Source: https://guthlabs.ai/docs/instruments/culvert-pipe-sizing-calculator/
instrument / verified-clean
# Culvert/Pipe Sizing Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration
**Tranche**: tranche-6
**Evidence ID**: t6-124
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The Manning method is fundamentally appropriate for preliminary uniform-flow sizing, but the instrument is underspecified. It needs an explicit circular-segment geometry model, a clear definition that the supplied maximum fill ratio is the design operating fill ratio or a post-solution constraint, SI versus US customary unit handling, solver algorithm and tolerance, and input validation. The honest label 'preliminary hydraulic sizing' is appropriate only if these limitations are displayed.
### Formula and scope findings
- Manning's equation is the correct standard relation for steady, uniform open-channel or partially full pipe flow: Q=(1/n)A R_h^(2/3) S^(1/2), but the specification does not state whether the calculation assumes normal flow, steady uniform flow, and a known flow depth equal to the maximum fill ratio.
- For a circular pipe at specified fill ratio f=y/D, the area and hydraulic radius must be defined from circular-segment geometry: theta=acos(1-2f), A=(D^2/4)(theta-sin(theta)cos(theta)), wetted perimeter P=D theta, and R_h=A/P. The spec does not provide these equations.
- For fixed fill ratio, Q is proportional to D^(8/3), so a direct solution is possible: D=[Q n/(C(f) sqrt(S))]^(3/8), where C(f) is the dimensionless geometry coefficient. Calling the method iterative is acceptable, but the iteration algorithm is unspecified.
- It is ambiguous whether max fill ratio is an input constraint, the actual design operating depth, or a check applied after solving. A diameter cannot be uniquely computed from Q, n, S, and a maximum fill ratio unless the design is explicitly taken at that fill ratio.
- The specification does not state a minimum practical diameter, allowable velocity, freeboard requirement, inlet/outlet control, tailwater condition, entrance losses, or whether the result is intended only as preliminary uniform-flow sizing. These omissions matter for an honest civil-design label.
### Unit assumptions
- Q is in m^3/s.
- Diameter and all geometric dimensions are in m.
- Manning's n is dimensionless in the SI form of Manning's equation.
- S is the dimensionless longitudinal energy-grade-line slope; a slope stated as 0.1% must be converted to S=0.001.
- The vectors assume steady, uniform flow and that the actual design flow depth is exactly the supplied fill ratio f times diameter.
- For the full-flow vector, f=1, A=pi D^2/4, P=pi D, and R_h=D/4.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
Zero slope and zero Manning roughness produce undefined or nonphysical results unless explicitly rejected. The percent-slope convention can also produce a materially wrong diameter if the input is interpreted as S=1 instead of S=0.01.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"design_Q_m3_per_s": 3.11685,
"manning_n": 0.01,
"slope": 0.01,
"max_fill_ratio": 1,
"assumed_design_fill_ratio": 1,
"solver": "Newton-Raphson",
"initial_diameter_m": 0.8,
"tolerance_m": 0.000001
},
"expected_outputs": {
"required_diameter_m": 1,
"hydraulic_regime": "full circular pipe",
"geometry_coefficient_C": 0.311685,
"capacity_check_m3_per_s": 3.11685
},
"working": "For full flow, A=pi D^2/4 and R_h=D/4. Therefore Q=(1/n)(pi/4)(1/4)^(2/3)S^(1/2)D^(8/3)=K D^(8/3), with K=(1/0.01)(0.311685)(sqrt(0.01))=3.11685. Thus D=(Q/K)^(3/8)=(3.11685/3.11685)^(3/8)=1.00000 m. Newton solve on F(D)=D^(8/3)-1: D_(k+1)=D_k-(D_k^(8/3)-1)/[(8/3)D_k^(5/3)]. Starting D0=0.800000 m: D1=0.800000-(0.800000^(8/3)-1)/[(8/3)(0.800000^(5/3))]=1.04394 m. D2=1.04394-(1.04394^(8/3)-1)/[(8/3)(1.04394^(5/3))]=1.00153 m. D3=1.00000 m; convergence is below 0.000001 m. Check at D=1: Q=(1/0.01)(pi/4)(0.25)^(2/3)(0.01)^0.5=100(0.311685)(0.1)=3.11685 m^3/s."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche6/tranche6-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`