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Primary-source fixture candidates

Reviewed 2026-09-09 for CS-001. These records preserve source-native inputs and published results. They are research fixtures, not automatic engineering acceptance. CS-003 and CS-004 own method implementation; CS-006 owns executable cross-phase fixtures.

Use the source's customary-unit values when reproducing an old worked example. Convert to SI with exact unit definitions (1 ft = 0.3048 m and 1 ft³/s = 0.028316846592 m³/s) in the test setup, and do not substitute a publication's independently rounded SI caption. Solver tolerances must be wider than the source's displayed precision and must also allow for chart-reading precision where a nomograph supplies an intermediate value.

Bodhaine worked-example audit

The ten examples in USGS TWRI Book 3, Chapter A3 were reviewed on printed pages 52-60 (local PDF pages 61-69). They demonstrate the 1968 indirect peak-discharge procedure, including its coefficient charts; they do not define the project's HDS-5 inlet method.

Example Published case Final discharge Locator Disposition
1 Type 1, corrugated-metal pipe 725 ft³/s Printed p. 52; local PDF p. 61 Selected classification/reproduction candidate
2 Type 1, concrete box 531 ft³/s Printed p. 53; local PDF p. 62 Selected box reproduction candidate
3 Type 2, corrugated-metal pipe 268 ft³/s Printed pp. 53-54; local PDF pp. 62-63 Reviewed; redundant with Example 4
4 Type 2, concrete box 523 ft³/s Printed pp. 54-55; local PDF pp. 63-64 Reviewed; chart-dependent
5 Type 3, corrugated-metal pipe 251 ft³/s Printed pp. 55-56; local PDF pp. 64-65 Reviewed; backwater iteration
6 Type 4, concrete pipe 125 ft³/s Printed pp. 56-57; local PDF pp. 65-66 Selected full-flow reproduction candidate
7 Type 5, corrugated-metal pipe 120 ft³/s Printed p. 57; local PDF p. 66 Reviewed; chart-dependent
8 Type 6, concrete pipe 209 ft³/s Printed pp. 57-58; local PDF pp. 66-67 Selected Type 6 comparison candidate
9 Routing method, Type 3 251 ft³/s Printed pp. 58-59; local PDF pp. 67-68 Reviewed; reproduces Example 5
10 Type 3, irregular culvert 250 ft³/s Printed pp. 59-60; local PDF pp. 68-69 Reviewed; geometry outside initial scope

BOD-A3-EX1

  • Inputs: 10 ft diameter corrugated-metal pipe in a concrete headwall; r/D = 0.006; 100 ft length; slope 0.02; Manning n = 0.024; headwater h1 = 12.00 ft; invert fall z = 2.00 ft; downstream depth h4 = 6.00 ft; approach area 1,000 ft²; approach conveyance 300,000 in the source's customary units.
  • Expected quantity: final discharge 725 ft³/s (20.5297 m³/s after exact conversion), classified and proved as Type 1.
  • Published precision: whole ft³/s; intermediate chart coefficients are displayed to three or four significant figures.
  • Applicability: reproduction of Bodhaine's Type 1 reasoning for this steep circular case. It is not an HDS-5 inlet-control acceptance value because the result depends on Bodhaine Figures 9, 10, 20 and 21 and the historical coefficient formulation.

BOD-A3-EX2

  • Inputs: 8 ft square concrete box with square-edged entrance; 100 ft length; slope 0.02; Manning n = 0.015; headwater h1 = 10.00 ft; invert fall z = 2.00 ft; downstream depth h4 = 4.00 ft; approach area 330 ft²; approach conveyance 38,900 in the source's customary units.
  • Expected quantity: final discharge 531 ft³/s (15.0362 m³/s after exact conversion), classified and proved as Type 1.
  • Published precision: whole ft³/s; critical depth and losses are shown to 0.01 ft.
  • Applicability: simple rectangular geometry is representable, but the expected result uses Bodhaine Figure 23 and its critical-depth discharge coefficient. Keep it as an external historical-method reproduction, not a production-method oracle.

