Non Linear Term in the Saint Venant Equation of …

Note: Q full vs Q dynamic vs Q normal

1. It gets more flow than qFull because the water in the pipe has more than just the bed slope to push it - it also has the water surface slope. There is about a 5 meter head pushing the water out if…

Added by Robert Dickinson at 10:35am on March 27, 2009

Topic: Hydraulics Of SWMM5

ogram will calculate the cross sectional area, hydraulic radius top width and depth at the upstream, midpoint and downstream sections of the link. The link solution is pivoted on the midpoint cross sectional area in the dominant dynamic wave terms and and the non-linear term in the dynamic wave equation uses the upstream and downstream link cross sectional areas. In the finite difference equation in SWMM 5 the pipe shown below would have one length but use the cross sectional information from the upstream, midpoint and downstream points of the link. The bend in the pipe would be modeled using the "other" category of losses …

Added by Robert Dickinson to Hydraulics at 3:58pm on December 27, 2008

Blog Post: Defining Normal Flow in SWMM 5

Added by Robert Dickinson at 11:12pm on December 21, 2008

Page: External Blog List

15 GPM 4 Converter Information A Basic InfoSewer Wet Well A workaround for Hydrology only models that send all subcatchment flow to the pervious area. Adding New View Variables To the SWMM 5 Delphi

Added by Robert Dickinson at 8:41am on December 28, 2010

Note: Spatial Step

SWMM 3,4,5 uses a spatial step equal to the length of the link. Or, in terms of the 1D St. Venant Equation for the calculation of flow used in SWMM 5: In which is the length of the conduit. The p…

Added by Robert Dickinson at 1:15pm on July 2, 2008

Blog Post: Three Depths in A Link in SWMM 5

Note: An explanation of the three depths in a Link in SWMM 5 and a plot of the upstream, middle and downstream link…

Added by Robert Dickinson at 7:02pm on October 1, 2010

Topic: Dynamic Wave A and R calculation slider in SWMM 5.0.013

previous solution(s) would use only the midpoint area (Amid) and hydraulic radius (Rmid) in the dynamic wave solution.  The new solution will use a slider or linear combination of the midpoint area (Amid) and hydraulic radius (Rmid) and the upstream cross sectional area (A1) and hydraulic radius (R1).  The slider is based on the Froude number in the link.  The change involves the A and R link spacing in the two dominant terms of the St. Venant Equation: The new method is a linear combination or slider that weights the value of A and R in the St. Venant Equation based on the value of rho (), or where, Rho () is a function of the Froude number.   The effect of this addition is that as the Froude number increases from 0.5 to 1.0 and beyond the area and hydraulic radius used as the pivot point in the St. Venant equation moves from  the midpoint of the link to the upstream end of the link.  When the Froude number is above 1.0 the St. Venant and Normal Flow equation both use the same cross sectional area and hydraulic radius which makes for a more stable model.Just for reference, the equation for Qnorm or the Manning's Equation flow is The equations for the calculation of  Rho () as a function of the Froude Number (Fr) are: If ALL of the follow conditions are true Rho () is calculated: the pipe is not full, h1 >= h2, and qLast > 0. where,h1 is the head at the upstream end of the link,h2 is the head at the downstream end of the link andqLast is the last flow value in the link.  If any of these conditions are true then rho = 1.0 and the value of A and R are the values Amid and Rmid, respectively.The next graph shows the relationship between Rho and the Froude Number. The value of Awtd and Rwtd move from the midpoint of the link to the upstream end of the link as the Froude number increases from 0.5 to 1.0.     Conclusion: This change should make the solution more stable because there is no longer an oscillation between the St. Venant Equation A and R and the Normal Flow Equation A and R.…

Added by Hydraulics at 7:50pm on April 20, 2008

Note: Non Linear Term in the Saint Venant Equation of SWMM 5

Non Linear Term in the Saint Venant Equation of SWMM 5 The flow equation has six components that have to be in balance at each time step:  1.  The unsteady flow term or dQ/dt 2.   The friction loss…

Added by Robert Dickinson at 10:08am on January 20, 2010

Blog Post: SWMM 5 Iterations

These three graphs show how the number of iterations to solve the St. Venant equation in …

Added by Robert Dickinson at 9:27pm on February 27, 2010

Note: Automatic Weighting

Purpose:  The purpose of this note is to explain a significant dynamic wave routing difference between EPA SWMM 5.0.013 and EPA SWMM 5.0.011 and before.   A few people have detected a difference.  Th…

Added by Robert Dickinson at 10:07am on June 7, 2008