1. BIHE University
Department of Civil Engineering
Water Conveyance System – CIV4104-S12
Aug-2012
Overview
General Formulation of
Best Hydraulic Channel
Section
Course: Water Conveyance System
Course ID: CIV4104-S12
Instructor: Mr. Soroush Sorourian
Date: Thursday, August 02, 2012
Spring 2012

2. Outline
• Introduction
• Types of Channel Sections
• Best Hydraulic Section
• Conclusion

3. Introduction
• Lagrange’s Method for Optimization
Maximize f(x,y)
Subjected to g(x,y)=c.

4. Introduction [Cont’d]
• Lagrange’s Method in Channel Optimization
– Minimizing the wetted perimeter.
– (Minimizing the cross-sectional area)

5. Types of Channel Sections
• One independent variable
– Semicircle channels

6. Types of Channel Sections
• One independent variable
• Two independent variables
– Rectangular, triangular and parabolic channels

7. Types of Channel Sections
• One independent variable
• Two independent variables
• Three independent variables
– Trapezoid, round-bottom triangles , etc.

8. Types of Channel Sections
• One independent variable
• Two independent variables
• Three independent variables
• Four or more independent variables

9. Best Hydraulic Section
• Lagrange’s method of undetermined multipliers

10. Best Hydraulic Section [Cont’d]
• Section with TWO Variables:
– Results:

11. Best Hydraulic Section [Cont’d]
• Section with TWO Variables:
– Results:
• Example 1 (Rectangular section)
– x1=b , x2=y; P=2y+b and A=b.y
Then: b=2y

12. Best Hydraulic Section [Cont’d]
• Section with Three Variables:
– Results:

13. Best Hydraulic Section [Cont’d]
• Section with Three Variables:
Then: b=2y

14. Best Hydraulic Section [Cont’d]
VS.

15. Conclusion

16. Any Question?