Open-channel flow can be classified and described in various ways based on the change in flow depth with respect to time and space. The fundamental types of flow dealt with in open-channel hydraulics are:
Time as the criterion
The depth of flow does not change over time, or if it can be assumed to be constant during the time interval under consideration.
The depth of flow does change with time.
Space as the criterion
The depth of flow is the same at every section of the channel. Uniform flow can be steady or unsteady, depending on whether or not the depth changes with time, (although unsteady uniform flow is rare).
The depth of flow changes along the length of the channel. Varied flow technically may be either steady or unsteady. Varied flow can be further classified as either rapidly or gradually-varied:
The depth changes abruptly over a comparatively short distance. Rapidly varied flow is known as a local phenomenon. Examples are the hydraulic jump and the hydraulic drop.
The depth changes over a long distance.
The discharge is constant throughout the reach of the channel under consideration. This is often the case with a steady flow. This flow is considered continuous and therefore can be described using the continuity equation for continuous steady flow.
The discharge of a steady flow is non-uniform along a channel. This happens when water enters and/or leaves the channel along the course of flow. An example of flow entering a channel would be a road side gutter. An example of flow leaving a channel would be an irrigation channel. This flow can be described using the continuity equation for continuous unsteady flow requires the consideration of the time effect and includes a time element as a variable.
States of flow
The behavior of open-channel flow is governed by the effects of viscosity and gravity relative to the inertial forces of the flow. Surface tension has a minor contribution, but does not play a significant enough role in most circumstances to be a governing factor. Due to the presence of a free surface, gravity is generally the most significant driver of open-channel flow; therefore, the ratio of inertial to gravity forces is the most important dimensionless parameter. The parameter is known as the Froude number, and is defined as:
It is possible to formulate equations describing three conservation laws for quantities that are useful in open-channel flow: mass, momentum, and energy. The governing equations result from considering the dynamics of the flow velocityvector field with components . In Cartesian coordinates, these components correspond to the flow velocity in the x, y, and z axes respectively.
To simplify the final form of the equations, it is acceptable to make several assumptions:
The flow is incompressible (this is not a good assumption for rapidly-varied flow)
The Reynolds number is sufficiently large such that viscous diffusion can be neglected
where is the fluid density and is the divergence operator. Under the assumption of incompressible flow, with a constant control volume, this equation has the simple expression . However, it is possible that the cross-sectional area can change with both time and space in the channel. If we start from the integral form of the continuity equation:
it is possible to decompose the volume integral into a cross-section and length, which leads to the form:
Under the assumption of incompressible, 1D flow, this equation becomes: