Open channels include natural stream channels, as well as natural swales (depres-sions) along which water runs following rainfall events. In the constructed or urban-ized environment, open channels include street gutters, drainage ditches, pipes, lined or unlined stormwater collection channels, and natural or modified stream channels.
Figure 2.1 shows an example of flow in an open channel with a trapezoidal cross section.
Flow in a pipe is classified as open-channel flow if there is a water surface at atmo-spheric pressure (that is, a free water surface). For the purposes of this book, the term open-channel flow refers to any flow having a free water surface, regardless of whether it occurs in a closed conduit such as a culvert or storm sewer, aboveground channel, or other structure. Open-channel flow theory is presented in detail in Chapter 7. However, when the text refers simply to an open channel in the context of physical characteristics or design approaches, as in Chapter 8, the term is meant to describe nonpipe conveyances only.
Figure 2.1 Open-channel flow
Prismatic versus Nonprismatic Channels. Open channels exist in a wide variety of cross-sectional shapes. For analytical purposes, channels may be classified as prismatic or nonprismatic. In a prismatic channel the variables that describe the channel geometry—such as its width, side slopes, and longitudinal slope—remain constant along the length of the channel. In a nonprismatic channel one or more of these geometric variables changes along the channel length. Natural stream channels, whose widths and other channel properties are variable, are examples of nonprismatic open channels. Treatment of open-channel flow in this text deals primarily with pris-matic, man-made channels. Nevertheless, certain aspects associated with the hydrau-lics of flow in nonprismatic channels will be addressed where appropriate.
Materials. Open channels can also be classified on the basis of whether they are lined or unlined. The bottom and sides of an unlined channel consist of natural geo-logic materials such as earth, gravel, or rock. In a lined channel, the channel bottom and sides are covered with an erosion-resistant material such as concrete, asphalt, riprap, or vegetation.
As shown in Chapter 7, the channel’s lining material (or lack thereof) affects hydrau-lic performance characteristics such as flow depth and velocity. In turn, these same characteristics affect the erosive forces of the flow, thereby influencing the lining selection. The selection of the channel lining material is therefore a significant part of the hydraulic design process.
Model Representation. To model open-channel flow, the engineer must know the flow condition. With steady flow, flow characteristics such as discharge and veloc-ity are constant over time at a given point in the channel. When these characteristics do vary over time as a point, the condition is unsteady.
Steady flow can be further classified as either uniform flow or varied flow. Uniform flow is a condition in which the depth, velocity, cross-sectional area, and discharge are constant along the channel length. As a practical matter, this can happen only in a prismatic channel and only if the flow is steady. In uniform flow, the depth of flow is called normal depth.
Two models that can be used to describe uniform flow are the Manning equation and the Chézy equation. In their simplest forms, either of these equations may be used to calculate velocity or discharge as a function of channel slope, roughness and geome-try. In design, these models are used in a variety of ways. For example, for a given channel geometry, slope, roughness, and depth, the discharge may be calculated.
Alternatively, if the channel geometry, material roughness, discharge and maximum allowable depth are specified, the required slope can be calculated. An example of a computer model used for uniform flow calculations is FlowMaster. Modeling of uni-form flow is covered in more detail in Section 7.3.
Varied flow is a condition in which the depth and velocity of flow change along the length of the channel. If the depth and velocity change only gradually, the flow is said to be gradually varied flow (GVF). If the depth and velocity change quickly over a short distance, as in a hydraulic jump, the flow is said to be a rapidly varied flow (RVF). Gradually varied flow occurs in all nonprismatic channels and in prismatic channels under the influence of a flow control other than normal depth. Because the curvatures of flow streamlines are small in a gradually varied flow, the pressure forces can be assumed to be hydrostatic. Constitutive relationships developed for uniform flow, such as the Manning equation, can be assumed to be valid for computing friction losses in gradually varied flow.
Because of the variable channel geometry and the presence of flow controls, the data required for gradually varied flow analysis are considerably more complex than for uniform flow analysis. The input includes channel cross-section geometry, reach lengths, channel roughness, and the water surface elevation at the control section.
HEC-RAS is an example of a computer program frequently used in gradually varied flow profile calculations. For more information on gradually varied flow calculations, see Section 7.8.
Channel routing is a procedure by which the outflow at the downstream end of a channel reach is computed from inflow data and channel characteristics. It accounts for the effects of channel storage and travel time on discharge rates; thus, it is a type of unsteady flow modeling. Channel routing is applicable to both open channels and sewer systems when channel storage and/or travel time affect flow rate to a significant degree.
