St. Venant Terms in SWMM 5 and how they change for Force Mains

Note:  An explanation of the four StVenant Terms in SWMM 5 and how they change for Force Mains.  The HGL is the water surface elevation in the upstream and downstream nodes of the link.  The HGL for a full link goes from the pipe crown elevation up to the rim elevation of the node + the surcharge depth of the node.  dq1 is calculated differently based on full or partially full force mains and gravity mains


            dq2 = Time Step * Awtd * (Head Downstream – Head Upstream) /  Link Length  or


            dq2 = Time Step * Awtd * (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 StVenant equation:


            dq2 = Time Step * Awtd * (Head Downstream – Head Upstream) /  Link Length



via Blogger http://www.swmm5.net/2013/07/st-venant-terms-in-swmm-5-and-how-they.html

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