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Ogee Spillway Calculator

Compute USBR high-overflow ogee spillway discharge from crest length L, head H, and design head Hd. Runs locally. C is 3.98 (H/Hd)^{0.12}, not an input. Not a thin-plate weir, not broad-crested, not a sluice, not Manning, and not Q=Av.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · USBR high-overflow ogee Q_cfs=C L_ft H_ft^{3/2} with C=3.98 (H/Hd)^{0.12}, + O3 mpmath tabulated Q.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
USBR high-overflow ogee Q_cfs=C L_ft H_ft^{3/2} with C=3.98 (H/Hd)^{0.12}, + O3 mpmath tabulated Q.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, alias, awkward, tall, invalid-domain) · Matrix
Deferred
Not thin-plate (2/3)Cd, not broad-crested, not sluice, not Manning, not submerged, not Q=Av.
Numerical scope
O2: USBR high-overflow ogee vs a separate-module identity (≤2 ULP). Not thin-plate, not broad-crested, not sluice, not Manning, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated ogee vectors. Not thin-plate, not broad-crested, not sluice, not Manning, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
USBR high-overflow ogee spillway discharge or head. SI L, H, Hd, Q.
Scope
USBR high-overflow ogee: Q_cfs = C L_ft H_ft^{3/2}; C = 3.98 (H/Hd)^{0.12}; SI L, H, Hd, Q; C is reported, not an input
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · USBR high-overflow ogee Q_cfs=C L_ft H_ft^{3/2} with C=3.98 (H/Hd)^{0.12}, + O3 mpmath tabulated Q.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision
2026-09-26.o2-o3 · 1/1 property · digest c52bed685698
Legacy regression
6/6 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
4/4 golden · 1/1 CVP boundary · 3/3 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
Sources
Evidence
1 legacy golden · legacy regression suite · 4/4 oracle-backed golden · 3/3 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

DischargeQ_cfs = C L_ft H_ft^{3/2}
CoefficientC = 3.98 (H / Hd)^{0.12}
iSI. Convert with 1 ft = 0.3048 m and 1 cfs = 0.028316846592 m³/s. Envelope H/Hd∈[0.2, 1.33]. Optional P with P/Hd≥1.7. Do not send query v — that is calculation_version.

How to use

1

Enter crest length L

Ogee crest in metres. This is not broad-crested width b.

2

Enter design head Hd

The head the ogee profile was designed for. Thin-plate weirs have no Hd.

3

Enter head H or discharge Q

Give one, not both. H is upstream head above the crest, not flume Ha.

Example calculations

Common configurations with formula and result.

ϟ

Design-head overflow

L=1 m, H=1 m, Hd=1 m

C = 3.98 (1)^{0.12}
Q≈2.19731 m³/s
ϟ

Invert H from that Q

L=1 m, Hd=1 m, Q≈2.19731 m³/s

H from Q = C(H) L H^{3/2}
H=1.0000 m

Ogee Spillway calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
USBR high-overflow ogee with vertical upstream face. Q_cfs = C L_ft H_ft^{3/2} with C = 3.98 (H/Hd)^{0.12}. Inputs and result are SI (L, H, Hd in m, Q in m³/s). C is the reported USBR fps coefficient, not an input. Envelope H/Hd∈[0.2, 1.33]. Optional height P with P/Hd≥1.7. Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not broad-crested (2/3)^{3/2} b √g H^{3/2}, not sluice a b √(2g y1), not Manning n, not Q=Av, not Francis 3.33.
What it calculates
USBR high-overflow ogee spillway discharge or head. SI L, H, Hd, Q.
Inputs
  • mode?
  • L
  • Hd
  • H | Q
  • P?
Outputs
  • Q
  • L
  • H
  • Hd
  • C
  • P
  • mode
  • model
Formula
Q_cfs = C L_ft H_ft^{3/2}; C = 3.98 (H/Hd)^{0.12}
Assumptions
  • USBR high-overflow ogee: Q_cfs = C L_ft H_ft^{3/2}; C = 3.98 (H/Hd)^{0.12}; SI L, H, Hd, Q; C is reported, not an input
  • H/Hd∈[0.2, 1.33]; optional P with P/Hd≥1.7; vertical upstream face; free overflow
  • Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not broad-crested (2/3)^{3/2} b √g H^{3/2}, not sluice, not Manning n, not Q=Av, not Francis 3.33
Units
  • SI; L, H, and Hd in m; Q in m³/s; C is the USBR fps coefficient
Boundary conditions
  • missing L, Hd, H, or Q when required → MISSING_REQUIRED_INPUT
  • Cd, broad-crested b, sluice a/y1, Manning n/R/S, Q=Av v, g, orifice A/d → MIXED_INPUT_ENCODING
  • H/Hd outside [0.2, 1.33] or P/Hd < 1.7 → VALUE_OUT_OF_RANGE
  • mode=rectangular|thin-plate|broad-crested|sluice or unknown mode → MIXED_INPUT_ENCODING or INVALID_MODE
Example
L=1 H=1 Hd=1 → Q≈2.19731
Validation cases

