(14) $\frac{dw}{dt} = K \frac{dN}{dt}$
where $K$ is a constant.
We may state the relationship (13) in terms of rate of transfer and area of the opening, assuming $\frac{dN}{dz}$ to be constant across the opening:
(15) $\frac{dw}{dt} = -K_1 D \frac{dc}{dz} A$
where:
$\frac{dw}{dt}$ = mass transfer of lifting gas
$\frac{dc}{dz}$ = variation of concentration of lifting gas in direction $z$
$A$ = area of opening
In order, then, to determine the rate of loss of lifting gas by diffusion through the open appendix we must:
(a) determine the relationship between the coefficient of diffusion, $D$ , and altitude (or pressure and temperature)
(b) determine the loss of lift by diffusion through the appendix at any convenient altitude (i.e. at the ground)
(c) derive a relationship between loss at the ground and loss at any altitude.
However, determination of valid relationships to find diffusion through the appendix opening would require large scale laboratory testing and then tedious derivation of mathematical equations, a study in research in itself. It was deemed more practical to reduce or eliminate this type of loss of lift by reduction of the area of the opening by use of a relief valve system as explained in Part II of this report, "Operations," pp. 8-14.
F. Bursting Pressure and Appendix Considerations
Bursting pressure of a balloon can be computed from the equation:
(1) $\Delta p = \frac{4Srt}{D}$ for failure of the fabric or film,
where:
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