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Name: Howard K.
Status: educator
Age: 30s
Location: N/A 
Country: N/A
Date: 9/19/2004

It deals with compressed nitrogen. I am doing some testing using nitrogen and am using more than I expected. I have no flow gauge to tell me the SCF/min being used. I have a hose attached to the regulator that has an inside diameter of 1/8" and set to 10 psi. The hose is terminated with a tube that has several 1/16" holes drilled through its wall to direct the nitrogen onto a circuit board during a cold test. The bottle had 1000 psi to begin the test and it was emptied in about 30 minutes. Can you tell me if there is any mathematical relationship between the psi setting and the volume flowing from the tank? Is there any way that you know of to determine this or must I use a flow gauge?

It is not easy to determine flow from size of tubing and apparatus. The best way to determine flow is to measure the flow. There are easy ways to measure flow without needing to purchase a flow meter.

One way is to take a container of known volume, fill it with water and put it inverted into a shallow pan of water. Run the hose under the water and under the lip of the container. When you turn on the nitrogen, the water will be displaced and the water level will go down. You can calculate flow rate by the dividing the amount of nitrogen by the filling time.

Another way to measure volume is to blow up a balloon with the nitrogen. You can calculate the amount of gas using standard geometrical equations for volume, depending on whether it is a spherical or a cylindrical balloon.

Bob Erck


I think I have some ideas that will help.

I notice that several 1/16th inch holes have more flow cross-sectional area than your one 1/8" ID hose. So virtually all the pressure drop from +10psig (25psi absolute) to 0 psig (15psi abs) will be in the hose. I am sure this is counterproductive.

A typical large gas bottle has about 3300 StdLiters (Liters of gas when at "standard" room temperature and pressure) when filled to 2500 psi. If you had 1000 psi, that would be roughly 1000 StdLiters too. Spending it in 30 minutes indicates 30 StdLiters/minute (SLPM). At the exit end of the hose, pressure is near atmospheric, so the velocity in your 1/8" ID. is around 50 m/sec (really whistling), or about 1/6 the speed of sound. Flow can be very weakly responsive to pressure at that kind of speed in long narrow tubing.

If you must use 10 psig and several 1/16th-inch holes, you need a larger hose; perhaps 1/4" ID is enough. But I think you need smaller holes and higher pressure, more. Then you may not need a bigger hose.

At your flow rate and hose size, flow is approximately proportional to the square-root of pressure drop per unit tubing length. So if your regulator is cranked up to 50 psig you might get about twice the flow. (if the regulator can provide that much flow.) It's difficult to figure exactly, because of the gas having a different density and speed at each point in the length of the hose. Difficult to decrease the flow much, starting from only 10 psig. To get half the flow would require 2.5 psig. Typical regulators are poor at consistently providing such low pressures. And there would be almost no expansion cooling generated.

You need smaller holes, and perhaps fewer, perhaps a wider hose, and turn up the regulator pressure slightly. Implementing that will shift the pressure drop from the tube length to the holes. Then, most of the expansion-cooling will be generated right where you want it, jetting at the test object. Less of the cooling power will be lost into the room, through the walls of the hose. This will allow some reduction in gas flow rate, maybe by half. If the hose is still cold, I'd insulate it with some plastic foam. The hose can lose more than half the cooling power.

Further reduction of hole size will allow you to turn the regulator up to 50 psig. (100 would be even nicer. But such tiny holes!) This will roughly double the cooling power released at the expansion point (hopefully now the nozzles). So you can halve your mass-flow again. With less flow from 1000 psi to < 100 psi, your regulator will not be getting quite so cold.

Choose your orifice size by assuming that the pressure will be at least 2 atmospheres inside, and 1 atmosphere outside, so the emerging jet will have approximately the speed of sound. This is a constant. It cannot go faster, and it will not be slower. Assume you want 1/4 the flow rate you have been using. The sum of the orifice areas will be less than one 1/16 inch hole. Perhaps 0.020 inch holes will work out well. Smaller holes are pretty inconvenient to drill. PC-board drills are available in these sizes. A 2:1 diameter-ratio of conical expansion in the exits of the holes, (included angle < 45 degrees), like tiny rocket nozzles, might help. I think you can find some pointy conical reamer tips for the Dremel tool that will help. You may not need the motor-tool, just your fingers.

If you have a sonic nozzle with a perfect expansion cone, the flow is linearly proportional to the incoming gas density, i.e., to the inside absolute pressure. Outside pressure changes (up to ~50% of the inside pressure) cannot influence the flow rate. I'd put a pressure gauge at the point-of-use, instead of a flow gauge.

If your holes are straight-walled instead of conical, then the speed-of-sound choke-point is just before the exit, where the gas is least dense, having dropped pressure to near-ambient levels. Then I think inside pressure changes cannot influence the flow very well.

If you are not seeking refrigeration but merely room-temperature airflow cooling of a hot object, You could use the kinetic energy from tiny high-pressure jets to aspirate some room air through a larger (1/4"? 1/2"?) orifice and short tube. I suspect it is easy to double the gas flow that way.

Many mechanical gas-flow gauges will vary in actual scale-factor depending on the gas pressure at their point in the flow path. So they may not make things entirely clear for you.

good luck optimizing-

Jim Swenson

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