Equivalent Flow Path

The equivalent flow path is given by:

1)	$\begin{array}{l}\displaystyle \Delta x_e = \displaystyle \frac{\overline{A} _c \overline{S} _{fc} \Delta x_c + \overline{A} _f \overline{S} _{ff} \Delta x_f}{\overline{A} _f \overline{S} _{f}}\end{array}$

If we assume:

2)	$\begin{array}{l}\displaystyle \overline{\phi} = \displaystyle \frac{\overline{K} _c}{\overline{K} _c + \overline{K} _f}\end{array}$

where $\begin{array}{l}\overline{\phi}\end{array}$ is the average flow distribution for the reach, then:

3)	$\begin{array}{l}\displaystyle \Delta x_e = \displaystyle \frac{\overline{A} _c \Delta x_c + \overline{A} _f \Delta x_f}{\overline{A} _f}\end{array}$

Since $\begin{array}{l}\Delta x_e\end{array}$ is defined explicitly:

4)	$\begin{array}{l}\displaystyle \Delta x_{ej} = \displaystyle \frac{(A_{cj} + A_{cj+1}) \Delta x_{cj} + (A_{fj} + A_{fj+1}) \Delta x_{fj}}{A_j + A_{j+1}}\end{array}$