Open channel flow is flow characterized by a free water surface. We'll restrict our study to cases where flow is in a man-made channel, as opposed to natural channels such as rivers. In our analysis, we will assume that the section of channel under study is prismatic, ie, the channel is unvarying in cross-section and has constant bottom slope. Also, we will focus on steady (), uniform () flow. Except for flow of very thin films of water, open channel flow is turbulent; we will assume this is always the case. Finally, we will assume that streamlines are always parallel to the channel bottom so that the pressure distribution in the direction normal to the streamlines is hydrostatic. Taken together, these conditions mean that we are studying the simplest type of open channel flow. If you are interested in learning more about open channel flow, tune in to CE 4123.
Geometric Properties of Channels
A = cross-sectional area
The Froude Number
For open channel flow, gravity is the primary driving force. Consequently, the appropriate dimensionless number to study open channels (and to scale model results) is the Froude number (rhymes with "food"), which expresses the ratio of inertial forces (kinetic energy) to gravity forces. It is given by
A related quantity is the wave celerity, c, which is the speed at which a small disturbance (eg, a wave caused by throwing a small stone in the water) propagates. Wave celerity can be computed from the relation
The Energy Equation for Open Channel Flow
In our analysis of open channel flow, we will make a few additional assumptions to simplify the equations:
Specific Energy and Critical Depth
Specific energy, E, is the energy in the channel relative to the channel bottom, ie,
Critical slope is defined to be the channel slope that produces a flow in the channel equal to the critical depth. We'll use the symbol Sc. If So > Sc , then the flow is supercritical. If So < Sc , then the flow is subcritical.
The depth of water under conditions of steady, uniform flow is called the normal depth, yn. From the energy equation, it can be shown that normal depth is achieved when So = Sf where Sf is the slope of the energy grade line (the "f"riction slope). This relation tells us that for uniform flow, the driving force due to gravity (So) is just balance by the frictional resistance of the channel walls Sf . Manning used this information coupled with numerous empirical studies to come up with the famous uniform flow formula that bears his name