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Capitulo 5 manual de drenaje americano

5-1
5. ROADSIDE AND MEDIAN CHANNELS
Roadside and median channels are open-channel systems which collect and convey stormwater from the pavement surface, roadside, and median areas. These channels may outlet to a storm drain piping system via a drop inlet, to a detention or retention basin or other storage component, or to an outfall channel. Roadside and median channels are normally trapezoidal in cross section and are lined with grass or other protective lining. This chapter presents design concepts and relationships for the design of roadside and median channels.
5.1 Open Channel Flow Concepts
The design and/or analysis of roadside and median channels follows the basic principles of open channel flow. Summaries of several important open channel flow concepts and relationships are presented in the following sections. A more complete coverage of open channel flow concepts can be found in References 7, 31 and 32.
5.1.1 Energy
Conservation of energy is a basic principal in open channel flow. As shown in Figure 5-1, the total energy at a given location in an open channel is expressed as the sum of the potential energy head (elevation), pressure head, and kinetic energy head (velocity head). The total energy at given channel cross section can be represented as: E
t
= Z + y + (V
2
/ 2g) (5-1) where: E
t
= Total energy, m (ft) Z = Elevation above a given datum, m (ft) y = Flow depth, m (ft) V = Mean velocity, m/s (ft/s) g = Gravitational acceleration, 9.81 m/s
2
(32.2 ft/s
2
) Written between an upstream cross section designated 1 and a downstream cross section designated 2, the energy equation becomes
L22222111
hg2VyZg2VyZ
(5-2) where: h
L
= Head or energy loss between section 1 and 2, m (ft) The terms in the energy equation are illustrated in Figure 5-1. The energy equation states that the total energy head at an upstream cross section is equal to the total energy head at a downstream section plus the energy head loss between the two sections.
5-2
Figure 5-1. Total energy in open channels. 5.1.2 Specific Energy
Specific Energy, E, is defined as the energy head relative to the channel bottom. It is the sum of the depth and velocity head: E = y + (V
2
/ 2g) (5-3)
5.1.3 Flow Classification
Open channel flow is generally classified using the following characteristics:
Steady or unsteady
Uniform or varied
Subcritical or supercritical A
steady flow
is one in which the discharge passing a given cross-section remains constant in time. When the discharge varies in time, the flow is
unsteady
. A
uniform flow
is one in which the flow rate and depth remain constant along the length of the channel. When the flow rate and depth vary along the channel, the flow is considered
varied
. Gradually-varied flows are nonuniform flows in which the depth and velocity change gradually enough in the flow direction that vertical accelerations can be neglected. A typical example of a gradually varied flow is the stream channel condition upstream of a culvert with ponded flow. In rapidly varied flow the changes occur in a very short reach and the vertical accelerations cannot be neglected. A typical example of a rapidly varied flow is the flow profile through a constricted bridge opening. Most natural flow conditions are neither steady nor uniform. However, in roadside and median channels the flow can often be assumed to be steady and uniform for short periods and distances which simplifies hydraulic analysis and design.
5-3
Subcritical Flow
is distinguished from
supercritical flow
by a dimensionless number called the Froude number (F
r
), which represents the ratio of inertial forces to gravitational forces and is defined for rectangular channels by the following equation:
gyVFr
(5-4) where: V = Mean velocity, m/s (ft/s) g = Acceleration of gravity, 9.81 m/s
2
(32.2 ft/s
2
) y = Flow depth, m (ft)
Critical Flow
occurs when the Froude number has a value of one (1.0). The flow depth at critical flow is referred to as critical depth. This flow depth represents the minimum specific energy for a given discharge. Critical depth is also the depth of maximum discharge when the specific energy is held constant. These relationships are illustrated in Figure 5-2.
Figure 5-2. Specific energy diagram. Subcritical Flow
occurs when the Froude number is less than one (F
r
< 1). In this state of flow, depths greater than critical depth occur (refer to Figure 5-2), small water surface disturbances travel both upstream and downstream, and the control for the flow depth is always located downstream. The control is a structure or obstruction in the channel which affects the depth of flow. Subcritical flow can be characterized by slower velocities, deeper depths and mild slopes while supercritical flow is represented by faster velocities, shallower depths and steeper slopes.
Supercritical Flow
occurs when the Froude number is greater than one (F
r
> 1). In this state of flow, depths less than critical depth occur (refer to Figure 5-2), small water surface disturbances are always swept downstream, and the location of the flow control is always upstream. Most natural open channel flows are subcritical or near critical in nature. However, supercritical flows are not uncommon for smooth-lined ditches on steep grades.
5-4 It is important that the Froude number be evaluated in open channel flows to determine how close a particular flow is to the critical condition. As illustrated in Figure 5-2 and discussed in the next section, significant changes in depth and velocity can occur as flow passes from subcritical to supercritical. When the Froude number is close to one (1.0) small flow disturbances can initiate a change in the flow state. These possible changes and any resulting impacts on flow depth or channel stability must be considered during design.
5.1.4 Hydraulic Jump
A hydraulic jump occurs as an abrupt transition from supercritical to subcritical flow. There are significant changes in depth and velocity in the jump and energy is dissipated. Figure 5-3 illustrates a hydraulic jump.
Figure 5-3. Hydraulic jump.
As discussed above, the potential for a hydraulic jump to occur should be considered in all cases where the Froude number is close to one (1.0) and/or where the slope of the channel bottom changes abruptly from steep to mild. The characteristics and analysis of hydraulic jumps are covered in detail in References 31 and 35.
5.1.5 Manning’s Equation
Water flows in an open channel due to the force of gravity. Flow is resisted by the friction between the water and the channel boundary. In steady, uniform flow there are no accelerations, streamlines are straight and parallel, and the pressure distribution is hydrostatic. This is the simplest flow condition to analyze, but one that rarely occurs in the real world. However, for many applications the flow is essentially steady and changes in width, depth or direction (resulting in nonuniform flow) are so small that the flow can be considered uniform. The depth of flow in steady, uniform flow is called the normal depth. The most commonly used equation for solving steady, uniform flow problems is the Manning’s equation (expressed in the discharge form): Q = (K
u
/n) A R
0.67
S
0.5
(5-5)

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