Manning Formula Calculator

Open Channel Flow Calculator

Channel Type:

Meter (m)

Feet (ft)

The banks are on the same slope.

Left Vertical Rate:

Left Horizontal Rate:

Right Vertical Rate:

Right Horizontal Rate:

Vertical Rate:

Horizontal Rate:

Depth (Height) (m):

Bottom Width (m):

Radius (m):

Water Surface Slope:

Manning's n Values:

Natural Channels	Minimum	Normal	Maximum
Minor Streams (top width at flood stage < 30 meters)
Streams on plain:
Clean, straight, full stage, no rifts or deep pools	0.025	0.030	0.033
Same as above, but more stones and weeds	0.030	0.035	0.040
Clean, winding, some pools and shoals	0.033	0.040	0.045
Same as above, but some stones and weeds	0.035	0.045	0.050
Same as above, but lower stages, more ineffective slopes and sections	0.040	0.048	0.055
Clean, winding, some pools and shoals, some weeds and many stones	0.045	0.050	0.060
Sluggish reaches, weedy, deep pools	0.050	0.070	0.080
Very weedy reaches, deep pools, or floodways with heavy stand of timber and underbrush	0.075	0.100	0.150
Mountain streams, no vegetation in channel, banks usually steep, trees and brush along banks submerged at high stages:
Bottom: gravel, cobbles, and few boulders	0.030	0.040	0.050
Bottom: cobbles with large boulders	0.040	0.050	0.070
Flood Plains
Pasture, no brush:
Short grass	0.025	0.030	0.035
High grass	0.030	0.035	0.050
Cultivated areas:
No crop	0.020	0.030	0.040
Mature row crops	0.025	0.035	0.045
Mature field crops	0.030	0.040	0.050
Brush:
Scattered brush, heavy weeds	0.035	0.050	0.070
Light brush and trees, in winter	0.035	0.050	0.060
Light brush and trees, in summer	0.040	0.060	0.080
Medium to dense brush, in winter	0.045	0.070	0.110
Medium to dense brush, in summer	0.070	0.100	0.160
Trees:
Dense willows, summer, straight	0.110	0.150	0.200
Cleared land with tree stumps, no sprouts	0.030	0.040	0.050
Same as above, but with heavy growth of sprouts	0.050	0.060	0.080
Heavy stand of timber, a few down trees, little undergrowth, flood stage below branches	0.080	0.100	0.120
Same as above, but flood stage reaching branches	0.100	0.120	0.160
Major Streams (top width at flood stage >30 meters)
Regular section with no boulders or brush	0.025	--	0.060
Irregular and rough section	0.035	--	0.100
Lined Channels
Concrete-lined	0.012	--	0.018
Concrete rubble	0.017	--	0.030
Unlined Channels
Earth, straight and uniform	0.017	--	0.025
Winding and sluggish	0.022	--	0.030
Rocky beds, weeds on bank	0.025	--	0.040
Earth bottom, rubble sides	0.028	--	0.035
Rock cuts	0.025	--	0.045

Results of Water Velocity and Discharge

Parameters	Results
Wetted Area (m²):
Wetted Perimeter (m):
Slope:
Manning's N Value:
V(m/s):
Q(m³/s):

Froude Number and Shear Stress

Parameters	Results
Froude Number:
Shear Stress (N/m²):

		Permissible Shear Stress
Lining Category	Lining Type	N/m²	lb/ft²
Bare Soils Cohesive (PI=10)	Clayey sands	1.8 - 4.5	0.037 - 0.095
	Inorganic silts	1.1 - 4.0	0.027 - 0.11
	Silty sands	1.1 - 3.4	0.024 - 0.072
Bare Soils Cohesive (PI=>10)	Clayey sands	4.5	0.094
	Inorganic silts	4.0	0.083
	Silty sands	3.5	0.072
	Inorganic clays	6.6	0.14
Bare Soils Non-cohesive (PI<10)	Finer than coarse sand D75 < 1.3 mm (0.05 in)	1.0	0.02
	Fine gravel D75 = 7.5 mm (0.3 in)	5.6	0.12
	Gravel D75 = 15 mm (0.6 in)	11	0.24
Gravel Mulch	Coarse gravel D50 = 25 mm (1 in)	19	0.4
Gravel Mulch	Very coarse gravel D50 = 50 mm (2 in)	38	0.8
Rock Riprap	D50 = 0.15 m (0.5 ft)	113	2.4
Rock Riprap	D50 = 0.30 m (1.0 ft)	227	4.8

Height and Discharge of Freeboard

Parameters	Results
Freeboard (m):
Q for Depth+Freeboard (m³/s):

Channel Shape

Manning formula is an empirical formula for calculating the velocity of water in open channel flows and partially filled closed systems. In order to calculate the water flow rate with the Manning formula, wetted cross-sectional area, wetted perimeter, water surface slope and manning roughness coefficient values are needed. Thanks to the manning's equation, the structures to be made for open channels can be dimensioned and unmeasured discharge values can be calculated.

In the following manning's formula, V is defined as water flow velocity (m/s or ft/s), k: conversion factor between imperial and international units systems (k:1 for SI, k:1.49 for the imperial system), n: manning roughness coefficient, R: hydraulic radius (wetted cross-sectional area/wetted perimeter), and s: water surface slope.

V = k/n * (R)^2/3 * √s

The Froude number shows the regime of flow in open channel flows. If the Froude number is 1, the river is in the critical flow regime; if it is greater than 1, the river is in the flood regime; if it is less than 1, the river has a subcritical flow regime.

Fred number is calculated by the following formula. Fr in the formula: Froude number, v: water flow velocity (m/s or ft/sn), g: gravitational acceleration (9.81 m/s² or 32.185 ft/s²) and d is defined as the hydraulic depth (wetted cross-sectional area/width of the flow surface of the water).

Fr = V / √(g*d)

Shear stress is a measure of the force exerted by water due to friction against the flow channel in open channel flows.

In the shear stress formula, τ: shear stress, γ: unit volume weight of water (9807 N/m³ or 62.43 lbf/ft³), R: hydraulic radius (wetted cross-sectional area/wetted perimeter), s is defined as the slope.

τ = γ * R * s

The freeboard for open channels is the distance between the water surface in the channels and the upper surface of the structure. This distance is used as a precaution against fluctuations or swelling in the water. The freeboard can be accepted as between 10% and 20% of the water depth in the channel, or it is calculated with the help of the formula below.

In the freeboard formula, F: freeboard for open channels (m or ft), V: water flow velocity (m/s or ft/s) and h (m or ft) is defined as the depth.

F = 0.60 + 0.03731 * V * ∛h