Manning's Formula and Gravity Flow
Calculate crosssectional average velocity flow in open channels.
Manning's equation is an empirical equation that can be used to calculate crosssectional average velocity flow in open channels
v = (k_{n }/ n) R_{h}^{2/3} S^{1/2} (1)
where
v = crosssectional 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)
Download and print Gravity Flow  Mannings Equation Chart
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 = crosssectional 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 Timeoftravel, Mass Coriolis, Mass Thermal, Weir Vnotch, 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. 
HazenWilliams Friction Loss Equation  calculating Head Loss in Water Pipes
Friction head loss (ft_{H2O} per 100 ft pipe) in water pipes can be estimated with the empirical HazenWilliams equation. 
Manning's Roughness Coefficients
Manning's roughness coefficients for some common materials. 
Pipe Equations
Calculate crosssectional 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. 
StormWater Conductors
Roof drain capacities. 
StormWater Runoff Coefficients vs. Surface
Stormwater 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, m^{3}/h.