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e ! -" . e ~ '- . e Chow (1959) and in EM 1110-2-1601. It relates n 10 a function of k and the hydraulic radius (R). A k value is the equivalent diameter, in feet, of the predominant grain size in the channel or the average size of an overbank obstruction. Advantages to using k to calculate n include adjustments 10 k as depth changes are not required; n can be found directly from k and the R for the stage being evaluated, and errors in estimating k result in only small differences in the calculated value of n. The engineer must evaluate the significance of other factors influencing n, including bed form changes, channel align- ment, cross-sectional area changes, and bank vegetation. Field inspection of the study stream at varying states of flow is imperative for attaining appropriate estimates of n for ranges of discharge. It is not beyond reason 10 expect the hydraulic engineer to walk or float the entire reach of stream to determine friction values. (3) Expansion-contraction coefficients. Although water surface profiles are mostly influenced by friction forces, changes in the energy grade line, and the corre- sponding water surface elevations can result from signifi- cant changes in stream velocity between cross sections. This is most apparent in the vicinity of bridges which tend to force the discharge through an opening smaller than the upstream and downstream channels. Therefore, a contraction into and an expansion out of a bridge results in eddy energy losses. These losses are usually quantified with coefficients of expansion or contraction (when using a one-dimensional approach), based on the abruptness of the change. For most situations, the expan- sion/contraction energy losses are not great except in the vicinity of bridges and culverts. Using the appropriate coefficient at each streamflow obstroction is important, as well as adjusting the coefficient back to an appropriate value upstream of the obstruction. The references by Chow (1959) or U.S. Army Corps of Engineers (1988a, 1990b) provide typical values of expansion and contrac- tion coefficients. (4) Bridge losses. Bridges that cause relatively small changes in the energy grade and water surface profiles can be adequately modeled using appropriate values of Manning's n and expansion-contraction coefficients. Bridges that cause the profIle to become rapidly varied near and within the bridge require other methods of analysis. Weir flow over the roadway, pressure flow through the opening, and open channel flow where criti- cal depth in the bridge occurs are examples where detailed bridge analysis is required. To correctly model losses for these situations, bridge geometry becomes more important. The number, locatinn, and shape of bridge piers must be obtained; a roadway profIle and EM 1110-2-1416 15 Oct 93 weir coefficient are needed for weir flow calculations; guardrails and/or bridge abutments which serve 10 par- tially or fully obstruct weir flow must be defmed; the precise upstream and downstream road overtopping ele- vations must be identified (often through trial and error computations) and debris blockage estimated. Photo- graphs and verbal descriptions of each bridge and field dictated to a hand-held tape recorder are most useful when modeling each bridge. References by U.S. Army Corps of Engineers (1975, 19883, 1990b) should be consulted for additional information. g. Study limits. The appropriate spatial scope for a hydraulic study is often incorrectly identified, particularly if all possible project effects are not envisioned. The study, or model, should not start and stop at the physical limits of the proposed project. Rather, the boundaries should extend far enough upstream and downstream from the project limits to completely encompass the full effects of the project on the basin. Reservoir, channel- ization, levee, and navigation projects may produce changes in stage, discharge, and sediment conditions that can affect reaches well removed from the physical loca- tion of the project. For example, major channelization, resulting in shortening of the stream, may generate upstream headcutting and downstream deposition that can continue for decades. Reservoirs can cause upstream deposition, thereby increasing water surface elevations over time, and may cause downstream degradation because of the relatively sediment-free waters that are released. The deposition and degradation can extend up tributaries also. Study limits must be establisbed so that all effects of the project, both positive and negative, can be identified and evaluated. Figure 3-2 illustrates some considerations for establishment of study limits for a reservoir project and the type of data required at various locations within the study area. h. Possible needs for additional data. Not all data needs can be foreseen at the start of a study. Consulta- tions with experienced personnel early in the study are often useful in identifying data needs. Some common needs that often surface well into a study include stage and/or discharge duration data (especially where stage- frequency near a stream junction becomes important), surficial soils analysis 10 estimate sediment yield for ungaged areas (particularly where the amount of sand compared 10 the amount of fines is important), type and gradation of bed material present at different times for movable bed model calibration, measurement of velocity directions and magnitudes at various stages, times, and locations for use in multidimensional model calibration. 3-9