Mannings Equation Evaluation Worksheet
Required Input Parameters Geometry Dependent Inputs Input Parameters Lining = Soil = n= Vmax = Slope (%) = Slope ('/') = INPUT Geometry Depth, d (ft) [all] = Top Width. t (ft) [parabolic] = Side slope, z [triangular & trapezoidal] = Base width, b (ft) [trapezoidal] = Parabolic Geometry Area, A (ft2) = Wetted Perimeter, Wp (ft) = Hydraulic Radius, R (ft) = 2.67 10.04 0.27 ft2 ft ft Velocity = Flow Rate, Q = Freeboard = ft2 ft ft Velocity = Flow Rate, Q = Freeboard = ft2 ft ft Velocity = Flow Rate, Q = Freeboard = none silt loam 0.04 2 fps 7 0.07 0.4 10 6 8 % ft/ft ft ft ft
4.06 fps 10.82 cfs 0.30 ft
EROSION
Triangular Geometry Area, A (ft2) = Wetted Perimeter, Wp (ft) = Hydraulic Radius, R (ft) = 0.96 4.87 0.20
3.33 3.20 0.30
fps cfs ft
EROSION
Trapezoidal Geometry Area, A (ft2) = Wetted Perimeter, Wp (ft) = Hydraulic Radius, R (ft) = 4.16 12.87 0.32
4.63 fps 19.25 cfs 0.30 ft
EROSION
Mannings Equation Design Worksheet
for
n = Constant
Design Constraints Discharge, Q (cfs) = Slope (%) = Slope (ft/ft) = Lining = n (Assumed Constant) = Vmax = Design Velocity, V (fps) = Hydraulic Radius, R (ft) = Parabolic Geometry Depth, d (ft) = 3R/2 = Area, A (ft2) = Q/V = Design dimension, top width, t (ft) = Freeboard, F (ft) = Total Depth, D (ft) = d + F = Froude Number, Fr = Flow Regime = 30 0.2 0.002 cfs % ft/ft Required Input Parameters
Grass Mixture 0.02 1.75 fps 1.75 0.38 0.70 17.14 36.62 0.30 1.00 0.20 Sub fps ft
Depth and Design Parameter for each Geometry
d (ft) 0.70
t (ft) 36.62
Ract (ft) 0.47
Diff 0.09
Use Goal Seek to set H20 to 0.0 while changing E20.
Triangular Geometry Depth, d (ft) = 2R = Area, A (ft2) = Q/V = Design dimension, side slope, z = Top width, t (ft) = 2dz = Freeboard, F (ft) = Total Depth, D (ft) = d + F = Froude Number, Fr = Flow Regime = Trapezoidal Geometry Side Slope, z = Depth, d (ft) = R = Area, A (ft2) = Q/V = Design dimension, base width, b = Top width, t (ft) = b+2dz = Freeboard, F (ft) = Total Depth, D (ft) = d + F = Froude Number, Fr = Flow Regime =
0.76 17.14 29.34 44.85 0.30 1.06 0.25 Sub
3 0.39 17.14 42.36 75.71 0.30 0.69 0.42 Sub
d (ft) 0.39
b (ft) 42.36
Ract (ft) 0.38
Diff 0.00
Use Goal Seek to set H42 to 0.0 while changing E42.
each Geometry
Mannings Equation Design Worksheet
for
Rock Lined Channels
Design Constraints Discharge, Q (cfs) = Slope (%) = Slope (ft/ft) = Lining = D50 = D50 = Vmax = Design Velocity, V (fps) = Parabolic Geometry Hydraulic Radius, R (ft) = Manning's Roughness, n = Depth, d (ft) = Area, A (ft2) = Q/V = Design dimension, top width, t (ft) = Freeboard, F (ft) = Total Depth, D (ft) = d + F = Froude Number, Fr = Flow Regime = 80 5 0.05 Rock 4 0.33 7.5 7.5 cfs % ft/ft Hydraulic Radius for each Velocity and Shape inch ft fps fps Depth of flow in the channel
Required Input Parameters Select any combination of Depth, Design Parameter & Velo
0.55 0.0334 4.56 10.67 3.51 2.57 7.13 0.57 Sub
ft
Evaluation of Depth, Manning's n and Hydraulic Radius for Parab Design Velocity = 7.5 fps Depth R t Ract ft n ft ft ft 4.56 0.0334 0.66 3.49 0.55
Use Goal Seek to set J24 to 0.0 by changing D24.
