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\Delta p(L)=- \frac{j_m^2}{\rho_0} \cdot \frac{f_0 \, L}{2 \, d } = - \frac{8}{\pi^2} \frac{\rho_0 \, q_0^2}{d^5} \, f_0 \, L

\Delta p (L) =- \frac{\rho_0}{c^*} \cdot  \left[
1 - \sqrt{  1 - j_m^2 \cdot \frac{c^* \rho^*}{\rho_0^2} 
\cdot \frac{f_0 L}{d}}
\right]

\Delta p (L) =- p_0 \cdot \left[ 1- \sqrt{ 

1 - \frac{j_m^2}{\rho_0 \, p_0} \cdot \frac{f_o0 L}{d} 

} \right] 

\Delta p (L) =- \frac{j_m^2}{\rho_0} \cdot \frac{f_0}{2 \, d} \cdot 
\frac{ 1- \exp \left( - c^* \rho^* G \, L \right)}{c^* \rho^* G}