HY8:Polynomial Coefficients: Difference between revisions

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For circular, box, elliptical, and pipe arch culverts, polynomial coefficients, found in Tables 1-4, are utilized in the inlet control headwater computations.  Tables 5-10 show the HW/D points A(1) through A(10) for interpolation.  Each row of coefficients represents different entrance conditions for different culvert shapes.
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
== Table 1. Polynomial Coefficients - Circular ==


[[Image:HY8Poly_Table_1.JPG]]
[[Image:HY8Poly_Table_1.JPG]]
Line 13: Line 13:
1-10: Hydraulic Computer Program (HY) 1, FHWA, 1969, page 18
1-10: Hydraulic Computer Program (HY) 1, FHWA, 1969, page 18


 


   
   


Table 2. Polynomial Coefficients - Box
== Table 2. Polynomial Coefficients - Box ==


[[Image:HY8Poly_Table_2.JPG]]
[[Image:HY8Poly_Table_2.JPG]]
Line 33: Line 33:
   
   


Table 3. Polynomial Coefficients - Ellipse
== Table 3. Polynomial Coefficients - Ellipse ==


[[Image:HY8Poly_Table_3.JPG]]
[[Image:HY8Poly_Table_3.JPG]]
Line 47: Line 47:
   
   


Table 4. Polynomial Coefficients - Pipe Arch
== Table 4. Polynomial Coefficients - Pipe Arch ==


[[Image:HY8Polynomial_PipeArch.JPG]]
[[Image:HY8Polynomial_PipeArch.JPG]]
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12,16,20: Hydraulic Computer Program (HY) 2, FHWA, 1969, page 17
12,16,20: Hydraulic Computer Program (HY) 2, FHWA, 1969, page 17


Table 5. Arch HW/D Values.
[[Image:HY8Arch%20Table.JPG]]
Table 6. High Profile Arch HW/D Values.
[[Image:HY8Arch%20High%20Profile.JPG]]
Table 7. Low Profile Arch HW/D Values.
[[Image:HY8Arch%20Low%20Profile%20Table.JPG]]
Table 8. Metal Box HW/D Values.
[[Image:HY8Metal%20Box.JPG]]
Table 9. User Defined HW/D Values.
[[Image:HY8User%20Defined%20Table.JPG]]




Table 10. Polynomial Coefficients - Concrete Open-Bottom Arch
== Table 5. Polynomial Coefficients - Concrete Open-Bottom Arch ==
{| class="wikitable"
{| class="wikitable"
! Span:Rise Ratio !! Wingwall Angle (Inlet Edge Condition) !! KE !! SR !! A !! B !! C !! D !! E !! F !! Diagram/Notes
! Span:Rise Ratio !! Wingwall Angle (Inlet Edge Condition) !! KE !! SR !! A !! B !! C !! D !! E !! F !! Diagram/Notes
Line 243: Line 213:
* Thiele, Elizabeth A.  Culvert Hydraulics: Comparison of Current Computer Models.  (pp. 121-126), Brigham Young University Master's Thesis (2007).
* 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)
* Chase, Don.  Hydraulic Characteristics of CON/SPAN Bridge Systems.  Submitted Study and Report (1999)
== Table 6. Arch HW/D Values. ==
[[Image:HY8Arch%20Table.JPG]]
== Table 7. High Profile Arch HW/D Values. ==
[[Image:HY8Arch%20High%20Profile.JPG]]
== Table 8. Low Profile Arch HW/D Values. ==
[[Image:HY8Arch%20Low%20Profile%20Table.JPG]]
== Table 9. Metal Box HW/D Values. ==
[[Image:HY8Metal%20Box.JPG]]
== Table 10. User Defined HW/D Values. ==
[[Image:HY8User%20Defined%20Table.JPG]]





Revision as of 23:19, 16 June 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 B C D E F Diagram/Notes
2:1

0 Degrees (Mitered to Conform to Slope)

0.7

0.5

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)

0.2 if beveled, use 0.5 if not beveled (square edge)

0.5

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

0.5

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

0.5

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)

0.2 if beveled, use 0.5 if not beveled (square edge)

0.5

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

0.5

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


Related Topics

Introduction

Analysis

Head Water Computations

Inlet Control
Outlet Control

Tables and Plots