## Thursday, April 2, 2015

### SWMM5 Link Upstream Weighting

SWMM5 Link Upstream 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. The 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.

Purpose: The purpose of this note is to explain a significant dynamic wave routing difference between EPASWMM 5.0.013/5.0.018 and EPA SWMM 5.0.011 and before. A few people have detected a difference. The 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 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. Note: This was originally a Google Knol (which has be deprecated by Google).

#### 1 comment:

Unknown said...

MTT chuyên cung cấp những sản phẩm tăng cường sức khỏe đời sống như thuốc bổ cho mắt
thuốc tăng cường trí nhớ
viên uống trắng da ivory caps glutathione
triple omega 3-6-9
thuoc multivitamin
thuoc giam can tot nhat
mỹ phẩm sakura nhật bản
nature made prenatal multi dha
Bạn đang thắc mắc hay phân vân lựa chọn cho mình loại kem chống nắng cho những ngày hè sắp tới ? Hãy đọc bài viết của chúng tôi để có sự lựa chọn tốt nhất cho mình
kem chống nắng nào tốt nhất hay phân vân vì thuoc uong trang da an toan nhất.

### XPSWMM to ICM SWMM or ICM Process Pathways

# Process Description 1 Technical details about how XPSWMM models a feature This process involves understanding the specific algorithms, e...