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Rock Creek Canal, Montana

Rock Creek Canal, Montana. http://wwwrcamnl.wr.usgs.gov/sws/fieldmethods/Indirects/nvalues/. Steady, uniform flow: Y 1 = Y 2 , U 1 = U 2 ,. Energy grade line. horizontal line. Energy loss. U 1 2 2g. U 2 2 2g. Water surface. Y 1. U 1. Y 2. U 2. Channel bed. Z 2. Z 1. x

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Rock Creek Canal, Montana

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  1. Rock Creek Canal, Montana http://wwwrcamnl.wr.usgs.gov/sws/fieldmethods/Indirects/nvalues/

  2. Steady, uniform flow: Y1 = Y2, U1 = U2, Energy grade line horizontal line Energy loss U12 2g U22 2g Water surface Y1 U1 Y2 U2 Channel bed Z2 Z1 x Channel slope = Z = H x x Elevation datum

  3. non-uniform flow: Y1Y2, U1 U2, Energy grade line horizontal line Energy loss U12 2g Water surface U22 2g Y1 U1 Y2 U2 Channel bed Z2 Z1 Elevation datum x Channel slope = Z H x x

  4. Pathways of water particles in laminar and turbulent flow

  5. Cross sectional average water velocity (U) in an open channel For turbulent flow: U = (channel conductivity)(energy gradient)1/2 Energy gradient = d H d x Where H = hydraulic head x = distance along the channel H = potential energy + kinetic energy + pressure + inertia H = Z + U2+ Y + 1dU 2g g dt Z = elevation above base g= acceleration due to gravity U = velocity t = time Y = water depth

  6. Energy gradient = d H = Z + (U2/2g) + Y + 1U d x x x x g t If flow is steady with respect to time, then U =0 t If flow is uniform with respect to distance down the channel, then (U2/2g) = 0 and Y = 0 xx For steady, uniform flow, d H = Z = channel bed slope in the direction of flow d x x

  7. Empirical formula for average flow velocity in an open channel Chezy formula U = C ·(R1/2)·(H / x )1/2 where: U = mean flow velocity (ft/sec or m/sec) R = hydraulic radius (ft or m) R = cross sectional Area/Wetted perimeter = A/P H= hydraulic head x = horizontal distance C = Chezy resistance factor For steady, uniform flow, H/ x = Z/ x = channel slope U = C (R1/2)(Z/ x )1/2 = C (R1/2)(S)1/2 S = bed slope in the direction of flow, Z / x (dimensionless)

  8. Empirical formula for average flow velocity Manning’s Equation: U = um·(R2/3)·(H / x )1/2 n where: U = mean flow velocity (ft/sec or m/sec) R = hydraulic radius = Cross sectional Area = A (ft or m) Wetted perimeter P H / x = energy gradient n = Manning’s roughness coefficient. um = unit conversion factor um = 1.49 if R is expressed in feet and U in ft/sec um = 1.0 if R is expressed in meters and U in m/sec For steady, uniform flow: U = um·(R2/3)·(H / x )1/2 n S = bed slope, Z / x (dimensionless)

  9. Wetted Perimeter (P) and Hydraulic Radius (R) for a rectangular channel P = d + w + d = 2 • d + w P = wetted perimeter d = depth w = width Example 1: w = 6 ft, d = 2 ft P = 2 • 2 ft + 6 ft = 10 ft A = 2 ft • 6 ft = 12 ft2 R = A/P = 12ft2/10ft = 1.2 ft Example 2: w = 60 ft, d = 2 ft P = 2 • 2 ft + 60 ft = 64 ft A = 2 ft • 60 ft = 120 ft2 R = A/P = 120ft2/64ft = 1.9 ft

  10. Wetted Perimeter (P) and Hydraulic Radius (R) for a Trapezoidal channel A = (b • d) + (e • d) P = b + 2 • [(d2 +e2)1/2] b= base width (L) d = depth in center (L) Z = horizontal:vertical bank slope, e/d e = Z•d Example: b = 6 ft, d = 2 ft, Z =1 e = 2ft A = (6ft • 2 ft) + (2 ft • 2ft) A = 12 ft2 + 4 ft2 = 16 ft2 P = 6 ft + 2 • [(22 + 22)1/2] P = 6 ft + 5.7 ft = 11.7 ft R = A/P = 16ft2/11.7 ft = 1.37 ft

  11. n = (no + n1 + n2 + n3 + n4 )· m5 From Chow, 1959

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