1 Introduction

The flow resistance parameters (or flow friction factors) of channel controls are often difficult to determine precisely. In engineering practice, they are often expressed as Strickler coefficient \(K_S\) or Manning coefficient \(n\), one being the opposite of the other (\(n=1/K_S\)). There exist look-up tables of typical values (e.g., Chow’s table, or this illustrated catalogue) and calculation methods based on a more detailed description of flow conditions (e.g., Cowan method, or the method of Arcement and Schneider, 1989).

Other interesting references on friction factor estimation:

Barnes, H.H. (1967) Roughness characteristics of natural channels. U.S. Geological Survey Water-Supply Paper 1849, 213.
Hey, R.D. (1979) Flow resistance in gravel-bed rivers. J. Hydraul. Div., Am. Soc. Civ. Eng., 105(4), 365–379.
Hicks, D.M., Mason, P.D. (1998) Roughness Characteristics of New Zealand Rivers, Water Resources Publications, Littleton, CO, 329 pp., ISBN:0-477-02608-7.
Jarrett, R.D. (1985) Determination of roughness coefficients for streams in Colorado. U.S. Geological Survey Water-Resources Investigations Rep. 85-4004, 54.
Limerinos, J.T. (1970) Determination of the Manning coefficient from measured bed roughness in natural channels. U.S. Geological Survey Water Supply Paper 1898-B, 47.

2 Chow Table, 1959 (Strickler)

The following table gives the values of Strickler coefficient in m\(^{1/3}\)/s, for given channel types, and for minimum, ‘normal’ and maximum friction.

Source: Ven Te Chow (1959). Open-Channel Hydraulics. McGraw-Hill, New York.

Type of channel and description	Minimum	Normal	Maximum
1. Main channels, natural watercourses - minor streams (full width < 30 m / 100 ft)
a. clean, straight, full stage, no rifts or deep pools	40	33	30
b. same as above, but with more stones and weeds	33	29	25
c. clean, winding, some pools and shoals	30	25	22
d. same as above, but with some weeds and stones	29	22	20
e. same as above, lower stages, more ineffective slopes and sections	25	21	18
f. same as ‘d’ with more stones	22	20	17
g. sluggish reaches, weedy, deep pools	20	14	13
h. very weedy reaches, deep pools, or floodwayswith heavy stand of timber and underbrush	13	10	7
2. Mountain streams, no vegetation in channel, banks usually steep, trees and brush along banks submerged at high stages
a. bottom: gravels, cobbles, and a few boulders	33	25	20
b. bottom: cobbles with large boulders	25	20	14
3. Floodplains
a. pasture, no brush
1. short grass	40	33	29
2. high grass	33	29	20
b. cultivated areas
1. no crop	50	33	25
2. mature row crops	40	29	22
3. mature field crops	33	25	20
c. brush
1. scattered brush, heavy weeds	29	20	14
2. light brush and trees, in winter	29	20	17
3. light brush and trees, in summer	25	17	13
4. medium to dense brush, in winter	22	14	9
5. medium to dense brush, in summer	14	10	6
d. trees
1. dense willows, summer, straight	9	7	5
2. cleared land with tree stumps, no sprouts	33	25	20
3. same as above, but with heavy growth of sprouts	20	17	13
4. heavy stand of timber, a few down trees, little undergrowth, flood stage below branches	20	21	22
5. same as 4. with flood stage reaching branches	10	8	6
4. Excavated or dredged channels
a. earth, straight, and uniform
1. clean, recently completed	63	56	50
2. clean, after weathering	56	45	40
3. gravel, uniform section, clean	45	40	33
4. with short grass, few weeds	45	37	30
b. earth, winding, and sluggish
1. no vegetation	43	40	33
2. grass, some weeds	40	33	30
3. dense weeds or aquatic plants in deep channels	33	29	25
4. earth bottom and rubble sides	36	33	29
5. stony bottom and weedy banks	40	29	25
6. cobble bottom and clean sides	33	25	20
c. dragline-excavated or dredged
1. no vegetation	40	36	30
2. light brush on banks	29	20	17
d. rock cuts
1. smooth and uniform	40	29	25
2. jagged and irregular	29	25	20
e. channels not maintained, weeds and brush uncut
1. dense weeds, high as flow depth	20	13	8
2. clean bottom, brush on sides	25	20	13
3. same as above, highest stage of flow	22	14	9
4. dense brush, high stage	13	10	7
5. Lined or constructed channels
a. cement
1. neat surface	100	91	77
2. mortar	91	77	67
b. wood
1. planed, untreated	100	83	71
2. planed, creosoted	91	83	67
3. unplaned	91	77	67
4. plank with battens	83	67	56
5. lined with roofing paper	100	71	59
c. concrete
1. trowel finish	91	77	67
2. float finish	77	67	63
3. finished, with gravel on bottom	67	59	50
4. unfinished	71	59	50
5. gunite, good section	63	53	43
6. gunite, wavy section	56	45	40
7. on good excavated rock	59	50
8. on irregular excavated rock	45	37
d. concrete bottom float finish with sides of:
1. dressed stone in mortar	67	59	50
2. random stone in mortar	59	50	42
3. cement rubble masonry, plastered	63	50	42
4. cement rubble masonry	50	40	33
5. dry rubble or riprap	50	33	29
e. gravel bottom with sides of:
1. formed concrete	59	50	40
2. random stone mortar	50	43	38
3. dry rubble or riprap	43	30	28
f. brick
1. glazed	91	77	67
2. in cement mortar	83	67	56
g. masonry
1. cemented rubble	59	40	33
2. dry rubble	43	31	29
h. dressed ashlar/stone paving	77	67	59
i. asphalt
1. smooth	77	77
2. rough	63	63
j. Vegetal lining	33		2

3 Chow table, 1959 (Manning)

The following table gives the values of the Manning coefficient in s/m\(^{1/3}\), for given channel types, and for minimum, ‘normal’ and maximum friction.

Source: Ven Te Chow (1959). Open-Channel Hydraulics. McGraw-Hill, New York.

TEXTS TO BE FIXED AS DONE ABOVE FOR STRICKLER TABLE

Channel type and description	Minimum	Normal	Maximum
1. Main channels, natural watercourses - minor streams (full width < 30 m / 100 ft)
a. clean, straight, full stage, no rifts or deep pools	0.025	0.030	0.033
b. same as above, but with 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 with 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 floodwayswith 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: gravel, cobbles, and a 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 brushb
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, in summer, straight	0.110	0.150	0.020
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	0.050	0.048	0.045
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	0.150
5. Lined or constructed channels
a. Cement
1. Neat surface	0.010	0.011	0.013
2. Mortar	0.110	0.013	0.015
b. Wood
1. Planed, untreated	0.010	0.012	0.014
2. planed, creosoted	0.110	0.012	0.015
3. unplaned	0.110	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	0.110	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	0.110	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. Vegetation lining	0.030		0.500

Sections

Hydraulic analysis

Hydraulic controls

Friction coefficients

The uncertainties of gaugings

Rating curve equation

Uncertainties in stage time series

Statistical model

Uncertainties in discharge time series

Bayesian basics

MCMC Sampling