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 S 1/2 (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) = m 1/3 / s = 1.4859 ft 1/3 / 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 S 1/2 (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 S 1/2

= (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.

Related Topics

  • Flow Measurements

    Flow metering principles - Orifice, Venturi, Flow Nozzles, Pitot Tubes, Target, Variable Area, Positive Displacement, Turbine, Vortex, Electromagnetic, Ultrasonic Doppler, Ultrasonic Time-of-travel, Mass Coriolis, Mass Thermal, Weir V-notch, Flume Parshall and Sluice Gate flow meters and more.
  • Fluid Mechanics

    The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

Related Documents

Search

Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .

Citation

This page can be cited as

  • The Engineering ToolBox (2004). Manning's Formula and Gravity Flow. [online] Available at: https://www.engineeringtoolbox.com/mannings-formula-gravity-flow-d_800.html [Accessed Day Month Year].

Modify the access date according your visit.

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

















































11.4.12

.