What is the Pressure inside the balloon?

Questions Questions!

The more you work on a project the more questions you have. In trying to better anticipate (in other words: predict) possible problems and successes we have had to address questions like:

How much helium will we need? What size balloon do we need? How high can it go? What will happen to it, as it gets high up? What can we use for a fill tube? How can we hold on to the balloon while it is filling?

All questions lead to other questions and most of these brought up the question of: What is the pressure inside the balloon and how does it change with the size?

As you know from blowing up party balloons, you have to blow really hard at first and then it gets easy until just before it bursts. This would suggest that the pressure inside changes dramatically depending on the size of the balloon. Is this the same as for our huge meteorological balloons? How much of a pressure difference is this anyway?

This is the kind of fundamental question that we can directly measure.

Planning the Setup

We try to keep this simple. We have instruments that can measure pressure and after trying it out we can stretch the neck of a balloon enough to get a barometric sensor inside.

We need a source of gas. No it doesn't have to be helium. What about air? OK but it has to be under some pressure and capable of very large volume. My lung-power is out. The lab has a spigot marked "air".

The barometer will record the pressure inside the balloon twice a second and we can fill at a constant flow rate. However, we want to relate this to the size of the balloon.

It is very hard to measure diameter. However, we know that both diameter and volume are easily calculated from circumference. We try a tape measure and it is too stiff to go around a balloon. We take a string and mark it off in feet instead.

The Experiment

We recruit extra people and clear an area for space to work and to remove any sharp edges. One person holds the balloon, one holds the circumference string, & one has a stopwatch and a data table. The stopwatch and barometer are started and the room air pressure data is collected for a few seconds before we start the air flowing into the balloon. When the balloon first gets rounded out we record the time and circumference. As the balloon's circumference increases to each additional footmark, we record the time.

It is getting longer and longer between each new foot of circumference. This makes sense because the volume is going up as the cube of the diameter. How long do we continue this? Not much appears to be happening but we are nowhere near the bursting point. We decide to inflate well past the largest size we expect to need on the ground and then extrapolate for the expected size gain as the balloon rises to our 1000 ft standard height. The last foot seems to take forever. We mark the time, shutoff the air, open the balloon neck, and it seems to take forever to deflate also.

However, when we examine the data it looks good. There is definitely a relationship between the pressure and time (inflation). But what does it mean?

Time	circumference in ft.	radius in ft.	diameter in ft.	volume in ft^3
0	-	-	-	-
37	5.25	0.84	1.67	2.44
59	6	0.95	1.91	3.65
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90	7	1.11	2.23	5.79
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130	8	1.27	2.55	8.65
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186	9	1.43	2.86	12.31
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240	10	1.59	3.18	16.89
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307	11	1.75	3.50	22.48
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405	12	1.91	3.82	29.18
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519	13	2.07	4.14	37.10
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644	14	2.23	4.46	46.34
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839	15	2.39	4.77	56.99
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921	15.5	2.47	4.93	62.88
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990	16	2.55	5.09	69.17

Analysis

Looking at the graph, note that the horizontal scale is in seconds. 1000 seconds is about 17 minutes. Note the vertical scale. It starts at 0.976 atm instead of zero. This means that the vertical changes are exaggerated. The graph starts off fairly constant at just above 0.977 atm. This must be the room pressure in the lab about 98% of average standard air pressure.

The pressure rapidly goes up to a high of 0.982 before it drops back down slowly to a low of 0.979 from which it slowly starts to rise again.

The first high pressure corresponds with the point at which the balloon first became round and turgid. The lowest pressure occurred when the balloon was about 4 feet in diameter.

Conclusion

The pressure is never more than 0.005 atm greater than ambient pressure. At our normal working size (5 ft diameter), the pressure difference is at its least of 0.002 atm or 0.2% of ambient.

Answer 1: We can assume that the pressure inside the balloon is EQUAL to the outside with only a 0.2% error.

Answer 2: Since the pressure at 5 ft is still well below the maximum, we can feel confident that we are operating a long way from the pop point.