What Is the Manning Formula?

The Manning formula is an equation developed by Robert Manning in 1891 that characterizes the flow of gravity-fed water in streams and channels. Manning determined that the flow velocity characteristics of open channels of running water are dependent on several factors. This includes the slope of the stream bed, the roughness of the channel walls or stream banks, and the hydraulic radius of the channel. Hydraulic radius is calculated by dividing the cross-sectional area of the stream or channel by its wetted perimeter and walls of a channel, or the stream bed and banks of an open stream.

Hydrologists use the Manning formula to determine the flow character of streams in normal and flood conditions. It can also be used to determine the optimum size and slope of a man-made channel such as a water supply aqueduct. Manning's equation does not relate to closed pipe or pressurized systems, simply for water streams or channels open to the atmosphere.

A critical element in the Manning formula is the value for wall roughness, known as the Gauckler-Manning coefficient. This number is based on a complex set of factors. The shape of the channel, the specific vegetation in the area, and the amount of stream flow are all considered, as is the season of the year.

Hydrologists who may not be able to survey an entire stream can access reference sites on the Internet showing roughness factors for different streams. These may be listed as photographs of the stream beds or banks. The researcher can observe the stream and compare the stream bank to the photographic reference set to determine the roughness factors for the equation.

The complexity of the Manning formula changes for streams that are flooding. The Manning formula should be considered an estimate in the best of conditions, particularly since natural stream beds change character in very short distances. An accurate flow calculation may be technically impossible.

Stream flow measurements can be made using a calibrated weir or flow channel to measure the volume of water over time. Weirs have a specific cross-section that permits awater to flow over it for each unit of water height. These measurements can then be used to fine-tune the variables in the Manning formula to improve the estimate. The value of the Manning formula is typically used in situations where the stream flow cannot be measured, either due to complex stream dynamics or in the event flooding is underway.