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Physics calculator

Drowned Sluice Calculator

Compute Swamee 1992 drowned undershot sluice discharge from opening a, width b, upstream depth y1, and downstream depth y2. Runs locally. C_d is reported, not an input. Not free-flow sluice, not a Villemonte weir, not a tank orifice, 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 · Swamee 1992 drowned undershot sluice Q=C_d a b √(2g y1) with θ from y1,y2,a, + O3 mpmath tabulated Q.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Swamee 1992 drowned undershot sluice Q=C_d a b √(2g y1) with θ from y1,y2,a, + O3 mpmath tabulated Q.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, alias, awkward, deep, invalid-domain) · Matrix
Deferred
Not free-flow sluice without y2, not Villemonte H1/H2, not orifice Cd/A, not Manning, not Q=Av.
Numerical scope
O2: Swamee drowned undershot sluice vs a separate-module identity (≤2 ULP). Not free-flow sluice without y2, not Villemonte H1/H2, not orifice Cd/A, not Manning, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated drowned-sluice vectors. Not free-flow without y2, not Villemonte H1/H2, not orifice, not Manning, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Drowned undershot sluice discharge Q or opening a (Swamee 1992).
Scope
Drowned undershot sluice; y2 required
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Swamee 1992 drowned undershot sluice Q=C_d a b √(2g y1) with θ from y1,y2,a, + 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 23e051cc2209
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 = C_d a b √(2 g y1)
Discharge coefficientC_d = θ · 0.611 [(y1 − a)/(y1 + 15 a)]^{0.072}
Drowned factorθ = (y1 − y2)^{0.7} / {0.32 [0.81 y2 (y2/a)^{0.72} − y1]^{0.7} + (y1 − a)^{0.7}}
iSI g = 9.80665 m/s² unless given. C_d is reported. Free-flow (no y2) is /calc/physics/sluice-gate. Villemonte weir H1+H2 is /calc/physics/submerged-weir.

How to use

1

Enter gate opening a

Vertical opening in metres. This is not orifice area A.

2

Enter gate width b

Span across the channel. This is not weir crest L.

3

Enter y1 and y2

Upstream and downstream depths. y2 is required. Omitting y2 is not a free-flow sluice on this page.

Example calculations

Common configurations with formula and result.

ϟ

Drowned a=0.2 m

a=0.2 m, b=1 m, y1=1 m, y2=0.8 m

C_d = θ · 0.611 [(1−0.2)/(1+15·0.2)]^{0.072}
Q≈0.13961 m³/s
ϟ

Invert a from that Q

b=1 m, y1=1 m, y2=0.8 m, Q≈0.13961 m³/s

solve C_d(a) a b √(2g y1) = Q
a≈0.20000 m

Drowned Sluice calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Swamee 1992 drowned undershot sluice. Q=C_d a b √(2g y1) with C_d=θ·0.611[(y1−a)/(y1+15a)]^{0.072} and θ from y1, y2, and a. Requires downstream y2. Drowned when y1 < 0.81 y2 (y2/a)^{0.72}. C_d is reported, not an input. Envelope a/y1∈[0.05, 0.65], y1>y2>a. Not free-flow sluice without y2, not Villemonte H1+H2, not tank orifice C_d A √(2gH), not Manning n, not Q=Av.
What it calculates
Drowned undershot sluice discharge Q or opening a (Swamee 1992).
Inputs
  • mode?
  • a | Q
  • b
  • y1
  • y2
  • g?
Outputs
  • Q
  • a
  • b
  • y1
  • y2
  • Cd
  • theta
  • g
Formula
Q = C_d a b √(2g y1); C_d = θ·0.611[(y1−a)/(y1+15a)]^{0.072}
Assumptions
  • Drowned undershot sluice; y2 required
  • SI g=9.80665 unless given
  • Swamee 1992 θ and (y1+15a) form; C_d is reported
  • Drowned when y1 < 0.81 y2 (y2/a)^{0.72}
  • Not free-flow sluice, not Villemonte weir, not orifice, not Manning, not Q=Av
Units
  • SI; a, b, y1, y2 in m; Q in m³/s; g in m/s²
Boundary conditions
  • missing a, b, y1, y2, or Q when required → MISSING_REQUIRED_INPUT
  • a, b, y1, y2, Q, or g ≤ 0 → VALUE_MUST_BE_POSITIVE
  • a ≥ y1 or a/y1 outside [0.05, 0.65] → VALUE_OUT_OF_RANGE
  • y2 free-flow, H1/H2, L/H, A/v, n, given Cd → MIXED_INPUT_ENCODING
  • unknown mode → INVALID_MODE
Example
a=0.2 b=1 y1=1 y2=0.8 → Q≈0.13961
Validation cases

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

  • a=0.2 b=1 y1=1 y2=0.8 → Q ≈ 0.13961
  • mode=opening Q=0.13961 b=1 y1=1 y2=0.8 → a ≈ 0.20000
  • a=0.2 b=1 y1=1 → MISSING_REQUIRED_INPUT
  • a=0.2 b=1 y1=1 y2=0.5 → MIXED_INPUT_ENCODING
Sources
  • Swamee, P.K. Sluice-gate discharge equations — J. Irrig. Drain. Eng. 118(1), 1992
    Supports: Drowned Cd=θ·0.611[(y1−a)/(y1+15a)]^{0.072} with θ from y1, y2, a; free/drowned split y1 ≶ 0.81 y2 (y2/a)^{0.72}
  • ISO 80000-4 — Mechanics — Volume flow rate
    Supports: Q is volume flow; a, y1, and y2 are lengths
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute drowned undershot sluice discharge from opening a, width b, upstream y1, and downstream y2 (Swamee).

Supported and not supported

Supported — Q from a, b, y1, y2 · invert a · API physics.fluid.drowned_sluice

Not supported — free-flow sluice without y2; Villemonte H1+H2; tank orifice; Manning n; Q=Av

Agent / API notes

Capability id: physics.fluid.drowned_sluice · tool id: drowned-sluice · pin 1.0.0.

{ "a": 0.2, "b": 1, "y1": 1, "y2": 0.8 }

Invert a: { "mode": "opening", "Q": 0.13961, "b": 1, "y1": 1, "y2": 0.8 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/drowned-sluice. 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 the free-flow sluice?

No. Free-flow a, b, y1 with no y2 is /calc/physics/sluice-gate. Sending y2 there is MIXED_INPUT_ENCODING. Omitting y2 here is MISSING_REQUIRED_INPUT.

Is this a submerged weir?

No. Villemonte drowned nappe from H1 and H2 is /calc/physics/submerged-weir. Sending H1/H2 here is MIXED_INPUT_ENCODING.

Is this a tank orifice?

No. Q=C_d A √(2gH) with given C_d is /calc/physics/orifice-discharge. Sending A or given C_d here is MIXED_INPUT_ENCODING.

Is this Manning?

No. Uniform-flow Q from n, A, R, and S is /calc/physics/manning-formula. Sending n here is MIXED_INPUT_ENCODING.

Is this Q = A·v?

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

Where does this run?

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