When the flow velocity V1 is rapid or supercritical the surge dissipates energy through a moving

hydraulic jump. When V1 equals the celerity c of the surge the jump is stationary and Equation

2.125 is the equation for a hydraulic jump on a flat slope. Solutions for a hydraulic jump on a

sloping channel are given in HEC-14. Equation 2.125 can be rearranged to the form:

1/ 2

1 y2 y2

V1

+ 1

= Fr1 =

(2.126)

2 y1 y1

gy 1

or

{

}

y2 1

(1 + 8Fr12 )1/ 2 - 1

=

(2.127)

y1 2

The corresponding energy loss in a hydraulic jump is the difference between the two specific

energies. It can be shown that this head loss is:

(y 2 - y1 )3

hL =

(2.128)

4y1 y 2

Equation 2.128 has been experimentally verified along with the dependence of the jump length Lj

of these experiments are given in Figure 2.16.

When the Froude number for rapid flow is less than 1.7, an undulating jump with large surface

waves is produced. The waves are propagated for a considerable distance downstream. In

addition, when the Froude number of the approaching flow is less than three, the energy

dissipation of the jump is not large and jets of high velocity flow can exist for some distance

downstream of the jump. These waves and jets can cause erosion a considerable distance

downstream of the jump. For larger values of the Froude number, the rate of energy dissipation

in the jump is very large and Figure 2.16 is recommended. The U.S. Bureau of Reclamation

(Chow 1959) classifies the hydraulic jump on a flat slope into various types as illustrated in Figure

2.17. For additional information on hydraulic jumps, see HEC-14, Chow (1959) and Rouse

(1950).

Under certain conditions on steep slopes, surges of an intermittent nature may occur which are

called roll waves or slug flow (Figure 2.18). Such flow is not at all uncommon with harmless thin

sheets of flow on sloping sidewalks, for example. When these roll waves occur in large open

channels, however, they may cause considerable damage, or force the operation of the channel

at inefficient discharges in order to prevent damage.

Roll waves can be superposed over the normal flow in an open channel. They travel at velocities

greater than the normal flow and grow in size as they progress downstream.

2.35

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