BOD-A3-EX6

  • Inputs: 4 ft diameter concrete pipe with bell entrance; 50 ft length; Manning n = 0.012; relative rounding w/D = 0.075; h1 = 7.00 ft, h4 = 5.00 ft, and zero invert fall.
  • Expected quantity: 125 ft³/s (3.53961 m³/s after exact conversion), Type 4.
  • Published precision: whole ft³/s; the source coefficient is C = 0.955.
  • Applicability: useful as a full-flow energy reproduction. The entrance geometry and Bodhaine coefficient must be supplied explicitly; neither may be inferred from concrete material.

BOD-A3-EX8

  • Inputs: 4 ft diameter concrete pipe with beveled entrance; 50 ft length; Manning n = 0.012; relative rounding w/D = 0.075; h1 = 8.00 ft, h4 = 1.00 ft, and 1 ft invert fall.
  • Expected quantity: 209 ft³/s (5.91822 m³/s after exact conversion), Type 6.
  • Published precision: whole ft³/s; the adjusted chart factor is displayed as 8.31.
  • Applicability: an independent classical Type 6 comparison, but not a direct fixture for the current high-head HDS-5 extension. Reproduction requires the source's Figure 17 relationship and explicit beveled-inlet context.

Corrected FHWA box example

FHWA-HRT-06-138 Appendix D, printed pages 127-140 (local PDF pages 140-153), provides the selected modern-box case. The authoritative reproduction basis is the customary-unit column because the example's independently rounded SI and customary-unit flow labels are not exact conversions.

Shared inputs are two 9 by 8 ft cells, 84 ft long, inlet invert 78.81 ft, outlet invert 78.79 ft, Manning n = 0.012, the downstream rating in Table 21, and the cross-section coordinates in Table 20. The field-cast FC-D-30 configuration has 6 in corner fillets, 30° flared wingwalls, a 45° top-edge bevel, and Table 11 Sketch 2 entrance-loss coefficient Ke = 0.32.

Case Flow Expected quantity Published precision Locator
BOX-APPD-Q25 773 ft³/s total Headwater elevation 85.907 ft 0.001 ft Table 25, local PDF p. 150
BOX-APPD-Q100 1,602 ft³/s total Headwater elevation 89.251 ft 0.001 ft Table 26; local PDF p. 151

The intermediate expected values include critical depths in Table 22, normal depths in Table 23, outlet starting conditions in Table 24, and inlet HGL/EGL values in Tables 25 and 26. The Q25 FC-D-30 case is executable as a bounded fixture using FilletedRectangularGeometry, the typed Sketch 2 inlet, Ke = 0.32, and the published approach area. The complete downstream and approach cross sections are not yet general boundary-condition objects; CS-029 owns that broader work. Substituting a sharp-corner rectangle would still change the published problem.

The report's Table 12 fifth-order polynomial is not the expected method for this outlet- controlled Appendix D result. Printed pages 72-73 (local PDF pages 85-86) limit those polynomials to their measured range, approximately 0.4 < HW/D < 2.3, and warn of low- and high-end numerical errors.

Austroads design-workflow case

AGRD05B-23 Section 3.15.1, printed pages 101-106 (local PDF pages 111-116), uses three 1,050 mm RCP barrels, 15.6 m long at slope 0.0065, carrying 6.25 m³/s total with tailwater 0.96 m. It publishes inlet headwater 1.40 m, outlet headwater 1.36 m, inlet control, outlet depth 0.75 m, outlet area 0.67 m², outlet velocity 3.08 m/s, and Froude number 1.17.

This case is accepted as a workflow and reporting checklist, not as a strict numerical fixture. Printed page 105 states full-flow velocity 2.5 m/s, then tabulates 2.75 m/s and uses 2.75 × 1.12 = 3.08 m/s. Its inlet and full-flow heads are also read from nomographs. CS-015 must reconcile that source inconsistency or identify a corrected edition before numerical acceptance; no solver value is tuned to it.