HY8:Polynomial Coefficients: Difference between revisions

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==''Related Topics''==
{{HY8Main}}
 
===Introduction===
* [[WMS:HY-8|Introduction]]
===Analysis===
* [[WMS:HY-8 Project Units|Project Units]]
* [[WMS:HY-8 Roadway Overtopping|Roadway Overtopping]]
====Head Water Computations====
=====Inlet Control=====
::* [[WMS:HY-8 Inlet Control Computations|Inlet Control Computations]]
::* [[WMS:HY-8 Polynomial Generation|Polynomial Generation]]
::* [[WMS:HY-8 Polynomial Coefficients|Polynomial Coefficients]]
=====Outlet Control=====
::* [[WMS:HY-8 Outlet Control Computations|Outlet Control Computations]]
::* [[WMS:HY-8 Exit Loss Options|Exit Loss Options]]
====Tables and Plots====
:* [[WMS:HY-8 Tables and Plots|Tables and Plots]]
:* [[WMS:HY-8 Crossing Summary|Crossing Summary]]
:* [[WMS:HY-8 Culvert Summary|Culvert Summary]]
:* [[WMS:HY-8 Water Surface Profiles|Water Surface Profiles]]
:* [[WMS:HY-8 Improved Inlet|Improved Inlet]]
:* [[WMS:HY-8 Customized|Customized]]
:* [[WMS:HY-8 Controlling Plot Display Options|Controlling Plot Display Options]]

Revision as of 16:20, 1 July 2011

For circular, box, elliptical, pipe arch, and concrete open-bottom arch (commonly called CON/SPAN) culverts, polynomial coefficients, found in Tables 1-5, are utilized in the inlet control headwater computations. Tables 6-10 show the HW/D points A(1) through A(10) for interpolation. Each row of coefficients represents different entrance conditions for different culvert shapes.


Table 1. Polynomial Coefficients - Circular

HY8Poly Table 1.JPG

EQ #'s: REFERENCE

1-9 : Calculator Design Series (CDS) 3 for TI-59, FHWA, 198O, page 60

1-10: Hydraulic Computer Program (HY) 1, FHWA, 1969, page 18



Table 2. Polynomial Coefficients - Box

HY8Poly Table 2.JPG

EQ #'s: REFERENCE

1-6: Hydraulic Computer Program (HY) 6, FHWA, 1969, subroutine BEQUA

1,4,5: Hydraulic Computer Program (HY) 3, FHWA, 1969, page 16

1,3,4,6: Calculator Design Series (CDS) 3 for TI-59, FHWA, 198O, page 16



Table 3. Polynomial Coefficients - Ellipse

HY8Poly Table 3.JPG

EQ #'s: REFERENCE

27-30: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 20

31-33: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 22



Table 4. Polynomial Coefficients - Pipe Arch

HY8Polynomial PipeArch.JPG

EQ #'s: REFERENCE

12-23: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 17

24-26: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 24

12,16,20: Hydraulic Computer Program (HY) 2, FHWA, 1969, page 17


Table 5. Polynomial Coefficients - Concrete Open-Bottom Arch

Span:Rise Ratio Wingwall Angle (Inlet Edge Condition) KE SR A BS C DIP EE F Diagram/Notes
2:1

0 Degrees (Mitered to Conform to Slope)

0.7

0.0

0.0356

0.5701

-0.162

0.0322

-0.0023

0.00006

0DegreeWingwallConspanCulvertDiagram.png

2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.

2:1

45 Degrees (45-degree Wingwall)

0.5

0.0

0.0393

0.5828

-0.1518

0.0284

-0.002

0.00005

45DegreeWingwallConspanCulvertDiagram.png

2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.

2:1

90 Degrees (Square Edge with Headwall)

0.5

0.0

0.0459

0.5762

-0.1436

0.0269

-0.0019

0.00005

90DegreeWingwallConspanCulvertDiagram.png

2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.

4:1

0 Degrees (Mitered to Conform to Slope)

0.7

0.0

0.0309

0.5211

-0.1258

0.0207

-0.0013

0.00003

0DegreeWingwallConspanCulvertDiagram.png

4:1 coefficients are used if the span:rise ratio is greater than 3:1

4:1

45 Degrees (45-degree Wingwall)

0.5

0.0

0.0318

0.5446

-0.1467

0.0273

-0.0019

0.00005

45DegreeWingwallConspanCulvertDiagram.png

4:1 coefficients are used if the span:rise ratio is greater than 3:1

4:1

90 Degrees (Square Edge with Headwall)

0.5

0.0

0.0283

0.5739

-0.1584

0.0292

-0.002

0.00005

90DegreeWingwallConspanCulvertDiagram.png

4:1 coefficients are used if the span:rise ratio is greater than 3:1

References for Concrete Open-bottom Arch polynomial coefficients:

  • Thiele, Elizabeth A. Culvert Hydraulics: Comparison of Current Computer Models. (pp. 121-126), Brigham Young University Master's Thesis (2007).
  • Chase, Don. Hydraulic Characteristics of CON/SPAN Bridge Systems. Submitted Study and Report (1999)

Table 6. Arch HW/D Values.

HY8Arch Table.JPG


Table 7. High Profile Arch HW/D Values.

HY8Arch High Profile.JPG


Table 8. Low Profile Arch HW/D Values.

HY8Arch Low Profile Table.JPG


Table 9. Metal Box HW/D Values.

File:HY8Metal Box.JPG


Table 10. User Defined HW/D Values.

HY8User Defined Table.JPG