4 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence

  • L=1 H=1 Hd=1 → Q≈2.19731 m³/s
  • L=1 H=1 → MISSING_REQUIRED_INPUT (Hd)
  • L=1 H=1 Hd=1 Cd=0.62 → MIXED_INPUT_ENCODING
  • kind=rectangular L=1 H=1 Hd=1 → MIXED_INPUT_ENCODING
Sources
  • USBR — Design of Small Dams — High overflow ogee, vertical upstream face
    Supports: C≈3.98 at design head; compact fit C=3.98 (H/Hd)^{0.12} on the high-overflow chart; P/Hd≥1.7
  • ISO 80000-4 — Mechanics — Volume flow rate
    Supports: Q is volume flow; L, H, and Hd are lengths
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute USBR high-overflow ogee spillway discharge from crest length, head, and design head.

Supported and not supported

Supported — USBR high-overflow Q from L, H, and Hd · invert H from Q · API physics.fluid.ogee_spillway

Not supported — thin-plate weir given C_d, broad-crested weir, sluice, Manning n, Q=Av, Francis 3.33, drowned spillway

Agent / API notes

Capability id: physics.fluid.ogee_spillway · tool id: ogee-spillway · pin 1.0.0.

{ "L": 1, "H": 1, "Hd": 1 }

Invert: { "mode": "head", "L": 1, "Hd": 1, "Q": 2.19731 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/ogee-spillway. There is no /calc/fluid.

Other calculators in this family: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator . Explore all Fluid Mechanics.

→ Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product. › → Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser. › → Broad-Crested Weir Calculator Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice. › → Cavitation Number Calculator Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²). › → Chezy Formula Calculator Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy. › → Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup. › → Concentric Reducer Calculator Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av. › → Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av. ›

Frequently asked questions

Key distinctions behind the calculation.

Is this a thin-plate weir?

No. Thin-plate Q=(2/3) C_d L √(2g) H^{3/2} is /calc/physics/weir-discharge. Sending Cd or kind=rectangular here is MIXED_INPUT_ENCODING. At L=1 m and H=1 m this page reports ≈2.19731 m³/s, not thin-plate C_d=0.62 ≈1.83053 m³/s.

Is this a broad-crested weir?

No. Rectangular broad-crested Q=C_d (2/3)^{3/2} b √g H^{3/2} is /calc/physics/broad-crested-weir. Sending b or Cd here is MIXED_INPUT_ENCODING.

Is this a sluice gate?

No. A free-flow undershot sluice with Swamee C_d from a/y1 is /calc/physics/sluice-gate. Sending a or y1 here is MIXED_INPUT_ENCODING.

Is this a side weir?

No. Borghei 1999 lateral overflow from B, y1, p, and Q1 is /calc/physics/side-weir. Sending kind=side here is MIXED_INPUT_ENCODING.

Is this the Manning formula?

No. Manning is uniform open-channel flow from n, A, R, and S at /calc/physics/manning-formula. Sending n, R, or S is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending v is MIXED_INPUT_ENCODING.

Can I send Francis 3.33?

No. Francis 3.33 L H^{3/2} and Kindsvater–Carter contractions are out of scope. C is reported from H/Hd, not an input.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine ogeeSpillway wrapper.