Overall continuity and the spray equation

Since the spray is composed of fuel droplets and since ii = m, in equation (88) R will be given by equation (66), which may be written in the form of equation (8) with k = 1 and with 

Under our present assumptions, the spray equation simplifies to equation (7) with the additional conditions M = l,ti = h, and A = constant. Since the solution to equation (7) given in Section 11.2 will also be vahd in the present problem, equation (15) is applicable here and reduces to 

The subscript 0 is used to identify the known conditions far upstream (at X = - 00) instead of conditions at x = 0 as in Section 11.2. 

Since the initial drop-size distribution is known, the integral in equation (92) is a known Tunction of (xM) dx, [see equation (91)]. Equation (92) is therefore an integrodifferential equation for determining the rate of disappearance of the liquid. 

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