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How is the St Venant Equation Solved for in the Dynamic Wave Solution of SWMM 5?

Subject:   How is the St Venant Equation Solved for in the Dynamic Wave Solution of SWMM 5? An explanation of the four St. Venant Terms in SWMM 5 and how they change for Gravity Mains and 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.  The four terms are: dq2 = Time Step * Awtd * (Head Downstream – Head Upstream)…See More
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i'm trying to find out, how works the surcharge flow in SWMM 5. Another programm (like Infoworks) use preissmann slot to simulate Surcharge flow in closed coduit. which approach is accurate? Could you give me some informations about this, robert? thanks a lot!

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Hi, Here is some background information

http://swmm5.blogspot.com/2011/06/3-types-of-manholes-in-swmm-5-and...

Specifically look at these sections of code:

       // --- allow surface area from last non-surcharged condition
        //     to influence dqdh if depth close to crown depth
        denom = Xnode[i].sumdqdh;
        if ( yLast < 1.25 * yCrown )
        {
            f = (yLast - yCrown) / yCrown;
            denom += (Xnode[i].oldSurfArea/dt -
                      Xnode[i].sumdqdh) * exp(-15.0 * f);
        }

        // --- compute new estimate of node depth
        if ( denom == 0.0 ) dy = 0.0;
        else dy = corr * dQ / denom;
        yNew = yLast + dy;
        if ( yNew < yCrown ) yNew = yCrown - FUDGE

This is how the surcharge algorithm is used in SWMM 5

 

Specifically look at these sections of code:

       // --- allow surface area from last non-surcharged condition
        //     to influence dqdh if depth close to crown depth
        denom = Xnode[i].sumdqdh;
        if ( yLast < 1.25 * yCrown )
        {
            f = (yLast - yCrown) / yCrown;
            denom += (Xnode[i].oldSurfArea/dt -
                      Xnode[i].sumdqdh) * exp(-15.0 * f);
        }

        // --- compute new estimate of node depth
        if ( denom == 0.0 ) dy = 0.0;
        else dy = corr * dQ / denom;
        yNew = yLast + dy;
        if ( yNew < yCrown ) yNew = yCrown - FUDGE;

To put this in words, we do not use a definitive slot but do use the slot idea to compute the surcharged depth with these important differences:

1. There is no slot width or added area to the surcharged node,

2. There is a exponentially shaped transition zone that quickly tapers from node crown to a depth 1.25 * node crown,

3. The solution for a surcharged node is a point iteration equation dH/dt - dQ/dQdh without an area term,

4. The dQdH term is the derivative of the connecting links St Venant Equation wrt to H or the Head,

5. The surcharged node should iterate until the  value of dQ is zero or the flow is in balance

I hope this helps.  I think that SWMM 5 has a slot of zero width - we do not need the width as we have no head computation point in the link

Thank you, Robert.
I'm always amazed of fast replies from you. Do you kwon some report that compares approach of surcharge flow in SWMM and preissmann slot? Which method is more accurate, do you think? 

I really want to understand this code, but I can't FORTRAN. Could you please write some easy understanding text? It is very important, because I want to do some experiments to compare surcharge flow in SWMM 5 and Preissmann slot in anorther programm (Infoworks). Thanks a lot!



Robert Dickinson said:

This is how the surcharge algorithm is used in SWMM 5

 

Specifically look at these sections of code:

       // --- allow surface area from last non-surcharged condition
        //     to influence dqdh if depth close to crown depth
        denom = Xnode[i].sumdqdh;
        if ( yLast < 1.25 * yCrown )
        {
            f = (yLast - yCrown) / yCrown;
            denom += (Xnode[i].oldSurfArea/dt -
                      Xnode[i].sumdqdh) * exp(-15.0 * f);
        }

        // --- compute new estimate of node depth
        if ( denom == 0.0 ) dy = 0.0;
        else dy = corr * dQ / denom;
        yNew = yLast + dy;
        if ( yNew < yCrown ) yNew = yCrown - FUDGE;

That is C code and not Fortran but here is the code in words:

The program will sum the value of dQ/dH for all of the links connected to the node.  The value of dQ/dH is the derivative of the  St Venant equation for the link.

Now, if you are trying to calibrate or compare the surcharge level you main tools are:

1. Smaller time step and 

2. The force main roughness value - this will change the flows, change the value of dQ/dH and give you some flexibility in computed depths.

More here  http://www.swmm2000.com/profiles/blogs/surcharged-node-and-the-link...

Remember, there is ONE computational point in a link  in SWMM 5 and one computational point at a node in SWMM 5 - the flow is from the middle of the linkl

Subject:  Link Simulated Parameters used in either the Normal Flow or St Venant Equation of SWMM 5

St. Venant equation – this is the link attribute data used when the St. Venant Equation is used in SWMM 5.  Simulated Parameters from the upstream, midpoint and downstream sections of the link are used.

Image004

Normal Flow Equation – this is the link attribute data used when the Normal Flow Equation is used in SWMM 5. Only simulated parameters from the upstream end of the link are used if the normal flow equation is used for the time step.

Image006

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