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2/15/2000. Channel Flow.ppt. 2. Lesson Objectives. 1.Understand the effects of waterway slope, shape, and roughness on the flow velocity of water.2.Know how to determine the area and hydraulic radius of the three major channel cross section shapes used in waterways.3.Be able to use the Manning Equation and the Continuity Equation to predict flow- velocity and flow-rate in a waterway..
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1. 2/15/2000 Channel Flow.ppt 1 Flow in Channels AST 324
Carl E. Anderson
2. 2/15/2000 Channel Flow.ppt 2
3. 2/15/2000 Channel Flow.ppt 3
4. 2/15/2000 Channel Flow.ppt 4 If you wanted to find a tire that would get better traction, what characteristics would you look for?
5. 2/15/2000 Channel Flow.ppt 5 Open Channel Flow
6. 2/15/2000 Channel Flow.ppt 6 MANNING EQUATION V = velocity of flow in feet per second (meters per second)
C = Constant = 1.49 for English units (1.00 for metric units)
R = Hydraulic Radius in feet (meters)
7. 2/15/2000 Channel Flow.ppt 7 MANNING EQUATION S = channel slope in ft/ft or m/m
n = Manning roughness coefficient
8. 2/15/2000 Channel Flow.ppt 8 MANNING EQUATION More roughness in the channel (n) will slow down the water
Smaller R (flow depth) will slow down the water
Smaller slope (S) will slow down the water
9. 2/15/2000 Channel Flow.ppt 9 MANNING ROUGHNESS COEFFICIENTS Smooth concrete n = 0.012
Corrugated pipe n = 0.025
Smooth soil n = 0.03
Cultivated soil n = 0.04
10. 2/15/2000 Channel Flow.ppt 10 CHANNEL HYDRAULIC RADIUS R = A / P (the average flow depth)
A = Area of the flow cross-section in sq. ft (sq. m)
P = Length of the line of contact between the channel and the water on the area in feet (meters)
11. 2/15/2000 Channel Flow.ppt 11 Manning EquationSimple Example: Rectangular cross-section A = BD
P = B + 2D
For
B = 5 ft.,
D = 2 ft.
A = 10 ft.2
P = 9 ft.
R = 10 / 9 = 1.11 ft.
12. 2/15/2000 Channel Flow.ppt 12 MANNING EQUATION
13. 2/15/2000 Channel Flow.ppt 13 Manning EquationSimple Example: continued Rectangular cross-section A = 10 ft.2
P = 9 ft.
R = 10 / 9 = 1.11 ft
For
S = 1% = 0.01 ft/ft
n = 0.04
14. 2/15/2000 Channel Flow.ppt 14 Manning EquationSimple Example: continued Rectangular cross-section
15. 2/15/2000 Channel Flow.ppt 15 PRINCIPLES OF WATER FLOW A = BD + ZD2
P = B + 2D(Z2+1)1/2
R = A/ P
16. 2/15/2000 Channel Flow.ppt 16 PRINCIPLES OF WATER FLOW A = pD2 / 4
P = pD
R = A/ P = D/ 4
17. 2/15/2000 Channel Flow.ppt 17 Example for Trapezoidal Channel B = 10 feet
D = 3 feet
n = 0.04
S = 0.1% = 0.001 ft/ ft
Z = 2 feet horizontal for each foot vertical on the side slopes.
Estimate the Velocity and Capacity
18. 2/15/2000 Channel Flow.ppt 18 Example for a full pipe D = 12 inches = 1 foot
p = 3.1416
n = 0.015
S = 0.1% = 0.001 ft/ ft
Estimate the flow velocity and the capacity of this pipe.
19. 2/15/2000 Channel Flow.ppt 19 Parabolic Channel Cross-section