ABSTRACT
In the conservative force field of gravity, the sum of kinetic and potential energies of fluid particles in a flow with uniform static pressure remains constant. This assumes that there are no losses associated with the particle motion in the flow. This concept parallels the technique used in courses in particle physics to find, for example, the maximum height reached by a ball of mass m thrown vertically in a vacuum (no air drag) with a given initial velocity 0V . This maximum height is calculated by equating the initial kinetic energy of the ball with the change in its potential energy corresponding to the maximum height where the ball has zero kinetic energy, as given by
1 2max 0
2mgh mV= (4.1)
2max
h V
g = (4.2)
Figure 4.1 shows a fluid particle P of unit mass moving on the free surface of an open channel flow between Sections 1 and 2. Assuming no loss in its path, the sum of the kinetic
energy and potential energy of this particle remains constant at each location. In other words, any change in the particle’s potential energy appears as an equal and opposite change in its kinetic energy. Thus we can write
2 2 2 1 2
2V gh
V gh
V gh+ = + = + (4.3)
Equation 4.3 can be conveniently used to determine the velocity of the particle at any location along its path from 1 to 2 by simply knowing the height (measured from the datum) of the location, assuming that we know its total energy at a given location along the path.
