Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Manning's Formula and Gravity Flow

Calculate cross-sectional average velocity flow in open channels.

Manning's equation is an empirical equation that can be used to calculate cross-sectional average velocity flow in open channels

v = (kn / n) Rh 2/3 S1/2                            (1)

where

v = cross-sectional mean velocity (ft/s, m/s)

kn = 1.486 for English units and kn = 1.0 for SI units

n = Manning coefficient of roughness - ranging from 0.01 (a clean and smooth channel) to 0.06 (a channel with stones and debris, 1/3 of vegetation)

Rh = hydraulic radius (ft, m)

S = slope - or gradient - of pipe (ft/ft, m/m)

The Manning coefficients n in the English (Imperial) are equal to the coefficients in the SI system. The Manning coefficient is not dimensionless but the units are often omitted.

Units for (kn / n) in the SI system vs. the Imperial system can be expressed as:

(kn / n) = m1/3 / s

    = 1.4859 ft1/3 / s

Hydraulic radius can be expressed as

Rh = A / Pw                                (2)

where

A = cross sectional area of flow (ft2, m)

Pw = wetted perimeter (ft, m)

Gravity flow velocity - Mannings equation

Download and print Gravity Flow - Mannings Equation Chart

The volume flow in the channel can be calculated as

q = A v

   = A (kn / n) Rh 2/3 S1/2                           (3)

where

q = volume flow (ft3/s, m3/s)

A = cross-sectional area of flow (ft2, m2)

Example - Flow in an Open Channel

A channel with the shape of an half circle is 100% filled. The diameter of the half circle is 500 mm (0.5 m) and the channel is made of concrete with Manning coefficient 0.012 . The slope of the channel is 1/100 m/m .

mannings formula open channel flow

make 3D models with the free Engineering ToolBox Sketchup Extension !

The cross section area of the half circle flow can be calculated as

A = (0.5 π ((0.5 m) / 2)2)

= 0.098 m2

The wetted perimeter of the half circle flow can be calculated as

P = 0.5 2 π (0.5 m) / 2)

= 0.785 m

The hydraulic radius of the channel can be calculated from (2) as

Rh = A / P

= ( 0.098 m2>) / ( 0.785 m)

= 0.125 m

The cross sectional mean velocity can be calculated from (1) as

v = (kn / n) Rh 2/3 S1/2

= (1.0 / 0.012) (0.125 m)2/3 (1/100 m/m)1/2

= 2.1 m/s

The volume flow can be calculated from (3) as

q = A v

=  ( 0.098 m2) (2.1 m/s)

= 0.20 m3/s

Gravity Flow Calculator - Half Filled Circular Pipe

The Gravity Flow Calculator is based on the equations and the example above above. It's valid for half filled circular pipe.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter


















































5.23.11

.