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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 Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Drowned undershot sluice discharge Q or opening a (Swamee 1992).
Scope
Drowned undershot sluice; y2 required
Verification
Engine tested · 5/5 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
5 property · Production surface contract 1/1 · Artifact integrity PASS
Production
Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T13:56:15.885Z
Semantic contract
PASS

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 · 5/5 tests · Production surface contract 1/1 · 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: Sluice gate, Submerged weir, Orifice discharge, Hydraulic jump, Manning formula .

Q Sluice gate › Q Submerged weir › Q Orifice discharge › y2 Hydraulic jump › Q Manning formula ›
}

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.