Open Channel Hydraulics Solutions Manual Chow Pdf
Landers Hoang
There is a wide variety of entrance conditions found at culverts, including square edge, angled wingwalls, beveled edges, entrance mitered to slope, et cetera. Some of these common culvert end treatments are shown in Figure 2. It is not uncommon for the opening of a culvert to be smaller than the original channel cross-section prior to the culvert installation. All else being equal, a smaller waterway opening will result in a lower channel conveyance, that is, a lower carrying capacity of the channel. For the same flow, a lower conveyance will, in turn, result in a higher depth of water upstream of the structure, called the headwater.
For a given design discharge (Q), there will be a corresponding headwater depth (HW) upstream of the culvert entrance. In fact, it is the headwater depth that pushes or forces the design discharge through the culvert opening. For a given culvert opening, a higher discharge will typically result in a higher headwater depth since more energy is needed to force the flow through the culvert. In open-channel hydraulics, energy is synonymous with water depth as shown in Equation 1.
Outlet control is different from inlet control in that the barrel or tailwater cannot accept as high a flow as the inlet may allow. This may occur with a high tailwater or a long culvert with a rough interior. Outlet control may be mathematically modeled using water surface profile methods or by an energy balance. Because outlet control conditions in culverts can be calculated with open-channel hydraulic principles, there is no need for empirical testing and regression formulas to describe the relationship between the flow through the culvert and the headwater. However, testing on scale models can provide valuable information about the head loss coefficients associated with the culvert entrance. Once the outlet control situation has been modeled as accurately as possible based on known information, the headwater may be calculated to evaluate the culvert design.
The coefficients C, n, and f are friction factors.The Darcy-Weisbach friction factor, f, is nondimensional and isa function of Reynolds number, 4RhV/L, and relativeroughness, k/4Rh, in which L is kinematicviscosity, and k is a linear measure of boundary roughness size.The Reynolds number accounts for variation of viscosity. This functionis given in the form of plots in any fluid mechanics textbook; for example,Streeter (1951), Rouse (1950), and Chow (1959). These plots are generallyin terms of pipe diameter, D, which should be replaced with 4Rhfor open channel flow. Values of k have been determined empiricallyand are constant for a given flow boundary material as long as the roughnesscan be considered a homogenous texture rather than large roughness elementsrelative to the depth.