The Roswell Report: Fact vs. Fiction in the New Mexico Desert

Example: If a 20-foot diameter balloon $ \frac{1}{1 0} $ full were tested at sea level and found to have a leakage rate of 50 gm/hr. the leakage rate of a full 20-foot balloon at sea level would be:

$$
L _ {f} = 5 0 \frac {G M}{H R} (1 0) ^ {\frac {5}{6}} = 3 4 0 \frac {G M}{H R}
$$

The leakage of a full 70-foot diameter balloon at sea level in this case would be:

$$
L _ {f} = 5 0 \frac {\mathrm {G M}}{\mathrm {H R}} \left[ 1 0 \left(\frac {7 0}{2 0}\right) ^ {3} \right] ^ {\frac {5}{6}} = 7 8 2 0 \mathrm {G M} / \mathrm {H R}
$$

Values for leakage at several different altitudes for 20-foot and 70-foot diameter ballcons, assuming a leakage of 50 gm/hr. for a 20-foot balloon $ \frac{1}{10} $ full at sea level are:

Altitude(MSL)	0	40,000 ft.	100,000 ft.
20-ft. diam.	340 gm/hr.	83.2 gm/hr.	15 gm/hr.
70-ft. diam.	7820 gm/hr.	1912 gm/hr.	345 gm/hr.

Another consideration is that relationship expressed by the kinetic theory of gases regarding gases at low pressures. The kinetic theory states that there is a molecular type of flow across a thin diaphragm through openings whose dimensions are of the order of the length of the mean free path of the molecules involved. Mass flow of the gas is then:

$$
L = \Delta p \cdot A \sqrt {\frac {d g}{2 \Pi}}
$$

where:

$ \Delta p= $ is the pressure difference across the film

A = area of the opening

$ \mathbf{d}_{g}= $ density of the gas in question

This relationship, however, becomes valid only at extremely low pressures, and when considering balloon systems at normal floating levels the more common fluid-flow relationship will control the rate of loss of lift through openings in the film. It would be of little use then to investigate further the leakage of gas through openings by means of the relationships involved in the kinetic theory.