# Manning-Strickler's formula

## Definition

Manning-Strickler formula is written as follows:

$V = K_s R_h^{2/3} i^{1/2}$

with:

• $$V$$ la vitesse moyenne de la section transversale en m/s
• $$K_s$$ Strickler's coefficient
• $$R_h$$ Hydraulic radius in m
• $$i$$ slope en m/m

The Strickler coefficient $$K_s$$ varies from 20 (rough stone and rough surface) to 80 (smooth concrete and cast iron).

Manning's coefficient $$n$$ is obtained by :

$n = \frac{1}{K_s}$

## Chow's table (1959)

Type of channel and description $$K_S$$ min. $$K_S$$ normal $$K_S$$ max.
1. Main channels
a. clean, straight, full stage, no rifts or deep pools 30 33 40
b. same as above, but more stones and weeds 25 29 33
c. clean, winding, some pools and shoals 22 25 30
d. same as above, but some weeds and stones 20 22 29
e. same as above, lower stages, more ineffective slopes and sections 18 21 25
f. same as "d" with more stones 17 20 22
g. sluggish reaches, weedy, deep pools 13 14 20
h. very weedy reaches, deep pools, or floodways with heavy stand of timber and underbrush 7 10 13
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 20 25 33
b. bottom: cobbles with large boulders 14 20 25
3. Floodplains
a. Pasture, no brush
1. short grass 29 33 40
2. high grass 20 29 33
b. Cultivated areas
1. no crop 25 33 50
2. mature row crops 22 29 40
3. mature field crops 20 25 33
c. Brush
1. scattered brush, heavy weeds 14 20 29
2. light brush and trees, in winter 17 20 29
3. light brush and trees, in summer 13 17 25
4. medium to dense brush, in winter 9 14 22
5. medium to dense brush, in summer 6 10 14
d. Trees
1. dense willows, summer, straight 5 7 9
2. cleared land with tree stumps, no sprouts 20 25 33
3. same as above, but with heavy growth of sprouts 13 17 20
4. heavy stand of timber, a few down trees, little undergrowth, flood stage below branches 22 21 20
5. same as 4. with flood stage reaching branches 6 8 10
4. Excavated or Dredged Channels
a. Earth, straight, and uniform
1. clean, recently completed 50 56 63
2. clean, after weathering 40 45 56
3. gravel, uniform section, clean 33 40 45
4. with short grass, few weeds 30 37 45
b. Earth winding and sluggish
1. no vegetation 33 40 43
2. grass, some weeds 30 33 40
3. dense weeds or aquatic plants in deep channels 25 29 33
4. earth bottom and rubble sides 29 33 36
5. stony bottom and weedy banks 25 29 40
6. cobble bottom and clean sides 20 25 33
c. Dragline-excavated or dredged
1. no vegetation 30 36 40
2. light brush on banks 17 20 29
d. Rock cuts
1. smooth and uniform 25 29 40
2. jagged and irregular 20 25 29
e. Channels not maintained, weeds and brush uncut
1. dense weeds, high as flow depth 8 13 20
2. clean bottom, brush on sides 13 20 25
3. same as above, highest stage of flow 9 14 22
4. dense brush, high stage 7 10 13
5. Lined or Constructed Channels
a. Cement
1. neat surface 77 91 100
2. mortar 67 77 91
b. Wood
1. planed, untreated 71 83 100
2. planed, creosoted 67 83 91
3. unplaned 67 77 91
4. plank with battens 56 67 83
5. lined with roofing paper 59 71 100
c. Concrete
1. trowel finish 67 77 91
2. float finish 63 67 77
3. finished, with gravel on bottom 50 59 67
4. unfinished 50 59 71
5. gunite, good section 43 53 63
6. gunite, wavy section 40 45 56
7. on good excavated rock 50 59
8. on irregular excavated rock 37 45
d. Concrete bottom float finish with sides of:
1. dressed stone in mortar 50 59 67
2. random stone in mortar 42 50 59
3. cement rubble masonry, plastered 42 50 63
4. cement rubble masonry 33 40 50
5. dry rubble or riprap 29 33 50
e. Gravel bottom with sides of:
1. formed concrete 40 50 59
2. random stone mortar 38 43 50
3. dry rubble or riprap 28 30 43
f. Brick
1. glazed 67 77 91
2. in cement mortar 56 67 83
g. Masonry
1. cemented rubble 33 40 59
2. dry rubble 29 31 43
h. Dressed ashlar/stone paving 59 67 77
i. Asphalt
1. smooth 77 77
2. rough 63 63
j. Vegetal lining 2 33

Table: Chow's table (1959)