**2.6 STEADY RAPIDLY VARYING FLOW**

**2.6.1 Flow Through Transitions**

Steady flow through relatively short transitions where the flow is uniform before and after the

transition can be analyzed using the Bernoulli equation. Energy loss due to friction may be

neglected, at least as a first approximation. Refinement of the analysis can be made in a second

step by including friction loss (see HEC-14, Chapter 4). For example, the water surface elevation

through a transition is determined using the Bernoulli equation and then modified by determining

the friction loss effects on velocity and depth in short reaches through the transition. Energy

losses resulting from flow separation cannot be neglected, and transitions where separation may

occur need special treatment which may include model studies. Contracting flows (converging

streamlines) are less susceptible to separation than for expanding flows. Also, any time a

transition changes velocity and depth such that the Froude number approaches unity, problems

such as waves, blockage, or choking of the flow may occur. If the approaching flow is

supercritical, a hydraulic jump may result. Unsubmerged flow through bridges or culverts can be

considered as flow through transitions.

Transitions are used to contract or expand a channel width (Figure 2.19a); to increase or

decrease bottom elevation (Figure 2.19b); or to change both the width and bottom elevation. The

first step in the analysis is to use the Bernoulli equation (neglecting any head loss resulting from

friction or separation) to determine the depth and velocity changes of the flow through the

transition. Further refinement depends on importance of freeboard, whether flow is supercritical

or approaching critical conditions.

Figure 2.19. Transitions in open channel flow.

The Bernoulli equation for flow in Figure 2.19b is:

V12

V22

+ y1 =

+ y 2 + ∆z

(2.134)

2g

2g

or

2.38