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Hydraulic Engineering - Channel Hydraulics

Online Calculation of Open Channel Flow


1. Calculate Channel Geometry

2. Formula of Manning-Strickler; calculation of slope, mass-flow or mean velocity of flow, Reynold- and Froudenumber

3. Formula of Darcy-Weisbach; calculation of slope, mass-flow or mean velocity of flow, Reynold- and Froudenumber


Channel Geometry:

Rectangle

Rectangle
width b: [ m ] depth h: [ m ]

Trapezoid

Trapezoid
slope ml: [ m ] slope mr: [ m ]
or
angle of slope α left: ° angle of slope β rechts: °
width b: [ m ] depth h: [ m ]

2-stage
Trapezoid

two-stage Trapezoid
slope m_left_down: [ m ] slope m_right_down: [ m ]
or
angle of slope α_left_down: ° angle of slope α_right_down: °

width b1: [ m ]
slope m_left_up: [ m ] slope m_right_up: [ m ]
or
angle of slope α_left_up: ° angle of slope α_right_up: °

width b2 left: [ m ]
width b2 right: [ m ]
depth h1: [ m ] total depth h: [ m ]

Triangle

Triangle
slope m: [ m ]
or
angle of slope α: °
 depth h: [ m ]

Circle

Circle
diameter D: [ m ] depth h: [ m ]

Parabola

Parabola
width B: [ m ] depth h: [ m ]

irregular
Channel

irregular Channel
area A: [ m ] wetted perimeter O: [ m ]
reference: http://en.wikipedia.org/wiki/Hydraulic_diameter
http://de.wikipedia.org/wiki/Hydraulischer_Durchmesser



Geometry resumed:

area A:
[ m2 ]
wetted perimeter O:
[ m ]
hydraulic radius Rh:
[ m ]


2. Formula of Manning-Strickler:

Manning-Strickler

V mean velocity of flow [ m / s ]
Rh gravity acceleration [ m ]
Io slope [ 1 / m]
n Manning's roughness coefficient [ s / m1/3 ]



Surface Material Manning's Roughness

 n  [ s / m1/3 ]
Asbestos cement0.011
Asphalt0.016
Brass0.011
Brick0.015
Canvas0.012
Cast-iron, new0.012
Clay tile0.014
Concrete - steel forms0.011
Concrete (Cement) - finished0.012
Concrete - wooden forms0.015
Concrete - centrifugally spun0.013
Copper0.011
Corrugated metal0.022
Earth, smooth0.018
Earth channel - clean0.022
Earth channel - gravelly0.025
Earth channel - weedy0.030
Earth channel - stony, cobbles0.035
Floodplains - pasture, farmland0.035
Floodplains - light brush0.050
Floodplains - heavy brush0.075
Floodplains - trees0.15
Galvanized iron0.016
Glass0.010
Gravel, firm0.023
Lead0.011
Masonry0.025
Metal - corrugated0.022
Natural streams - clean and straight0.030
Natural streams - major rivers0.035
Natural streams - sluggish with deep pools0.040
Natural channels, very poor condition0.060
Plastic0.009
Polyethylene PE - Corrugated with smooth inner walls0.009 - 0.015
Polyethylene PE - Corrugated with corrugated inner walls0.018 - 0.025
Polyvinyl Chloride PVC - with smooth inner walls0.009 - 0.011
Rubble Masonry0.017
Steel - Coal-tar enamel0.010
Steel - smooth0.012
Steel - New unlined0.011
Steel - Riveted0.019
Vitrified Sewer0.013 - 0.015
Wood - planed0.012
Wood - unplaned0.013
Wood stove pipe, small diameter0.011 - 0.012
Wood stove pipe, large diameter0.012 - 0.013



Manning's n for Channels (Chow, 1959)

