Culvert/Pipe Sizing Calculator

Inspectable records

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