Open-Channel Flow — Manning's Equation mechanism

Model scope

Forward Manning calculations pass the standard formula checks under the stated unit assumptions. Verdict is NEEDS_REVIEW because the specification is ambiguous about the exact US coefficient and pipe regime, and it claims inverse normal-depth output without defining the iterative algorithm or convergence tolerance.

• The forward formulas are standard: V=(1/n)R^(2/3)S^(1/2), Q=VA, and R=A/P.
• The inverse normal-depth capability is underspecified: the target quantity (usually Q), channel geometry function, iterative method, initial guess/bracketing, stopping criterion, and convergence tolerance are not defined.
• The wording 'pipes' is ambiguous: Manning's open-channel equation applies to a partially full pipe using the wetted area and wetted perimeter; a full pressurized pipe requires a different hydraulic model.
• The US coefficient 1.49 is an accepted rounded form, but the specification should state whether US customary calculations use 1.49 or the more precise 1.486.

Units and conventions

• SI case: lengths in m, A in m^2, P and R in m, n dimensionless, S dimensionless slope expressed as m/m, V in m/s, and Q in m^3/s; the coefficient is 1.
• US customary case: lengths in ft, A in ft^2, P and R in ft, n dimensionless, S dimensionless ft/ft, V in ft/s, and Q in ft^3/s; the coefficient 1.49 is used.
• A slope entered as a percentage must be divided by 100 before using S; for example, 0.1% means S=0.001.
• For each channel, A and P must be the wetted cross-sectional area and wetted perimeter at the stated flow depth, excluding the free surface from P.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "system": "SI",
    "shape": "rectangular",
    "width_m": 3,
    "depth_m": 1,
    "mannings_n": 0.025,
    "slope": 0.001
  },
  "expected_outputs": {
    "hydraulic_area_m2": 3,
    "wetted_perimeter_m": 5,
    "hydraulic_radius_m": 0.6,
    "velocity_m_per_s": 0.899831,
    "discharge_m3_per_s": 2.69949
  },
  "working": "A=b y=3*1=3 m^2. P=b+2y=3+2(1)=5 m. R=A/P=3/5=0.6 m. V=(1/0.025)(0.6)^(2/3)(0.001)^(1/2). (0.6)^(2/3)=0.711378661 and sqrt(0.001)=0.0316227766, so V=40*0.711378661*0.0316227766=0.8998307 m/s, or 0.899831 m/s. Q=VA=0.8998307*3=2.699492 m^3/s, or 2.69949 m^3/s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification has no stated validation for n=0 or negative slope. n=0 causes division by zero, while a signed negative slope makes the square-root argument invalid; both can produce undefined results unless rejected or assigned an explicit convention.

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