Type of Channel and Description

 Minimum Normal Maximum
Natural streams - minor streams (top width at floodstage < 100 ft)
1. Main Channels
a. clean, straight, full stage, no rifts or deep pools 0.025 0.030 0.033
b. same as above, but more stones and weeds 0.030 0.035 0.040
c. clean, winding, some pools and shoals 0.033 0.040 0.045
d. same as above, but some weeds and stones 0.035 0.045 0.050
e. same as above, lower stages, more ineffective
slopes and sections		 0.040 0.048 0.055
f. same as "d" with more stones 0.045 0.050 0.060
g. sluggish reaches, weedy, deep pools 0.050 0.070 0.080
h. very weedy reaches, deep pools, or floodways
with heavy stand of timber and underbrush		 0.075 0.100 0.150
2. Mountain streams, no vegetation in channel, banks usually steep,
trees and brush along banks submerged at high stages
a. bottom: gravels, cobbles, and few boulders 0.030 0.040 0.050
b. bottom: cobbles with large boulders 0.040 0.050 0.070
3. Floodplains
a. Pasture, no brush
     1.short grass 0.025 0.030 0.035
     2. high grass 0.030 0.035 0.050
b. Cultivated areas
1. no crop 0.020 0.030 0.040
     2. mature row crops 0.025 0.035 0.045
     3. mature field crops 0.030 0.040 0.050
c. Brush
     1. scattered brush, heavy weeds 0.035 0.050 0.070
     2. light brush and trees, in winter 0.035 0.050 0.060
     3. light brush and trees, in summer 0.040 0.060 0.080
     4. medium to dense brush, in winter 0.045 0.070 0.110
     5. medium to dense brush, in summer 0.070 0.100 0.160
d. Trees
     1. dense willows, summer, straight 0.110 0.150 0.200
     2. cleared land with tree stumps, no sprouts 0.030 0.040 0.050
     3. same as above, but with heavy growth of sprouts 0.050 0.060 0.080
     4. heavy stand of timber, a few down trees, little
     undergrowth, flood stage below branches 		0.080 0.100 0.120
     5. same as 4. with flood stage reaching branches 0.100 0.120 0.160
4. Excavated or Dredged Channels
a. Earth, straight, and uniform
     1. clean, recently completed 0.016 0.018 0.020
     2. clean, after weathering 0.018 0.022 0.025
     3. gravel, uniform section, clean 0.022 0.025 0.030
     4. with short grass, few weeds 0.022 0.027 0.033
b. Earth winding and sluggish
     1. no vegetation 0.023 0.025 0.030
     2. grass, some weeds 0.025 0.030 0.033
     3. dense weeds or aquatic plants in deep channels 0.030 0.035 0.040
     4. earth bottom and rubble sides 0.028 0.030 0.035
     5. stony bottom and weedy banks 0.025 0.035 0.040
     6. cobble bottom and clean sides 0.030 0.040 0.050
c. Dragline-excavated or dredged
     1. no vegetation 0.025 0.028 0.033
     2. light brush on banks 0.035 0.050 0.060
d. Rock cuts
     1. smooth and uniform 0.025 0.035 0.040
     2. jagged and irregular 0.035 0.040 0.050
e. Channels not maintained, weeds and brush uncut
     1. dense weeds, high as flow depth 0.050 0.080 0.120
     2. clean bottom, brush on sides 0.040 0.050 0.080
     3. same as above, highest stage of flow 0.045 0.070 0.110
     4. dense brush, high stage 0.080 0.100 0.140
5. Lined or Constructed Channels
a. Cement
     1. neat surface 0.010 0.011 0.013
     2. mortar 0.011 0.013 0.015
b. Wood
     1. planed, untreated 0.010 0.012 0.014
     2. planed, creosoted 0.011 0.012 0.015
     3. unplaned 0.011 0.013 0.015
     4. plank with battens 0.012 0.015 0.018
     5. lined with roofing paper 0.010 0.014 0.017
c. Concrete
     1. trowel finish 0.011 0.013 0.015
     2. float finish 0.013 0.015 0.016
     3. finished, with gravel on bottom 0.015 0.017 0.020
     4. unfinished 0.014 0.017 0.020
     5. gunite, good section 0.016 0.019 0.023
     6. gunite, wavy section 0.018 0.022 0.025
     7. on good excavated rock 0.017 0.020
     8. on irregular excavated rock 0.022 0.027
d. Concrete bottom float finish with sides of:
     1. dressed stone in mortar 0.015 0.017 0.020
     2. random stone in mortar 0.017 0.020 0.024
     3. cement rubble masonry, plastered 0.016 0.020 0.024
     4. cement rubble masonry 0.020 0.025 0.030
     5. dry rubble or riprap 0.020 0.030 0.035
e. Gravel bottom with sides of:
     1. formed concrete 0.017 0.020 0.025
     2. random stone mortar 0.020 0.023 0.026
     3. dry rubble or riprap 0.023 0.033 0.036
f. Brick
     1. glazed 0.011 0.013 0.015
     2. in cement mortar 0.012 0.015 0.018
g. Masonry
     1. cemented rubble 0.017 0.025 0.030
     2. dry rubble 0.023 0.032 0.035
h. Dressed ashlar/stone paving 0.013 0.015 0.017
i. Asphalt
     1. smooth 0.013 0.013
     2. rough 0.016 0.016
j. Vegetal lining 0.030 0.500



Manning's n for Closed Conduits Flowing Partly Full (Chow, 1959)

