The following boundary conditions are modeled by the EXTRAN Model:
EXTRAN computes the current value of hydrograph inflow to each input node in the sewer system at each large time-step. It then reads current values of hydrograph ordinates from an external interface file if the Runoff Block (or any other block) immediately precedes the EXTRAN Block, and/or from line input runoff hydrographs (from the user inflow dialog). EXTRAN then performs a linear interpolation between hydrograph input points and computes the discharge at each input node at the full time step, t+t.
EXTRAN provides for input of up to 100 inflow (standard value, actual value is defined in SWMM, CFG files) hydrographs as input data lines in cases where it is desirable to run EXTRAN alone without prior use of an upstream model or to add additional input hydrographs, either at the same or different nodes, to those computed by the upstream model.
EXTRAN computes seven tide coefficients (if needed), Al through A7, which are in turn used to compute the current tide elevation according to the Fourier series:
HTIDE = A1 + A2 sin wt + A3 sin 2wt + A4 sin 3wt
+ A5 cos wt + A6 cos 2wt + A7 cos 3wt
t = current time, hours (units of seconds are used internally),
w = angular frequency 2 pi radians/W (radius/hr), and
W = tidal period in hours
Typical tidal periods are 12.5 or 25 hours. The coefficients A2 through A7 are developed by an iterative technique in which a sinusoidal series is fitted to the set of tidal stage-time points supplied as input data.
EXTRAN evaluates the tidal equations, or interpolates the stage history boundary condition, or uses a lookup table for an outfall defined by a rating curve. It determines the tidal coefficients during the simulation to determine the current tidal elevation for multiple boundary conditions.
Generally, the boundary conditions are calculated using the following procedures: