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Physics calculator

Sluice Gate Calculator

Compute free-flow undershot sluice discharge from gate opening a, width b, and upstream depth y1. Runs locally. C_d is Swamee 1992, not an input. Not a tank orifice, not a weir, not a flume, not Manning, and not Q=Av.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 6/6 tests · Production surface contract 1/1 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Swamee 1992 free-flow undershot sluice discharge, opening, or upstream depth. SI a, b, y1, Q.
Scope
Swamee 1992 free-flow undershot sluice: Q = C_d a b √(2g y1); C_d = 0.611 [(y1−a)/y1]^{0.072}; SI a, b, y1, Q; C_d is reported, not an input
Verification
Engine tested · 6/6 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
6 property · Production surface contract 1/1 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T02:44:05.986Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

DischargeQ = C_d a b √(2 g y1)
Discharge coefficientC_d = 0.611 [(y1 − a)/y1]^{0.072}
iSI. a, b, and y1 in metres; Q in m³/s. Envelope a/y1∈[0.05, 0.65]. Submerged flow is out of scope. Do not send query v — that is calculation_version.

How to use

1

Enter gate opening a

Vertical opening in metres. This is not orifice area A or diameter d.

2

Enter gate width b

Span across the channel. This is not flume throat W or weir crest L.

3

Enter upstream depth y1 or discharge Q

Give a and y1 to compute Q, or Q and y1 to invert a. y1 is not weir H.

Example calculations

Common configurations with formula and result.

ϟ

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

Free-flow undershot sluice

C_d = 0.611 (0.8)^{0.072}
Q≈0.53256 m³/s
ϟ

Invert a from that Q

b=1 m, y1=1 m, Q≈0.53256 m³/s

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

Sluice Gate calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Swamee 1992 free-flow undershot sluice. Q = C_d a b √(2g y1) with C_d = 0.611 [(y1−a)/y1]^{0.072}. a is the vertical gate opening, not orifice area A. b is gate width, not flume throat W or weir crest L. y1 is upstream depth, not weir H or flume Ha. C_d is reported, not an input. Envelope a/y1∈[0.05, 0.65], y1>a, free flow only. Default g=9.80665 m/s². Not tank orifice C_d A √(2gH), not thin-plate weir, not broad-crested weir, not Parshall, not cutthroat, not Manning n, not Q=Av, not submerged y2.
What it calculates
Swamee 1992 free-flow undershot sluice discharge, opening, or upstream depth. SI a, b, y1, Q.
Inputs
  • mode?
  • b
  • a | Q
  • y1 | Q
Outputs
  • Q
  • a
  • b
  • y1
  • Cd
  • g
  • mode
  • model
Formula
Q = C_d a b √(2g y1); C_d = 0.611 [(y1−a)/y1]^{0.072}
Assumptions
  • Swamee 1992 free-flow undershot sluice: Q = C_d a b √(2g y1); C_d = 0.611 [(y1−a)/y1]^{0.072}; SI a, b, y1, Q; C_d is reported, not an input
  • Gate opening a is not orifice area A; y1 is upstream depth, not weir H; a/y1∈[0.05, 0.65]; y1 > a; free flow only
  • Not thin-plate weir, not tank orifice C_d A √(2gH), not a flume, not Manning n, not Q=Av, not submerged y2
Units
  • SI; a, b, and y1 in m; Q in m³/s; C_d dimensionless
Boundary conditions
  • missing a, b, y1, or Q when required → MISSING_REQUIRED_INPUT
  • Cd, orifice A/d/D/H, weir L, flume W/Ha/L_f, Manning n/R/S, Q=Av v, y2 → MIXED_INPUT_ENCODING
  • a ≥ y1 or a/y1 outside [0.05, 0.65] → VALUE_OUT_OF_RANGE
  • mode=orifice|weir|parshall|cutthroat or unknown mode → MIXED_INPUT_ENCODING or INVALID_MODE
Example
a=0.2 b=1 y1=1 → Q≈0.53256
Validation cases

4 published on this page · 6/6 tests · Production surface contract 1/1 · View evidence

  • a=0.2 b=1 y1=1 → Q≈0.53256 m³/s
  • a=0.2 b=1 y1=1 Cd=0.61 → MIXED_INPUT_ENCODING
  • A=0.2 b=1 y1=1 → MIXED_INPUT_ENCODING
  • kind=orifice a=0.2 b=1 y1=1 → MIXED_INPUT_ENCODING
Sources
  • Swamee, P.K. — Sluice-Gate Discharge Equations — Free-flow undershot C_d
    Supports: C_d = 0.611 [(y1−a)/y1]^{0.072}; Q = C_d a b √(2g y1); not a given orifice C_d=0.61
  • ISO 80000-4 — Mechanics — Volume flow rate
    Supports: Q is volume flow; a, b, and y1 are lengths
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute free-flow undershot sluice discharge from gate opening, width, and upstream depth.

Supported and not supported

Supported — Swamee 1992 free-flow Q from a, b, and y1 · invert a from Q · invert y1 from Q · API physics.fluid.sluice_gate

Not supported — tank orifice given C_d, thin-plate weir, broad-crested weir, Parshall, cutthroat, Manning n, Q=Av, submerged y2

Agent / API notes

Capability id: physics.fluid.sluice_gate · tool id: sluice-gate · pin 1.0.0.

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

Invert opening: { "mode": "opening", "b": 1, "y1": 1, "Q": 0.53256 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/sluice-gate. There is no /calc/fluid.

Other calculators in this family: Orifice discharge, Thin-plate weir, Broad-crested weir, Cutthroat flume, Flow rate .

Q Orifice discharge › Q Thin-plate weir › Q Broad-crested weir › Q Cutthroat flume › Q Flow rate ›
}

Frequently asked questions

Key distinctions behind the calculation.

Is this a tank orifice?

No. Tank orifice Q=C_d A √(2gH) with a given C_d (default 0.61) is /calc/physics/orifice-discharge. Sending Cd, A, d, or H here is MIXED_INPUT_ENCODING. At a=0.2 m, b=1 m, y1=1 m this page reports ≈0.53256 m³/s, not 0.61·a·b·√(2gy1)≈0.54030 m³/s.

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 H or crest L here is MIXED_INPUT_ENCODING.

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 H or Cd here is MIXED_INPUT_ENCODING.

Is this a Parshall or cutthroat flume?

No. Parshall is /calc/physics/parshall-flume. Cutthroat is /calc/physics/cutthroat-flume. Sending W, Ha, or L_f here is MIXED_INPUT_ENCODING.

Is this an ogee spillway?

No. USBR high-overflow ogee Q from L, H, and design head Hd is /calc/physics/ogee-spillway. Sending kind=ogee 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 submerged y2?

No. This seed is free flow only. Downstream depth y2 is MIXED_INPUT_ENCODING.

Where does this run?

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