## Tuesday, January 24, 2012

### Keep and Dampen options and their effect on the four main terms of the St Venant equation

Note:  The Keep and Dampen options and their effect on the four main terms of the St Venant equation. ## The Keep and Dampen options and their effect on the four main terms of the St Venant equation in SWMM5

Note:  The Keep and Dampen options and their effect on the four main terms of the St Venant equation.

The four terms are are used in the new flow for a time step of Qnew:

Qnew = (Qold – dq2 + dq3 + dq4) / ( 1 + dq1)
when the force main or gravity main is full dq3 and dq4 are zero and  Qnew = (Qold – dq2) / ( 1 + dq1)

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
where Sigma is a function of the Froude Number and the Keep, Dampen and Ignore Inertial Term Options.  Keep sets Sigma to 1 always and Dampen set Sigma based on the Froude number, Ignore sets Sigma to 0 all  of the time during the simulation

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
dq1 = Time Step * RoughFactor / Rwtd^1.333 * |Velocity|

The weighted area (Awtd) is used in the dq2 term of the St. Venant equation: 