3.2 Gradually Varied, Steady Flow

Chapter 2 deals extensively with steady, gradually varied flow, in which there are small changes in velocity and depth with distance along the channel. The majority of popular floodplain hydraulic programs use steady, gradually varied flow assumptions to compute water surface elevations and to size channels, levees, and other flood reduction components. Watercourses to be modeled using a steady, gradually varied flow assumption must satisfy the following criteria:

The peak discharge is not affected by storage in the river system, or the storage has been addressed in a separate study using a hydrologic model. The storage could be a reservoir or natural, floodplain storage in the overbank areas. Analysis of storage using a hydrologic model is referred to as quasi-unsteady flow modeling and was first presented in Chapter 2. This subject is further discussed in Section 3.4. Chapter 8 describes the mechanics of analyzing reach storage with HEC-RAS.

The peak discharge and stage occur simultaneously throughout the reach under study. In reality, the peak discharge may occur only for a short time at a given location, but the flow rate at this time elsewhere in the reach is less than the peak discharge. For steady flow, however, the peak discharge is assumed to occur instantaneously at all locations in the reach. Compared to unsteady flow computations, the steady flow solution tends to give a slightly more conservative (higher) estimate of the water surface elevation. The difference does not necessarily mean that one method is more accurate than another, just that the computational procedures may result in a small difference in peak river stages. The reasons for this difference are presented in Section 3.3. With the level of uncertainty that exists in many of the required data for water surface profile calculations (further discussed in Chapter 5), a little conservatism is acceptable.

Channel sizes, levee heights, spillway dimensions, and floodway capacities are often designed for a peak flowrate with steady, gradually varied flow assumptions. Similarly, flood studies often concentrate solely on the peak discharge, without concern for the shape of the hydrograph prior to or after the peak discharge. Flood insurance studies, the subject of Chapters 9 and 10, are the prime example of this type of analysis.

Numerous hydraulic simulation packages have been developed to evaluate steady, gradually varied flow using the standard step method (covered in Chapter 2). The balance of this section provides an overview of the more popular computer programs that are available to the U.S. engineering community.

HEC-2

The U.S. Army Corps of Engineers' HEC-2, Water Surface Profiles program (USACE, 1990b), developed to compute water surface profiles for steady, gradually varied flow conditions, was probably the most widely used open channel hydraulics model worldwide from the early 1970s into the 1990s. HEC-2 grew out of early work by Bill S. Eichert, of the Corps' Hydrologic Engineering Center (HEC), and was initially released in 1968. The program was updated several times, with the last major release in 1990.

The program uses the standard step technique to compute water surface profiles in natural or man-made channels for either sub- or supercritical flow. The continuity and energy equations are the main basis for solutions, with the momentum equation applied where flow is rapidly varied through bridge openings. The program can analyze the effects of obstructions, such as bridges, culverts, weirs, and floodplain structures. HEC-2 can calculate a maximum of 15 water surface profiles in one run and include up to 800 cross sections for describing a profile, with a maximum of 100 points (elevation, distance) describing a single cross section.

The program was adapted for personal computers in 1984, but data input still reflected the days of punch cards and mainframes, and was not user-friendly. In 1991, the HEC decided to initiate a major effort to modernize and convert its most popular simulation packages to work with the Windows platform. The first of these programs, a replacement for HEC-2 called HEC-RAS, was released in 1995. HEC-2 is no longer supported by HEC, and the program is being phased out in favor of HEC-RAS.

HEC-RAS for Steady Flow

HEC-RAS (River Analysis System) was developed by HEC through the efforts of a program development team led by Gary W. Brunner (USACE, 2002). The HEC-RAS program will eventually replace three major HEC programs: HEC-2, HEC-UNET, and HEC-6. From 1995 through 2000, HEC-RAS featured only steady, gradually varied flow modeling; the computational engine within HEC-RAS for this type of modeling is referred to as SNET (Steady Network). One-dimensional, unsteady flow capability was added to the package in 2001; the computational engine for this type of modeling is UNET (Unsteady Network). A one-dimensional sediment transport module is scheduled to be included in the future.

Like HEC-2, HEC-RAS has been primarily used for steady, gradually varied flow situations in which a peak discharge is applied at each cross section to determine a maximum water surface elevation. The energy, continuity, and Manning equations are employed with the standard step method to solve for water surface elevations, with the momentum equation used as part of the analysis for bridges, supercritical flow, and rapidly varied flow. The program can compute and store up to 500 water surface profiles and an unlimited number of cross sections may be used for steady flow analysis. A maximum of 500 elevation-station points is allowed per cross section. The modeler must supply geometric information to describe the channel, floodplain, and major obstructions (such as bridges, culverts, and weirs), along with discharge, boundary conditions, friction coefficients, and other parameters. With a few exceptions, the data needs for HEC-2 and HEC-RAS in the steady flow mode are the same. Chapter 5 discusses in detail the necessary data.

Since HEC-RAS was released in 1995, it has undergone several upgrades. HEC-RAS is Windows-based and employs a variety of tabular and graphical features to readily display input and output for review and modification. HEC-RAS is a tremendous improvement over HEC-2 and is the most widely used program of its type. HEC-RAS offers a wide variety of applications for common and unique hydraulic modeling situations, including the following:

Simultaneous subcritical and supercritical flow computations, including the determination of flow regime

Ice hydraulics

Channel modification analysis

Levee modeling

Current bridge and culvert modeling using Federal Highway Administration (FHWA) HDS-S techniques

Scour analysis at bridges

Floodway analysis

Split flow optimization

Inline and lateral weirs and gates

Multiple bridge and culvert opening analysis

Multiple reach analysis

Geographic Information System (GIS) integration

WSP2

WSP2 (USDA, 1993) was developed by the U.S. Soil Conservation Service (SCS), now known as the Natural Resources Conservation Service (NRCS), and is similar to the Corps' HEC-2 program. It applies the standard step method to compute water surface profiles for either subcritical or critical flow. WSP2 does not perform supercritical flow computations. Although the program is limited to a maximum of 50 cross sections and 48 points per cross section, the output can be linked to additional sets of cross sections for longer stream reaches. Fifteen profiles may be computed in a single run. Computations include bridge and culvert modeling using the Bureau of Public Roads (BPR) analysis standards. A single bridge opening or up to four culverts can be analyzed at any cross section. This program has been largely superceded by HEC-RAS; the NRCS has recently phased out WSP2 and adopted HEC-RAS for its hydraulic modeling needs.

WSPRO (HY-7)

The U.S. Geological Survey developed the bridge waterway analysis model, WSPRO (FHWA, 1990) for the Federal Highway Administration (FHWA). The program is used specifically to analyze and design bridge openings. WSPRO is generally used for relatively short reaches of river to determine the bridge opening design and the bridge's effects on the upstream water surface profile. It can use a maximum of 20 profiles and 100 cross sections. WSPRO uses the standard step method for computations in subcritical flow and when the water surface is below the bridge low chord (bottom of the beam or low steel) elevation. The energy, continuity, and Manning equations are used to analyze water surface profiles through a bridge. WSPRO only considers friction and expansion losses; contraction losses into the bridge are neglected. Chapter 6 discusses these losses and the use of WSPRO.

Bridge design for the FHWA during the 1990s required the use of WSPRO because the bridge routines in HEC-2 were not acceptable to the FHWA. Although this program is still used for bridge design, HEC-RAS includes an option to use the WSPRO procedures when modeling bridges. The FHWA procedures have been integrated into the HEC-RAS source code and included in the documentation.