Culvert/Pipe Sizing Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json