the device." - From Dwyers manual

FWIW (which may not be much) ... is your calc right ?

you have constant volume, and a pressure drop (presumably at constant temperature), so you can calc the mass that's left the tank, no?

Suspect that nitrogen is throttling to atmospheric pressure. Can you confirm the constant temperature assumption at the flowmeter?

This may seem silly -- but are you sure your tank is full at the start?

Patricia Lougheed

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Well, it may not make enough difference to matter...but you are holding 3 place accuracy through your calculations, when the pressure measurement may only be valid for one sig. fig. (you are measuring a change of 1 psi with 0.1 psi resolution...which means the measurement might really be 0.9 psi, which has one sig. fig. of resolution).  Still, 500 scfh +/- 100 scfh does not equal or even approach 360 scfh, so something else is wrong.  Can you double check the tank volume - i.e. open a hatch, make sure there isn't a big pile of sand (or Jimmy Hoffa) lying in there taking up volume?

rb1957 - I showed my calculation to see if someone could find an error with it.  I've checked it multiple times.

dvd - I've confirmed constant temperature at the flowmeter.  Would a slight temperature difference cause a 48% difference in results?

vpl - I'm not sure what you mean by full.  Are you saying that the nitrogen gas is not occupying the full volume of the tank?

btrueblood - I can actually measure the pressure to 1 decimal place (it should be 62.0 to 61.0 psig).  There are two inspection ports on the tank that I will check to see if I might have actually found the location of Jimmy Hoffa.  

Will,

I mean your measurement is a change in pressure, ie a delta-P, which has (at least) 10% error associated with it (0.1 psi resolution in a measured change of 1 psi).  Similar problem with time measurement.  Finally, what is the change in tank temperature (you could assume adiabatic conditions, but ought to take it into account, and not just assume isothermal without checking to see if it makes any difference).

btrueblood - Well, I didn't find Jimmy Hoffa, but I think you are correct that I can't assume adiabatic conditions.  I checked the results and saw that a slight temperature difference could change the results closer to what I'm reading on the meter.  Thanks.

If, for throttling an ideal gas mixture isentropically, T1/T2=(p1/p2)^((k-1)/k)where k is the specific heat ratio, the temperature difference is fairly significant.  Consider what happens when the high pressure tank gas is throttled to very close to the atmospheric pressure.  You do the math.

 

Um, ok just clicked your link to the Dwyer meter, which is broken.  The link I give below should be the right one (please confirm)?  It's a rotatmeter.  It's only accurate when the gas pressure in the meter is at or very near atmospheric.  What is the pressure in the pipe just upstream of the meter?  If it's anything more than a few psi, the meter will read incorrectly due to compressibility effects.  I.e. if you are feeding 60 psi nitrogen straight into the meter inlet, the flow is going sonic and even supersonic inside the rotameter tube as it passes the float, and it ain't designed to measure accurately in those conditions.

http://www.dwyer-inst.com/Product/Flow/Flowmeters/VariableArea/SeriesRM-RMA-RMB-RMC-/Specs
 

That's the right link.  The Dwyer flow meters use a needle valve on the incoming gas before it goes to the ball float.  I have checked them against another meter we have here that uses Constant Temperature Differential technology in order to measure the flow rate and they are within stated accuracy.

All right, I'll trust you on that one.  Next possibility - how much holdup volume in the pipe between tank shutoff valve and the needle valve?  That volume must fill before meter reads a flow rate, and then bleeds down slowly after the shutoff valve closes.

Does the tank bulge?

btrueblood - the flow meter is open constantly at 360 SCFH.  The pressure is regulated to it at 50 psig.  The tank swings 1 psi up when the valve opens and 1 psi down when the valve closes.  The nitrogen gas from the process delivers more than the tank is flowing on its output.

I've attached a link of how the process is setup here:
http://dl.dropbox.com/u/41855723/VOLUME%20FLOW%20RATE.pdf

I also made a spreadsheet in Excel with the calculations:
http://dl.dropbox.com/u/41855723/volume%20flow%20rate.xls

I calculate the mass of N2 at each state and then determine the mass difference between the states.  Then using the density of N2 at standard conditions of 70F and 14.69 psia the flow rate is calculated.  If I left the process as adiabatic and didn't change the temperature between states the flow rate would be 536 SCFH.  If I change the temperature by 2F to 66F the resulting flow rate is closer to the meter reading.

Next step will be to experimentally measure the temperature of the gas in the tank.  

aterwill,

Could not open the first link, and don't like opening excel files from unknown sources, sorry.  But, rereading your first post it starts to make a bit more sense.  Can you measure the temperature of the N2 just before the meter - you are throttling from 50 psig to atmospheric, so there should be substantial Joule-Thompson cooling occurring there, affecting your reading if not accounted for properly (unless I'm still missing something).

Similar effects are happening in the tank - the throttling thru the inlet valve is injecting cold N2 into the tank, which then warms to some extent due to heat flow through the tank walls.  Knowing the temp's. at both ends will/should help you get closer agreement between the two measurements.