Type of Channel and Description

 Minimum Normal Maximum
1. Brass, smooth: 0.009 0.010 0.013
2. Steel:
     Lockbar and welded 0.010 0.012 0.014
     Riveted and spiral 0.013 0.016 0.017
3. Cast Iron:
     Coated 0.010 0.013 0.014
     Uncoated 0.011 0.014 0.016
4. Wrought Iron:
     Black 0.012 0.014 0.015
     Galvanized 0.013 0.016 0.017
5. Corrugated Metal:
     Subdrain 0.017 0.019 0.021
     Stormdrain 0.021 0.024 0.030
6. Cement:
     Neat Surface 0.010 0.011 0.013
     Mortar 0.011 0.013 0.015
7. Concrete:
     Culvert, straight and free of debris 0.010 0.011 0.013
     Culvert with bends, connections, and some debris 0.011 0.013 0.014
     Finished 0.011 0.012 0.014
     Sewer with manholes, inlet, etc., straight 0.013 0.015 0.017
     Unfinished, steel form 0.012 0.013 0.014
     Unfinished, smooth wood form 0.012 0.014 0.016
     Unfinished, rough wood form 0.015 0.017 0.020
8. Wood:
     Stave 0.010 0.012 0.014
     Laminated, treated 0.015 0.017 0.020
9. Clay:
     Common drainage tile 0.011 0.013 0.017
     Vitrified sewer 0.011 0.014 0.017
     Vitrified sewer with manholes, inlet, etc. 0.013 0.015 0.017
     Vitrified Subdrain with open joint 0.014 0.016 0.018
10. Brickwork:
     Glazed 0.011 0.013 0.015
     Lined with cement mortar 0.012 0.015 0.017
     Sanitary sewers coated with sewage slime
with bends and connections		 0.012 0.013 0.016
     Paved invert, sewer, smooth bottom 0.016 0.019 0.020
     Rubble masonry, cemented 0.018 0.025 0.030



Manning's n for Corrugated Metal Pipe (AISI, 1980)

Type of Pipe, Diameter and Corrugation Dimension

 n
1. Annular 2.67 x 1/2 inch (all diameters) 0.024
2. Helical 1.50 x 1/4 inch
     8" diameter 0.012
     10" diameter 0.014
3. Helical 2.67 x 1/2 inch
     12" diameter 0.011
     18" diameter 0.014
     24" diameter 0.016
     36" diameter 0.019
     48" diameter 0.020
     60" diameter 0.021
4. Annular 3x1 inch (all diameters) 0.027
5. Helical 3x1 inch
     48" diameter 0.023
     54" diameter 0.023
     60" diameter 0.024
     66" diameter 0.025
     72" diameter 0.026
     78" diameter and larger 0.027
6. Corrugations 6x2 inches
     60" diameter 0.033
     72" diameter 0.032
     120" diameter 0.030
     180" diameter 0.028



Manning n values associated with photos
Table of values of Manning's n values

Please enter the Manning-factor,   the slope, den mass-flow or the mean velocity of flow, plus the kinematic viscosity ν of water:

Manning's roughness coefficient n:
Slope Io:[ m ] slope per m of channel
mass-flow Q:[ m3 / s ]
mean velocity of flow V:[ m / s ]
kinematic viscosity ν: [ m2 / s ]
at   5°C: 1.519 x 10-6
at 10°C: 1.307 x 10-6
at 15°C: 1.139 x 10-6
at 20°C: 1.004 x 10-6
at 25°C: 0.893 x 10-6
at 30°C: 0.801 x 10-6


Manning_formula




Geometry resumed:

area A:
[ m2 ]
wetted perimeter O:
[ m ]
hydraulic radius Rh:
[ m ]


3. Formula of Darcy-Weisbach:

Darcy-Weisbach
V mean velocity of flow [ m / s ]
g gravity acceleration 9.81 [ m / s2]
Rh hydraulic radius [ m ]
Io slope [ m]
λ friction factor


In hydraulically rough area, ks /4 Rh > 5 . 10-3 applies to the friction coefficient λ:
lamda
ks Rougness of channel bottom; absolute roughness length; equivalent sand roughness [ mm ]

Type of channel

 ks [mm]
Smooth channel bottom:
sand or gravel: ks = dk 90 (Grain diameter which is below 90% of the material)
Grain size table		 dk 90
coarse gravel to rubble 60 - 200
heavy riprap 200 - 300
sole paving 30 - 50
Nonplanar channel bottom: (hT = height of the channel body with ripples)
Rippel		 hT
Embankment with:
farmland		 20 - 250
farmland with crops 250 - 800
forest floor 160 - 320
turf 60
rock fill 80/450 300
grass 100 - 350
grass and shrubs 130 - 400
grass pavers 15 - 30
Walls of:
brick masonry		 2 - 8
smooth concrete 1 - 6
rough concrete 6 - 20
crushed stone 15 - 20
rough stone wall 80 - 100
steel sheet piling depending on tread depth 20 - 100
Pipes made of:
PVC		 0.005 - 0.1
steel 0.1 - 5
concrete 0.1 - 50
Wooden channel planed - uncouth: 0.1 - 5

ks: [ mm ]


Please enter the slope, den mass-flow or the mean velocity of flow, plus the kinematic viscosity ν of water:

friction coefficient λ:
slope Io:[ 1 / m ] slope per m of channel
mass-flow Q:[ m3 / s ]
mean velocity of flow V:[ m / s ]
kinematic viscosity ν: [ m2 / s ]
at   5°C: 1.519 x 10-6
at 10°C: 1.307 x 10-6
at 15°C: 1.139 x 10-6
at 20°C: 1.004 x 10-6
at 25°C: 0.893 x 10-6
at 30°C: 0.801 x 10-6




Literature & Links

Wikipedia: Open-channel flow

Open Channel Flow:


if you found an error, please mail to: webmaster@peacesoftware.de
if you have a hint, a wish, or an idea for further calculation, also: webmaster@peacesoftware.de