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F(p, l)= 0.5 \cdot j_m^2 \cdot \left[ \left(  \frac{1}{\rho^2} - \frac{1}{\rho_0^2}   \right)  
+ \left(  \frac{f}{\rho^2} + \frac{f_0}{\rho_0^2}   \right)  
\cdot \frac{l}{ 2 \, d}  \right]

+ \int_{p_0}^p \frac{dp}{\rho} -g \, \Delta z(l) = 0

j_m =  \sqrt{ 2 } \cdot 
\left[
g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho}
\right]^{0.5}
\left[
\left(  \frac{1}{\rho^2} - \frac{1}{\rho_0^2}   \right)  
+ \left(  \frac{f}{\rho^2} + \frac{f_0}{\rho_0^2}   \right)  
\cdot \frac{l}{ 2 \, d}
\right]^{-0.5}

\dot m =  
A \sqrt{ 2 } \cdot 
\left[
g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho}
\right]^{0.5}
\left[
\left(  \frac{1}{\rho^2} - \frac{1}{\rho_0^2}   \right)  
+ \left(  \frac{f}{\rho^2} + \frac{f_0}{\rho_0^2}   \right)  
\cdot \frac{l}{ 2 \, d}
\right]^{-0.5}

q_0 =  
\frac{A \sqrt{ 2 }}{\rho_0} \cdot 
\left[
g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho}
\right]^{0.5}
\left[
\left(  \frac{1}{\rho^2} - \frac{1}{\rho_0^2}   \right)  
+ \left(  \frac{f}{\rho^2} + \frac{f_0}{\rho_0^2}   \right)  
\cdot \frac{l}{ 2 \, d}
\right]^{-0.5}