This blog shows the relationship between the terms dq1, dq2, dq3 and dq4 in the SWMM5 code and the St. Venant Partial Differential Equations. dq2 = Time Step * Area wtd * (Head Downstream – Head Upstream) / Link Length or dq2 = Time Step * Area wtd * (HGL) / Link Length Qnew = (Qold – dq2 + dq3 + dq4) / ( 1 + dq1) when the force 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 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...
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