Triangular Geometry Hydraulic Radius, R (ft) = Manning's Roughness, n = Depth, d (ft) = Area, A (ft2) = Q/V = Design dimension, side slope, z = Top width, t (ft) = 2dz = Freeboard, F (ft) = Total Depth, D (ft) = d + F = Froude Number, Fr = Flow Regime = Trapezoidal Geometry Hydraulic Radius, R (ft) = Manning's Roughness, n = Side Slope, z = Depth, d (ft) =
0.79 0.0378 1.57 10.67 4.30 13.55 0.89 2.46 2.22 Super
ft
Evaluation of Depth, Manning's n and Hydraulic Radius for Triang Design Velocity = 7.5 fps Depth R d = 2R ft n ft ft 1.57 0.0378 0.79 1.57 Use Goal Seek to set J35 to 0.0 by changing E35.
0.97 0.0384 2 1.41
ft
Evaluation of Depth, Manning's n and Hydraulic Radius for Trape Design Velocity = 7.5 fps Depth R b Ract ft n ft ft ft 1.41 0.0384 0.81 4.71 0.97
Area, A (ft2) = Q/V = Design dimension, base width, b = Top width, t (ft) = b+2dz = Freeboard, F (ft) = Total Depth, D (ft) = d + F = Froude Number, Fr = Flow Regime =
10.67 4.71 10.37 0.80 2.21 1.70 Super
Use Goal Seek to set J45 to 0.0 by changing D45. NOTE: Set cell D45 to 0.5 before starting Goal Seek.
, Design Parameter & Velocity
ty and Shape
draulic Radius for Parabolic Shaped Channels Diff ft -0.11
draulic Radius for Triangular Shaped Channels Diff ft 0.00
draulic Radius for Trapezoidal Shaped Channels Diff ft 0.16
Mannings Equation Evaluation Worksheet
for
Vegetation-Lined Channels
Input Parameters Lining = Soil = Retardance Class = Vmax = Slope (%) = Slope ('/') = INPUT Geometry Depth, d (ft) [all] = Top Width. t (ft) [parabolic] = Side slope, z [triangular & trapezoidal] = Base width, b (ft) [trapezoidal] = Parabolic Geometry Area, A (ft2) = Wetted Perimeter, Wp (ft) = Hydraulic Radius, R (ft) = 6.67 10.27 0.65 ft2 ft n= ft Velocity = Flow Rate, Q = Freeboard = ft2 ft n= ft Velocity = Flow Rate, Q = Freeboard = ft2 ft n= ft Velocity = Flow Rate, Q = Freeboard = 0.0369 6.78 fps 45.21 cfs 0.51 ft Required Input Parameters Geometry Dependent Inputs Bermuda Grass easily eroded D 6 fps 4 0.04 1.0 10 6 15 % ft/ft ft ft ft
Class A B C D E
x -0.5 2 5 7 11
EROSION
Triangular Geometry Area, A (ft2) = Wetted Perimeter, Wp (ft) = Hydraulic Radius, R (ft) = 6.00 12.17 0.49 0.0400 6.25 fps 37.47 cfs 0.47 ft
EROSION
Trapezoidal Geometry Area, A (ft2) = Wetted Perimeter, Wp (ft) = Hydraulic Radius, R (ft) = 21.00 27.17 0.77 0.0351 7.12 fps 149.43 cfs 0.53 ft
EROSION
Manning's n calculations by iteration
Good for n < 0.20. If n > 0.2 n equation not valid
Parabolic Geometry V (fps) V (m/s) 6.78 2.07
Use Goal Seek to set M23 to 0.0 by changing the Velocity, H23. VR (m2/s) n V 0.41 0.0369 6.78
Diff (fps) 0.00
Use Goal Seek to set M29 to 0.0 by
Triangular Geometry V (fps) V (m/s) 6.25 1.90
VR (m2/s) 0.29
n 0.0400
V 6.25
Diff (fps) 0.00
Use Goal Seek to set M35 to 0.0 by Trapezoidal Geometry V (fps) V (m/s) 7.12 2.17 VR (m2/s) 0.51 n 0.0351 V 7.12 Diff (fps) 0.00
Mannings Equation Design Worksheet
for
Vegetation Lined Channels
Required Input Parameters Design Constraints Discharge, Q (cfs) = Slope (%) = Slope (ft/ft) = Lining = Stability Retardance Class = Depth Retardance Class = Vmax = 60 4 0.04 cfs % ft/ft Class A B C D E x -0.5 2 5 7 11
Grass Mixture D D 6 fps
STABILITY DESIGN -- Design for lowest retardance condition; mowed grass, dormant sea
Design Velocity, V (fps) = 6.0 fps VR (m2/s) R (ft) R (m) n R (ft) 0.66 0.20 0.37 0.0377 0.66 Good for n < 0.20. If n > 0.2 n equation not valid FIRST, Use Goal Seek to set H changing C22. Use Goal Seek to set F30 to 0.0 Parabolic Geometry Depth, d (ft) = Area, A (ft2) = Q/V = Design dimension, top width, t (ft) = Froude Number, Fr = Flow Regime = d (ft) 1.01 t (ft) 14.88 Ract (ft) 0.66 Diff 0.00
Hydraulic Radius, R (ft) = Manning's Roughness, n =
0.66 0.0377
1.01 10.00 14.88 1.66 Super
Triangular Geometry Depth, d (ft) = 2R = Area, A (ft2) = Q/V = Design dimension, side slope, z = Top width, t (ft) = 2dz = Froude Number, Fr = Flow Regime =
1.33 10.00 5.66 15.05 1.68 Super
The FIRST iterative solution, to get the proper hydrau radius, using the data in Row 22. Then the Seek must be used to determine the correct depth of flow; either Row 30 for a parabolic shape or Row a Trapezoidal shape. If a triangular shape is desired, NO 2nd iteration is required b/c this is an explicit solution. The FIRST and 2nd iteration must be repeated until t hydraulic radius shown in C22, G22 E48 are all equal.
