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