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Cu06997 lecture 9_open channel

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Cu06997 lecture 9_open channel

1. 1. CU06997 Fluid Dynamics Open channel flow 1 5.1 Flow with a free surface (page 122) 5.2 Flow classification (page 122, 123) 5.3 Channels and their properties (page 123-125) 5.4 Velocity distributions (page 126,127) 5.5 Laminar and turbulent flow (page 127-129) 5.6 Uniform flow (page 129 -138)1
2. 2. Flow with a free surface1
3. 3. Classification of flows, see part 2 1. Steady uniform flow example: pipe with constant D and Q example: channel with constant A and Q 2. Steady non-uniform flow example: pipe with different D and constant Q example: channel with different A and constant Q 3. Unsteady uniform flow example: channel with constant A and different Q 4. Unsteady non-uniform flow example; channel with different A and Q2
4. 4. Types of flow2
5. 5. Geometric properties3
6. 6. Velocity distributions3
7. 7. Velocity distributions π π1 π΄1 + π2 π΄2 + π3 π΄3 πππ£πππππ = = π΄ π΄1 + π΄2 + π΄3 π π‘ππ‘πππ = π1 + π3 + π3 =π1 π΄1 + π2 π΄2 + π3 π΄33
8. 8. Reynolds number, see part 3 ππ = π. π· π π= Absolute viscosity [m2/s] π. 4π π= Kinematic viscosity [kg/ms] ππ = water, 20Β°C= 1,00 β 10β6 ππ = Density of liquid [kg/m3]π = Velocity [m/s]D = Hydraulic diameter [m]R= Hydraulic Radius = D/4 [m]ππ = Reynolds Number [1] πΉπ > ππππ Turbulent flow πΉπ < ππππ Laminar flow3 In this course we only look at turbulent flow
9. 9. Open channel, with bed slope >0 2 2 π’1 π’2π¦1 + π§1 + = π¦2 + π§2 + + βπ»1β2 2π 2π Q ο½ u1 ο A1 ο½ u2 ο A2 Head loss Reference line4
10. 10. Open channel, with bed slope <= 0 2 2 u u y1 ο« z1 ο« 1 ο½ y2 ο« z2 ο« ο« οH 1ο­ 2 2 2g 2g Head loss [m] u12/2g ΞH Total Head H [m] y1 u22/2g Velocity Head [m] P1 u1 Surfacelevel y +z [m] z1 y2 P2 u2 z24 Reference [m]
11. 11. Chezy formula π= πΆβ π β ππChezy formula describes the mean velocity of uniform, turbulent flow π= Mean Fluid Velocity [m/s] R= Hydraulic Radius [m] ππ = Hydraulic gradient [1] 8π πΆ= Chezy coefficient [m1/2/s] π ΞH ππ = πΏ ΞH5 Length
12. 12. Chezy coefficient In this course we assume a hydraulic rough boundary Boundary hydraulic rough 12 R C ο½ 18 log [m1/2/s] k kS = surface roughness [m]5
13. 13. Surface roughness kS [m] Equivalent Sand Roughness, Material (ft) (mm) Copper, brass 1x10-4 - 3x10-3 3.05x10-2 - 0.9 Wrought iron, 1.5x10-4 - 8x10-3 4.6x10-2 - 2.4 steel Asphalt-lined 4x10-4 - 7x10-3 0.1 - 2.1 cast iron 3.3x10-4 - 1.5x10- Galvanized iron 2 0.102 - 4.6 Cast iron 8x10-4 - 1.8x10-2 0.2 - 5.5 Concrete 10-3 - 10-2 0.3 - 3.0 Uncoated Cast 7.4x10-4 0.226 Iron Coated Cast Iron 3.3x10-4 0.102 Coated Spun 1.8x10-4 5.6x10-2 Iron Cement 1.3x10-3 - 4x10-3 0.4 - 1.2s Wrought Iron 1.7x10-4 5x10-2 Uncoated Steel 9.2x10-5 2.8x10-2 Coated Steel 1.8x10-4 5.8x10-2 Wood Stave 6x10-4 - 3x10-3 0.2 - 0.9 PVC 5x10-6 1.5x10-3 Compiled from Lamont (1981), Moody (1944), and Mays (1999)5
14. 14. Manningβs formula describes theManningβs formula mean velocity of uniform, turbulent flow 2 1 5 1 π3 β π2 1 π΄3 π2 1 π= π π= β β R 6 π 2 π Cο½ π π3 nπ= Mean Fluid Velocity [m/s]R= Hydraulic Radius [m]ππ = Slope Total head [1]π΄= Wetted Area [m2]π= Wetter Perimeter [m]π= Mannings roughness coefficient [s/m1/3]6
15. 15. Mannings roughness coefficient6
16. 16. Mean boundary shear stress π0 = π β π β π β π0 Ο0 = shear stress at solid boundary [N/m2] R= Hydraulic Radius [m] π0 = Slope of channel bed [1]7
17. 17. Flowing water and energy 2 u H1 ο½ z1 ο« y1 ο« 1 [m ] 2g Total head H [m] u12/2g Velocity head [m] Surface level [m] y1 y = Pressure head [m] u1 P1 z1 z = Potential head [m] Reference /datum [m]
18. 18. Specific Energy π2 πΈπ  = π¦ + 2π π= Mean Fluid Velocity [m/s] p y= = Pressure Head / water depth [m] Οβg Total head H or Specific energy Es [m] V2/2g Velocity head [m] Surface level [m] V y y = Pressure head [m] = water depth [m]8 Channel bed as datum [m]
19. 19. Equilibrium / normal depth Discharge, cross-section, energy gradient and friction are constant yn π0 = π π Side view π= πΆβ π β ππ yn A b. y Rο½ ο½ οy Cross-section P b ο« 2ο y π = π β π΄ = πΆ 2 π¦ β π πβ π¦ β π 3 π2 π¦π =9 π 2 β πΆ 2 β π0
20. 20. Equilibrium / normal depth π0 = π π 3 π2 π¦π = π 2 β πΆ 2 β π0 yn = normal depth [m] q= discharge [m3/s] b= width [m] π0 = bed slope [1] ππ = Hydraulic gradient caused by friction [1] 8π πΆ= Chezy coefficient [m1/2/s] π9
21. 21. Equilibrium / normal depthyn yn yn yn Dredged area 3 π2 π¦π = π 2 β πΆ 2 β π09