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&phhhhp kkDAppendix D. WATER-SURFACE PROFILE COMPUTATION SPREADSHEET
D.1 Introduction
The EXCEL spreadsheet WSProfile.xls allows computation and plotting of water-surface profiles calculated by the Standard Step Method described in section 9.4.2.2 (table 9.4, figure 9.8). This spreadsheet is a highly simplified version of widely used computer applications such as HEC-RAS (Brunner 2001a, 2001b) and WSPRO (Shearman 1990) intended to provide students with a hands-on introduction to the basic aspects of profile computation. Samples of an M1 and an M2 profile are shown, and an instructor can readily develop exercises by erasing the trial depths provided in the sample worksheets or by providing new channel and flow data.
The spreadsheet computations assume that a spatially constant discharge is contained within a wide rectangular channel at all cross sections, that the slope is mild [i.e. the flow is subcritical, so that computations progress upstream (sections i = 1, 2, , N) from the downstream-most cross section (i = 0)], that the flow is quasi-uniform, and that the Manning equation (section 6.8) relates depth, slope, and resistance to velocity.
D.2 Procedure
D.2.1 Overview
The spreadsheet contains two worked examples of profiles. Profile I = 1 is an M1 profile with the downstream-most elevation determined by critical flow, using British units. Profile I = 2 is an M2 profile with the downstream-most elevation determined by a fixed reservoir elevation, using S.I. units.
Each profile is generated by entering user-selected fixed quantities and trial depths on the worksheets designated GenerationI, where I = 1 or 2. As profile generation proceeds, a corresponding detailed table of computed values is produced on the worksheets designated ComputationsI, and a corresponding table of values to be used in generating graphs of the elevations of the channel bed, the water surface, the normal-depth surface, and the critical-depth surface is produced on the worksheets designated GraphDataI). Graphs showing the profiles for the worked examples are on the worksheets designated ChartI.
D.2.2 User-Selected Quantities (Generation Spreadsheets)
For each profile, user-selected fixed quantities defining the reach and flow to be modeled are entered in the cells colored in one of the GenerationI worksheets.
1. Enter "SI" or "Br" (British) units in cell D5. This determines the values of gravitational acceleration, g (cell C6), and the unit-conversion constant for the Manning equation, uM (cell F6).
2. Enter discharge, Q (cell B9); energy coefficient, ( (cell E9; see section 8.1.1); eddy coefficient keddy (cell H9; see section 9.4.2.1); and tolerance for depth calculations, Y (cell K9). The default tolerance used in the HEC-RAS is Y = 0.01 ft or Y = 0.003 m (Brunner 2001a); however, since the spreadsheet program gives depth values only to two decimal places, the minimum Y used should be 0.01 ft or 0.01 m. (The user can change the number of decimal places in any cell via the Format, Cells, Number commands.)
3. Enter predetermined distance, Xi, bed elevation, Z0i, width, Wi, and Manning's nMi, values for N measured cross sections in columns 2 5 in successive rows of the table, beginning in cells B30:E30. Section numbers, i (column 1) increase in the upstream direction. [Note that bed elevations must increase upstream (Z0i < Z0i+1) in order to avoid numerical problems in computing slopes.] The number of sections can be increased indefinitely by copying formulas into additional cells below the last row. (If this is done, the formulas on the Computations and Graph Data worksheets will also have to be copied into the appropriate number of rows below.)
4. Enter the known initial (Section 0) depth in first row of column 6 (cell F30).
D.2.3 Trial Depths (Generation Spreadsheets)
Trial depths, EMBED Equation.3 , are entered sequentially in column 6, colored beginning in
cell F31. Calculated depths, Yi, are computed following the standard-step method described in section 9.4.2.2; these appear in column 11. Columns 8, 10, 12, or 13, colored will indicate NO if the trial depth is unacceptable for the following reasons:
1. If the trial depth produces a violation of the laws of thermodynamics (section 4.1) by causing the total energy to increase downstream, NO appears in column 8. A new trial depth must be selected.
2. If the trial depth produces a violation of the laws of thermodynamics by causing the total potential energy to increase downstream, NO appears in column 10. A new trial depth must be selected.
3. If the trial depth produces a calculated depth that differs from it by more than Y (i.e., | EMBED Equation.3 " Yi | > Y ), NO appears in column 12. A new trial depth must be selected.
4. If the trial depth produces a critical or supercritical Froude number (i.e., Fri e" 1), NO appears in column 13. If this happens when there are no NO indications in columns 8, 10, or 12, the computation must be abandoned, because flow in the reach is supercritical. Profile computations must proceed in the downstream direction for supercritical flow.
If there are no thermodynamic or Froude number violations, depth agreement can often be achieved in the second trial if the second trial depth is set equal to the first calculated depth. A trial depth must be accepted in a given row before proceeding to the next row in order to produce a valid profile.
D.2.4 Computations and GraphData Worksheets
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