Channel routing may be accomplished by using either hydrologic or hydraulic routing methods. Hydrologic routing is computationally simpler and less data-intensive, but usually is also less accurate. Hydrologic routing algorithms are based on the physical principle of conservation of mass and on an assumed storage relationship. Hydraulic methods are more physically based and employ conservation of mass and conserva-tion of momentum. Their use requires considerable data on channel geometry and roughness variables and on initial and boundary conditions of the flow itself. The Muskingum, Modified Puls, and Convex routing methods are examples of hydrologic routing models. (See Section 5.8 and Appendix C.) Hydraulic routing involves a solu-tion of the Saint-Venant equasolu-tions, and may consist of kinematic, diffusion, or dynamic wave routing. Such methods are not well-suited to manual calculations but are coded into software packages such as HEC-RAS.
Culverts
A culvert is a relatively short underground water conveyance conduit. The primary purpose of a culvert, like that of a bridge, is to provide a means whereby the water in a stream or other open channel can pass through an obstruction such as a highway or railway embankment. Figure 2.2 shows a small culvert passing under a driveway.
Materials. Culverts come in a variety of shapes, sizes, and materials. As shown in Figure 2.3, cross-sectional shapes associated with culverts include circular, box, ellip-tical (horizontal or verellip-tical orientation), and arched.
Common materials used for culvert design are reinforced precast or cast-in-place con-crete and corrugated steel. Other materials include corrugated aluminum, polyethyl-ene, and polyvinyl chloride (PVC). Discussions of these materials, including available shapes and sizes and sources of further information, are presented in Section 9.2.
The inlet and/or outlet ends of a culvert often receive special treatment. A culvert end may simply project from the embankment, or it may be mitered to conform to the embankment slope. It may also be fitted with a special flared end section or with a headwall and wingwalls. Section 9.3 discusses various types of end treatments and their hydraulic performance characteristics, as well as special inlet configurations that can be used when allowable headwater depths are limited.
Model Representation. A complete theoretical analysis of the hydraulics of a particular culvert installation is complex. Flow conditions vary from one culvert to the next, and they also vary over time. The barrel of the culvert may flow full or partially full, depending on upstream or downstream conditions, barrel characteristics, and inlet geometry. A commonly used method of analysis of culvert hydraulics was devel-
Figure 2.2 A corrugated metal pipe culvert under a driveway
oped by the Federal Highway Administration and published as “Hydraulic Design Series No. 5: Hydraulic Design of Highway Culverts,” often referred to as HDS-5 (Norman, Houghtalen, and Johnston, 2001). Modeling software such as CulvertMas-ter follows the calculation methods set forth in HDS-5.
The following list describes the principal terms and concepts in culvert hydraulics More detailed information on culvert hydraulic analysis and HDS-5 methodologies is provided in Section 9.5 and Section 9.6.
• Headwater depth is the depth (relative to the culvert’s upstream invert eleva-tion) of flow just upstream of the culvert entrance. Any increase in energy required to push an increased discharge through a culvert translates into a greater headwater depth.
• Tailwater depth is the depth of water just downstream of the culvert outlet.
The tailwater surface elevation may be dictated by downstream channel characteristics, by obstructions, or by a receiving-water elevation. An exit condition in which the tailwater depth is significantly less than the depth of flow in the culvert, and thus does not affect the upstream hydraulics, is called a free outfall.
Figure 2.3 Common cross-sectional shapes for culverts
• The flow condition in a culvert can be characterized as either full (pressure) flow or partially full flow with a free water surface. Both free-surface and pressure flow can occur simultaneously at different locations within the same culvert. Uniform flow and gradually varied flow, as discussed earlier for open channels, apply to free-surface flow in culverts as well.
• The flow in a culvert may be controlled by conditions at either the inlet or the outlet of the culvert, so the type of control is classified as either inlet control or outlet control. In the case of inlet control, the hydraulic capacity of the culvert entrance limits the amount of water conveyed for a given headwa-ter depth; therefore, hydraulic characheadwa-teristics downstream of the inlet control section do not affect the culvert capacity. In an outlet control condition, the culvert barrel capacity or downstream tailwater elevation limits the amount of flow that can be conveyed by the culvert for a particular headwater eleva-tion. The control section for outlet control is located at the barrel exit or fur-ther downstream.
• The flow velocity at the exit of a culvert is typically higher than that of the stream channel into which the culvert discharges. High outlet velocity can cause streambed scour and bank erosion in the vicinity of the culvert outlet.
Minor problems occasionally can be avoided by increasing the barrel rough-ness, but structures such energy dissipators and/or outlet protection such as riprap are often necessary.