Trapezoidal Geometry Side Slope, z = Depth, d (ft) = Area, A (ft2) = Q/V =
Use Goal Seek to set F48 to 0.0 by changing the Depth, C48.
4 0.95 10.00
d (ft) 0.95
b (ft) 6.79
Ract (ft) 0.69
Diff 0.02
Design dimension, base width, b = Top width, t (ft) = b+2dz = Froude Number, Fr = Flow Regime =
6.79 19.63 2.19 Super
DEPTH DESIGN -- Design for highest retardance condition; unmowed grass, growing sea
Depth Retardance Class = Parabolic Geometry Parabolic Geometry Depth, d (ft) = Area, A (ft2) = Q/V = Design dimension, top width, t (ft) = Manning's Roughness, n = Froude Number, Fr = Flow Regime = d (ft) 0.97 0.97 9.63 14.88 0.0377 1.86 Super t (ft) 14.88 A (ft2) 9.63 R (ft) 0.64 D V1 = Q/A (fps) 6.23
Use Goal Seek to set K changing the Depth, C
If V1 does not equal V2, you may need to compute this iteration yourself.
Triangular Geometry Trial Triangular Geometry Depth, d (ft) = Area, A (ft2) = Q/V = Design dimension, side slope, z = Top width, t (ft) = 2dz = Manning's Roughness, n = Froude Number, Fr = Flow Regime = 1.24 8.78 5.66 14.10 0.0373 2.33 Super d (ft) 1.24 z 5.66 A (ft2) 8.78 R (ft) 0.61
V1 = Q/A (fps) 6.84 Use Goal Seek to set K changing the Depth, C
If V1 does not equal V2, you may need to compute this iteration yourself.
Trapezoidal Geometry Trial Trapezoidal Geometry Side Slope, z = Depth, d (ft) = Area, A (ft2) = Q/V = Design dimension, base width, b = Top width, t (ft) = b+2dz = Manning's Roughness, n = Froude Number, Fr = Flow Regime = 4 1.27 15.12 6.79 16.97 0.0389 0.55 Sub d (ft) 1.27 b (ft) 6.79 A (ft2) 15.12 R (ft) 0.87
V1 = Q/A (fps) 3.97 Use Goal Seek to set K changing the Depth, C
If V1 does not equal V2, you may need to compute this iteration yourself.
wed grass, dormant season
Diff 0.00
se Goal Seek to set H22 to 0.0 by
solution, to get the proper hydraulic . Then the 2nd Goal o determine the correct depth of or a parabolic shape or Row 48 for If a triangular shape is ation is required b/c this is an
teration must be repeated until the , G22, and either E30 or
wed grass, growing season
VR (m2/s) 0.37
n 0.0377
V2 = Man (fps) 5.85
Diff fps -0.39
Use Goal Seek to set K62 to 0.0 by changing the Depth, C62.
not equal V2, you may need to his iteration yourself.
VR (m2/s) 0.39
n 0.0373
V2 = Man (fps) 5.75
Diff fps -1.09
Use Goal Seek to set K75 to 0.0 by changing the Depth, C75.
not equal V2, you may need to his iteration yourself.
VR (m2/s) 0.32
n 0.0389
V2 = Man (fps) 6.98
Diff fps 3.02
Use Goal Seek to set K87 to 0.0 by changing the Depth, C87.
V2, you may need to