Toward a Computational Model

Given:

$$\begin{eqnarray*} p_m&=& \hbox{Mouth pressure} \\ p_b^{+}&=& \hbox{Incoming traveling bore pressure} \end{eqnarray*}$$

Find:

$$p_b^{-}= \hbox{Outgoing traveling bore pressure}$$

such that:

$$\begin{eqnarray*} 0 &=& u_m+u_b= \frac{p_{\Delta}}{R_m(p_{\Delta})} + \frac{p_b^... ...\mathrm{\Delta}}{=}}& p_m-p_b= p_m- (p_b^{+}+p_b^{-}) \nonumber \end{eqnarray*}$$

Solving for $p_b^{-}$ is not immediate because
$R_m$ depends on $p_{\Delta}$ which depends on $p_b^{-}$.