Manning Equation

Open channel flow calculator using Manning equation


Solve for:  Area, A (ft2):  
Wetted Perimeter, P (ft):  
Select units:  Channel Slope, S (ft/ft):  
Manning n:  
© 2014 LMNO Engineering, Velocity, V (ft/s):  
Research, and Software, Ltd. Discharge, Q (ft3/s):

Units in Manning calculator: ft=foot, m=meter, s=second.

Manning Equation: 

Manning Equation

k is a unit conversion factor: k=1.49 for English units (feet and seconds).  k=1.0 for SI units (meters and seconds).
A=Flow area of the pipe, culvert, or channel.
P=Wetted perimeter which is the portion of the circumference that is in contact with water.
Q=Discharge (flow rate).
S=Downward (longitudinal) slope of the culvert.
V=Average velocity in the pipe, culvert, or channel.

Manning n varies with the roughness of the pipe, culvert, or channel. The higher the n, the rougher the material. Table of Manning n values.

The Manning Equation is the most commonly used equation to analyze open channel flows.  It is a semi-empirical equation for simulating water flows in channels and culverts where the water is open to the atmosphere, i.e. not flowing under pressure, and was first presented in 1889 by Robert Manning.  The channel can be any shape - circular, rectangular, triangular, etc.  The units in the Manning equation appear to be inconsistent; however, the value k has hidden units in it to make the equation consistent.  The Manning Equation was developed for uniform steady state flow (see Discussion and References for Open Channel Flow).  S is the slope of the energy grade line and S=hf/L where hf is energy (head) loss and L is the length of the channel or reach.  For uniform steady flows, the energy grade line = the slope of the water surface = the slope of the bottom of the channel.

The product A/P is also known as the hydraulic radius, Rh.


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Related calculations:

Design of Rectangular Channels

Design of Trapezoidal Channels

Circular Culverts using Manning Equation

Culvert Design using Inlet and Outlet Control

Q=VA simple flowrate calculator

Manning n values

Unit Conversions

Other information:


Discussion and References for Open Channel Flow