Losses due to contraction and expansion of flow between cross sections are determined during the HEC‑RAS standard step profile calculations. Manning’s equation is used to calculate friction losses, and all other losses are described in terms of a coefficient multiplied by the absolute value of the change in velocity head between adjacent cross sections. When the velocity head increases in the downstream direction, a contraction coefficient is used; and when the velocity head decreases, an expansion coefficient is used.
Roadway Crossing Flow Contraction & Expansion
The below figure shows the contraction and expansion of flow as it passes through a bridge or culvert opening at a roadway crossing.
As shown in the above figure, flow contraction occurs between cross sections 4 and 3, while the flow expansion occurs between sections 2 and 1. The contraction and expansion coefficients are used to compute energy losses associated with changes in the shape of river cross sections (or effective flow areas). The loss due to expansion of flow is usually larger than the contraction loss, and losses from short abrupt transitions are larger than losses from gradual transitions.
Subcritical Flow Contraction & Expansion Coefficients
Typical values for contraction and expansion coefficients for subcritical flow conditions are shown in the table below. The maximum value for the contraction and expansion coefficient is 1.0.
Table 1
Subcritical Flow Contraction and Expansion Coefficients
| Contraction | Expansion | |
|---|---|---|
| No transition loss computed | 0 | 0 |
| Gradual transitions | 0.1 | 0.3 |
| Typical bridge sections | 0.3 | 0.5 |
| Abrupt transitions | 0.6 | 0.8 |
Supercritical Flow Contraction & Expansion Coefficients
In general, contraction and expansion coefficients for supercritical flow are lower than for subcritical flow. For typical bridges that are under class C flow conditions (totally supercritical flow), the contraction and expansion coefficients should be around 0.03 and 0.05, respectively. For abrupt bridge transitions under class C flow, values of 0.05 and 0.1 may be more appropriate.
Utilizing Contraction and Expansion Coefficients for Unsteady Flow
The application of contraction and expansion coefficients for unsteady flow differs from steady flow modeling. In general, contraction and expansion losses are not utilized for unsteady flow. Therefore, the default coefficients are 0.0. The losses due to contraction and expansion are handled in the momentum equation through pressure force differences.
However, since HEC-RAS is a one-dimensional unsteady flow model, the one-dimensional momentum equation may not fully capture all the forces acting on the flow field within zones of sharp contraction and/or expansion. To better approximate the forces acting on the water and the resulting water surface elevation, at a contraction and/or expansion, users can input empirical contraction and expansion coefficients during unsteady flow modeling.
In unsteady flow modeling, the contraction and expansion coefficients are typically used at the following structures:
- Bridges
- Culverts
- Other internal boundary locations where energy-based methods are applied
For these structures, the contraction and expansion coefficients are typically used to compute additional head losses.
In GeoHECRAS, the user can view and edit contraction and expansion coefficients in a tabular format using the Edit Contraction & Expansion Coefficients command.
Refer to this article in our knowledge base to learn more about editing contraction and expansion coefficients.