Application Note: Natural Selection
Hydraulics is an ancient discipline driven by man's need to control water for agriculture, transportation, personal hygiene, and enjoyment. The rules and practices of hydraulics have evolved by trial and error. In other words, by a process of natural selection in which actions that work are repeated and those that do not are discarded.
One objective in hydraulics is to predict flow rates in natural streams and man-made channels. Experience has taught that the roughness of the bed in the form of sand, pebbles, rocks, vegetation, or other types of surfaces has a strong influence on the flow rate. This is natural because flow rate depends on a balance between gravity pulling water down a slope and viscous resistance, which is related to boundary roughness.
Numerous investigators have sought ways to characterize channel flow rates in terms of a few simple parameters. Probably the most popular relation is Manning's formula, named after Robert Manning, an Irish engineer (1816-1897). Interestingly though, the form of the relation now in use was not devised by Manning. Furthermore, he would not have recommended it because he recognized that its non-dimensional form could not be trusted outside the data on which it was based (History of Hydraulics, Rouse and Ince, Dover Publications, N.Y.)
Natural selection doesn't guarantee an optimum solution, only a workable solution.
With this in mind, Manning's formula has been "selected" for practical
applications involving channels of simple cross-sectional shape and with relatively
small slopes. The formula contains an empirical parameter that is correlated
with bed roughness (e.g. Open Channel Hydraulics, Chow, McGraw-Hill).
Hydraulic engineering is still evolving as shown by the willingness of its practitioners to embrace new technology such as computational modeling. When it comes to practical matters, however, there are problems with using new technology. For example. how can boundary roughness be defined in a computational model to give results in agreement with Manning's formula? Roughness affects only the later of fluid adjacent to the channel wall, which must then be transmitted to the remainder of the fluid through turbulent, viscous stresses. The accompanying figure shows the cross section of a concrete channel 5 feet wide and 2 feet deep. Color indicates the computed axial flow rate in the channel.
In FLOW-3D we have resolved the correspondence problem by allowing users to enter the actual height of roughness on a boundary. A user can use the empirical "n" parameter in Manning's formula by converting it to a corresponding roughness using a simple formula. This is a good example of how FLOW-3D continues to evolve, becoming better adapted to user's needs.