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Andrew Stewart
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Open Channel Hydraulics Solutions Manual Chow Pdf



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.




Open Channel Hydraulics Solutions Manual Chow Pdf



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.


Chow, V. T. (1959). Open-channel hydraulics. McGraw-Hill Book Company, New York. Copeland, R. R. (2000). Determination of flow resistance coefficients due to shrubs and woody vegetation. Technical Note No. ERCD/CHL CHETN-VIII-3, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS. (pdf) Cowan, W. L. (1956). Estimating hydraulic roughness coefficients. Agricultural Engineering. 37(7). 473-475. Federal Interagency Stream Restoration Working Group (FISRWG) (1998). Stream Corridor Restoration: Principles, Processes, and Practices. GPO Item No. 0120-A; SuDocs No. A 57.6/2:EN 3/PT.653. ISBN-0-934213-59-3. (pdf) Freeman, G. E., Rahmeyer, W. H., & Copeland, R. R. (2000). Determination of resistance due to shrubs and woody vegetation. (Technical Report No. ERDC/CHL TR-00-25), U. S. Army Engineer Waterways Experiment station, Vicksburg, Mississippi, 62pp. (pdf) Henderson, F. M. (1966). Open-channel flow. New York, MacMillan Publishing Co., Inc., 522 pp. James, C. S. (1994). Evaluation of methods for predicting bend loss in meandering channels. Journal of Hydraulic Engineering,. 120(2): 245-253. Kouwen, Nicholas. (1988). Field estimation of the biomechanical properties of grass. Journal of Hydraulic Research, 26(5):559-567. Kouwen, N. & Fathi-Moghadam, M. (2000). Friction Factors For Coniferous Trees Along Rivers. Journal of Hydraulic Engineering, 126(10)732-740. Masterman, R. & Thorne, C. R. (1992). Predicting Influence of Bank Vegetation on Channel Capacity. Journal of Hydraulic Engineering, 118(7):1052-1058. Motayed A. K. & Krishnamurthy, M. (1980). Composite roughness of natural channels. Journal of Hydraulic Engineering Division, 106(HY6):1111-1116. Oplatka, M. (1998). Stablititat von weidenverbauungen an flussufern. Versuchsanstalt fur Wasserbau, Hydrologie und Glazioloige derETH Zurich. 156, 244.


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