PIP & PROFESSIONAL DEVELOPMENT

Erna Foronda
June 2004

Note: This document is also available as a PowerPoint presentation.

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Open Channel Transitions in Subcritical Flow
Overview

• Definition of Subcritical Flow

• Transition Structures

• Analysis of Transition Structures

• General Guidelines for Design

• Summary

• Q&A

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Subcritical Flow

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Subcritical Flow
What Is Subcritical Flow?

There are 3 types of flow in open channel:

• Critical F_r = 1.0

• Subcritical F_r < 1.0

• Supercritical F_r > 1.0

where F_r is called the Froude Number

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Subcritical Flow
OCFCD Criteria for Design

• Flow is unstable at Froude Numbers between:
  
  0.9 < F_r < 1.2

If possible, avoid design in this range

• (Stable) Subcritical Flow, F_r = 0.9

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Transition Structures

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Transition Structures
What Is A Transition Structure?

• Structure that joins two geometrically dissimilar cross-sections

• Contraction or expansion of flow

• Minimizes flow disturbance

• Affects the water surface elevation through energy loss

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Transition Structures
Contraction & Expansion

Plan View

[untitled diagram]

Contraction

b1 > b2

Expansion

b1 < b2

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Transition Structures
Application of Transition Structures

• Approach to bridge and culvert crossings

• A placeholder between existing and future improvements

• To create a choke in the channel

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Transition Structures
Types of Transition Structures

[diagram of structure shapes]

• Warped

• Straight Line

• Cylindrical Quadrant

• Wedge

• Abrupt (square)

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Analysis of Transition Structures

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Analysis of Transition Structures
Principles of Open Channel Hydraulics

Three Governing Principles

• Conservation of Mass
• Conservation of Momentum
• Conservation of Energy

E₁ = E₂ + Losses

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Basic Hydraulic Concepts
Energy Equation (Bernoulli's)

v₁²/2g + y₁ + z₁ + P₁/g = v₂²/2g + y₂ + z₂ + P₂/g + h_L,1-2

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Basic Hydraulic Concepts
Open Channel Energy Equation

[untitled diagram]

v₁²/2g + y₁ + z₁ = v₂²/2g + y₂ + z₂ + h_L,1-2

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Basic Hydraulic Concepts
Open Channel Energy Equation

[untitled diagram]

v₁²/2g + y₁ + z₁ = v₂²/2g + y₂ + z₂ + h_L,1-2

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Basic Hydraulic Concepts
Open Channel Energy Equation

[untitled diagram]

v₁²/2g + y₁ + z₁ = v₂²/2g + y₂ + z₂ + h_L,1-2

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Basic Hydraulic Concepts
Open Channel Energy Equation

[untitled diagram]

v₁²/2g + y₁ + z₁ + P₁/g = v₂²/2g + y₂ + z₂ + P₂/g + h_L,1-2

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Basic Hydraulic Concepts
Open Channel Energy Equation

• Head Losses
  
  h_L1-2 = Major Losses + Minor Losses

Friction between fluid and it's flow boundary

Change in velocity or change in flow

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Basic Hydraulic Concepts
Open Channel Energy Equation

• Losses due to Transitions are considered Minor Losses
  
  h_L1-2 = Major Losses + Minor Losses

Change in velocity or change in flow

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Basic Hydraulic Concepts
Open Channel Energy Equation

• General Equation for Minor Losses

  h_Lm = K_mV²/2g

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Design of Transition Structures

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Design of Transition Structures
OCFCD Design Manual (p.14-15)

Transition Loss Equations

• Contraction:
  
  h = K_i(V₂²-V₁²/2g)

• Expansion:
  
  h = K_e(V₁²-V₂²/2g)

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Design of Transition Structures
Transition Loss Coefficients

SHAPE	Ki (Contraction)	Ko (Expansion)
Abrupt (Square)	0.30	0.80
Straight Line 10° 15° 20° 30°	0.10 0.10 0.10 0.10	0.20 0.30 0.40 0.70
Warped Design	0.10	0.20

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Design of Transition Structures
Design Considerations

• Define purpose of structure

• Define project constraints

  • Right-of-Way

  • Site conditions

  • Economic feasibility

  • Location of transition structure

• Design will be case by case

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Design of Transition Structures
General Guidelines for Design

1. Define design parameters

   • Design discharge, Q (cfs)

   • Geometry of existing and proposed channel section

2. Determine location of transition structure

3. Length of transition structure

4. Determine transition head loss, H_t

5. Determine existing WSE at beginning and end of preliminary location of transition

6. Based on initial water surface elevation calculation (output), refine design of transition

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Summary
Key Points to Remember

• Transitions in Subcritical Flow are analyzed using the Energy Equation

• Transition losses are energy losses associated with a change in velocity

• If possible, avoid design of transitions in supercritical and unstable range of flows

• Design considerations

• Design of transitions is case by case and comes with experience

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Open Channel Transitions in Subcritical Flow
Questions & Answers

What is this?

[untitled diagram and photos]

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Open Channel Transitions in Subcritical Flow
References

1. Chow, V. T. , Open Channel Hydraulics, McGraw Hill Book Co., Inc. New York (1959)

2. Ippen, A. T., "Mechanics of Supercritical Flow", Transactions, ASCE, Vol. 116 (1951)

3. Ippen, A. T. and Dawson, J. H., "Design of Channel Contractions", Transactions, ASCE, Vol. 116 (1951)

4. Rouse, H., Bhoota, B. V., and Hsu, En-Yun, "Design of Channel Expansions", Transactions, ASCE Vol. 116 (1951)

5. Knapp, R. T., "Design of Channel Curves for Supercritical Flow", Transactions, ASCE, Vol. 116 (1951)

6. Morris, Henry M. and Wiggert, James M., Applied Hydraulics in Engineering, Second Edition, John Wiley & Sons

7. U. S. Army, Office, Chief of Engineer, Hydraulic Design of Flood Control Channels, Engineer Manual EM 1110-2-1601 (1970)

8. Mostafa, M. Gamal, Open Channel Transitions in Subcritical Flow, Final Report No. ERC-78-396FR, (1978)

9. Orange County Flood Control District Design Manual, O.C.F.C.D., Orange County, California

10. Majaj, Nadeem H., "Appendix A - Basics of Hydraulics", Basin Analysis Software User's Manual, Hydraulic Solutions, Inc. (2003)

11. Basic Wave Theory and Principles were obtained at this link (click on the highlited title to take you to the site).

Note: Graphics and text depicting the Energy Equation were obtained from another slide presentation on the web. Author was not named.