ABSTRACT
Use of the momentum principle is needed when forces control the direction or conditions associated with ¢uid motions, or when it is not possible to de’ne what is happening to the ¢uid on a small element basis but a large picture of a mass of ¢uid within a control volume is possible. If a vector quantity, such as force or velocity with both magnitude and direction, is the unknown, or is one of the important known variables of the problem, then it will most likely be necessary to use the momentum principle in solving the problem. In order to introduce and develop the momentum function for use in open channel hydraulics, an interesting phenomena, the hydraulic jump will be analyzed. A hydraulic jump abruptly takes the ¢ow in an open channel from supercritical ¢ow to subcritical ¢ow, so that through a hydraulic jump the depth of ¢ow rather abruptly increases. Downstream from a hydraulic jump there will be a control, which may be a ¢atter channel, a gate, or dam, etc. that requires the ¢ow to be at a subcritical depth. Upstream from the hydraulic jump something will cause the ¢ow to be supercritical, such as a gate, or steep channel. The supercritical ¢ow rushes down the channel with a velocity in excess of the speed of small amplitude gravity waves, and consequently receives no signal from the downstream ¢ow. Since it must change to subcritical ¢ow at some position because a downstream control dictates this, the change occurs in the form of a hydraulic jump. The sketch below illustrates these conditions resulting in a hydraulic jump. A hydraulic jump actually takes place over a ’nite length of several feet, but since sketches herein have an enlarged vertical to the horizontal scale the hydraulic jump is shown as a near vertical line.
