For low flow conditions (water surface below the highest point on the low chord of the bridge opening), the Energy and Momentum methods are the most physically based, and in general are applicable to the widest range of bridges and flow situations. Both methods account for friction losses and changes in geometry through the bridge. The energy method accounts for additional losses due to flow transitions and turbulence through the use of contraction and expansion losses. However, the energy method does not account for losses associated with the shape of the piers and abutments. The momentum method can account for additional losses due to pier drag. One draw back of the momentum method is that the weight force is computed with an average bed slope through the bridge. The computation of this bed slope can be very difficult for natural cross sections.

The FHWA WSPRO method was originally developed for bridge crossings that constrict wide flood plains with heavily vegetated overbank areas. The method is an energy-based solution with some empirical attributes (the expansion loss equation in the WSPRO method utilizes an empirical discharge coefficient). However, the expansion loss is computed with an idealized equation in which the C coefficient is empirically derived.

The Yarnell equation is an empirical formula. Yarnell developed his equation from 2600 lab experiments in which he varied pier shape, width, length, angle, and flow rate. His experiments were run with rectangular and trapezoidal channel shapes, but no overbank areas. When applying the Yarnell equation, the user should ensure that the problem is within the range of data that the method was developed for. Additionally, the Yarnell method should only be applied to channels with uniform sections through the bridge (no everbank areas upstream and downstream) and where pers are the primary obstruction to the flow.

The following examples are some typical cases where the various low flow methods might be used:

  1. .In cases where the bridge piers are a small obstruction to the flow, and friction losses are the predominate consideration, the energy based method, the momentum method, and the WSPRO method should give the best answers.
  2. In cases where pier losses and friction losses are both predominant, the momentum method should be the most applicable. But the energy and WSPRO methods can be used.
  3. Whenever the flow passes through critical depth within the vicinity of the bridge, both the momentum and energy methods are capable of modeling this type of flow transition. The Yarnell and WSPRO methods are for subcritical flow only.
  4. For supercritical flow, both the energy and the momentum method can be used. The momentum-based method may be better at locations that have a substantial amount of pier impact and drag losses. The Yarnell equation and the WSPRO method are only applicable to subcritical flow situations.
  5. For bridges in which the piers are the dominant contributor to energy losses and the change in water surface, either the momentum method or the Yarnell equation would be most applicable. However, the Yarnell equation is only applicable to Class A low flow.
  6. For long culverts under low flow conditions, the energy based standard step method is the most suitable approach. Several sections can be taken through the culvert to model changes in grade or shape or to model a very long culvert. This approach also has the benefit of providing detailed answers at several locations within the culvert, which is not possible with the culvert routines in HEC-RAS. However, if the culvert flows full, or if it is controlled by inlet conditions, the culvert routines would be the best approach. For a detailed discussion of the culvert routines within HEC-RAS, see "Modeling Culverts" of this manual.