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q_0^2 = 
\frac{2 \, d \, A^2 \, G}{f} \cdot \left [
1 + \frac{(\rho/\rho_0)^2-1}{1- \exp (2 \, c_0 \, \rho_0 \, G \, L)}
 \right]
=
\frac{2 \, d \, A^2  \, g}{f \, L} \cdot \left [ 
\Delta Z + ((\rho/\rho_0)^2 -1) \cdot  \frac{ \Delta Z}{1 - \exp(2 \, c_0 \, \rho_0 \, g \,  \Delta Z)}
\right]

\dot m = \rho_0 \, q_0

\rho =
\rho_0 \, \exp(c_0 \, \rho_0 \, G \, L) \, \sqrt{1 - \frac{f \, q_0^2}{2 \, d \, A^2} \cdot \frac{1- \exp(-2 \, c _0 \, \rho_0 \, G \, L)}{G}} 
=\rho_0 \, \exp (с_0 \, \rho_0 \, g \, \Delta Z) \cdot \sqrt{ 1 - \frac{8}{\pi^2} \cdot   \frac{f \, L}{d^5} \cdot q_0^2 \cdot \frac{1 - \exp(- 2 \, c_0 \, \rho_0 \, g \, \Delta Z) } { g \, \Delta Z}}

p(L) = p_0 + \frac{\rho/\rho_0 -1}{c_0} 

\rho = \rho_0 \, \exp (c_0 \, \rho_0 \, g \, \Delta Z)

p(L) =  p_0 + \frac{\exp (c_0 \, \rho_0 \, g \, \Delta Z) -1}{c_0}