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 (
where, Rho (
Just for reference, the equation for Qnorm or the Manning's Equation flow is
The equations for the calculation of Rho (
If ALL of the follow conditions are true Rho (
- 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 and
qLast 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.
Replies