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

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

# Manning's Formula and Gravity Flow

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

v = (k n / n) R h 2/3 S 1/2 (1)

where

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

k n = 1.486 for English units and k n = 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)

R h = 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 (k n / n) in the SI system vs. the Imperial system can be expressed as:

(k n / n) = m 1/3 / s = 1.4859 ft 1/3 / s

Hydraulic radius can be expressed as

R h = A / P w (2)

where

A = cross sectional area of flow (ft 2 , m)

P w = wetted perimeter (ft, m)

The volume flow in the channel can be calculated as

q = A v = A (k n / n) R h 2/3 S 1/2 (3)

where

q = volume flow (ft 3 /s, m 3 /s)

A = cross-sectional area of flow (ft 2 , m 2 )

### 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 .

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 m 2

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

R h = A / P

= ( 0.098 m 2 > ) / ( 0.785 m )

= 0.125 m

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

v = (k n / n) R h 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 m 2 ) (2.1 m/s)

= 0.20 m 3 /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 Measurement

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

### California Pipe Flow Metering Method

Calculate the discharge length from the open end of a partially filled horizontal pipe.

### Chezys Conduit Flow Equation

Calculating volume flow and velcity in open conduits.

### Flow Section Channels - Geometric Relationships

Geometric relationships like area, wetted perimeter and hydraulic diameter.

### Froude Number

Introduction to the Froude Number.

### Hazen-Williams Friction Loss Equation - calculating Head Loss in Water Pipes

Friction head loss (ftH2O per 100 ft pipe) in water pipes can be estimated with the empirical Hazen-Williams equation.

### Manning's Roughness Coefficients

Manning's roughness coefficients for some common materials.

### Pipe Equations

Calculate cross-sectional areas, weight of empty pipes, weight of pipes filled with water, inside and outside surface areas.

### Rainfall on Roofs and Gutter Slopes

Draining of roof areas and recommended gutter slopes

### Sewage Sludge - Viscosities

Viscosity of sewage sludge vs. content of solids.

### Sewer Pipes - Capacities vs. Slope

Carrying capacities of sewer and wastewater pipes - gpm and liter per second.

### Storm-Water Conductors

Roof drain capacities.

### Storm-Water Runoff Coefficients vs. Surface

Storm-water runoff coefficients for various surfaces

### Surface Roughness vs. Mechanical Processing

Mechanical production methods and their surface roughness.

### Volume Flow - Online Unit Converter

Convert between volume flow units like gpm, liter/sec, cfm, m3/h.

## Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

## SketchUp Extension - Online 3D modeling!

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 the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!