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)