Comparing rate of leakage at 40,000 feet with leakage at sea level:
$$
\frac{L_{40}}{L_0} = \sqrt{\frac{27}{112} \cdot \frac{188}{1013} \cdot \frac{288}{218}} = 0.243
$$
Comparing rate of leakage at 100,000 feet with leakage at sea level:
$$
\frac{L_{100}}{L_0} = \sqrt{\frac{27}{1880} \cdot \frac{10.9}{1013} \cdot \frac{288}{218}} = 0.044
$$
Therefore, if leakage of a full balloon at sea level is known, it is possible to compute theoretical leakage at any altitude. However, if it is not possible to completely inflate a balloon on the ground in order to make a sea level test (if lift would be great enough to rupture balloon or load lines), a method of comparing full balloon leakage with partially full balloon leakage must be found.
Let us assume that it is possible to obtain results of a leakage test for a balloon inflated to a volume $\frac{1}{x}$ of full balloon volume. Again starting with equation (1):
$$
Q = C_d A \sqrt{2gh}
$$
We see that in this case the total area of openings, $A$ is not constant but is a function of volume. Therefore, we have:
(8)
$$
Q \propto A \sqrt{h}
$$
We have shown that:
$$
h = \frac{\Delta p}{d_g} \cdot 144 = \frac{\Delta z \left( \frac{dp}{dz} \right)_{\text{air}} (1 - B)}{d_g} \cdot 144
$$
Since we are comparing partially inflated balloon leakage at sea level with full balloon leakage at sea level the variable in the above expression is $\Delta z$ . This is graphically illustrated in Figure 24.
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