Note: An explanation of the three depths in a Link in SWMM 5 and a plot of the upstream, middle and downstream link depth. The middle depth is an average of the upstream and downstream link depths. The plot of the variable depth or the middle depth is always between the upstream and downstream depths. All three depths are used in the computation of the St. Venant Flow in SWMM 5. The upstream area is a function of the upstream depth and the downstream area is a function of the downstream depth.
The dq4 term in dynamic.c uses the area upstream (a1) and area downstream (a2), the midpoint velocity, the sigma factor (a function of the link Froude number), the link length and the time step or
dq4 = Time Step * Velocity * Velocity * (a2 – a1) / Link Length * Sigma
the dq3 term in dynamic.c uses the current midpoint area (a function of the midpoint depth), the sigma factor and the midpoint velocity
dq3 = 2 * Velocity * ( Amid(current iteration) – Amid (last time step) * Sigma