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F(p, l)=\left(  \frac{1}{\rho^2} - \frac{1}{\rho_0^2}   \right)  
+ \left(  \frac{1f}{\rho^2} + \frac{1f_0}{\rho_0^2}   \right)  
\cdot \frac{f \, \cdot \, l}{ 2 \, d}  - (2/j_m^2) \,  \int_p^{p_0} \frac{dp}{\rho} - (2/j_m^2) \, g \, \Delta z(l) = 0

\frac{dp}{dl} = {\rm Numerical} \ {\rm Derivative}

q_0 =  
\frac{A}{\rho_s} \cdot \sqrt{ 2 \cdot \frac
{
g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho}
}
{
\left( \frac{1}{\rho^2} - \frac{1}{\rho_0^2} \right) 
+ \left( \frac{1f}{\rho^2} + \frac{1f_0}{\rho_0^2} \right) 
\cdot \frac{f \, \cdot \, l}{ 2 \, d}
}
}

u_0 = 
\frac{1}{\rho_s} \cdot \sqrt{ 2 \cdot \frac
{
g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho}
}
{
\left( \frac{1}{\rho^2} - \frac{1}{\rho_0^2} \right) 
+ \left( \frac{1ff}{\rho^2} + \frac{1ff_0}{\rho_0^2} \right) 
\cdot \frac{f \, \cdot \, l}{ 2 \, d}
}
}