HomeCalculatorsPhysicsFluid MechanicsOrifice Discharge Calculator
Physics calculator

Orifice Discharge Calculator

Compute sharp-edged orifice discharge. Tank Q=C_d A √(2gH). Meter Q=C_d E A_t √(2Δp/ρ) with E=1/√(1−β⁴). Runs locally. Not a weir, not Q=Av, not Darcy, and not Manning.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Tank orifice Q = Cd A √(2 g H) and meter orifice Q = Cd E A √(2 Δp/ρ), + O3 mpmath tabulated Q.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Tank orifice Q = Cd A √(2 g H) and meter orifice Q = Cd E A √(2 Δp/ρ), + O3 mpmath tabulated Q.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (tank, meter, alias, awkward, invalid-domain) · Matrix
Deferred
Not weir L, not Manning n, not Darcy f, and not Q=Av.
Numerical scope
O2: orifice vs a separate-module identity (≤2 ULP). Not weir L, not Manning n, not Darcy f, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated orifice vectors. Not weir L, not Manning n, not Darcy f, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Sharp-edged orifice discharge. Tank free discharge or incompressible meter with velocity-of-approach E.
Scope
Sharp-edged orifice; SI; default C_d=0.61; C_d in (0, 1]
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Tank orifice Q = Cd A √(2 g H) and meter orifice Q = Cd E A √(2 Δp/ρ), + 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 11fb832151f4
Legacy regression
15/15 tests · Production surface contract 5/5
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 · 9/9 CVP boundary · 9/9 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources
Sources
Evidence
1 legacy golden · 9 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 9/9 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.

TankQ = C_d A √(2g H)
MeterQ = C_d E A_t √(2Δp/ρ)
ApproachE = 1 / √(1 − β⁴)
iSI g = 9.80665 m/s² unless given. Default C_d = 0.61. C_d must be in (0, 1]. This page is not a thin-plate weir, not Q=Av, not Darcy–Weisbach, and not compressible ISO 5167 ε(Re).

How to use

1

Choose tank or meter

Tank is free discharge through a hole under head H. Meter is an incompressible orifice plate with pipe D and Δp. This is not a weir.

2

Enter geometry

Tank needs orifice d (or A) and H or Q. Meter needs d, D, ρ, and Δp or Q. d must be smaller than D.

3

Optional C_d

Leave blank for 0.61. C_d must be in (0, 1].

4

Read Q (or inverted H / Δp)

Q is in m³/s. Invert uses the same engine.

Example calculations

Common configurations with formula and result.

ϟ

Tank 50 mm under 2 m

d=0.05 m, H=2 m, default C_d=0.61

Q = 0.61 (π d²/4) √(2gH)
Q≈0.007502 m³/s
ϟ

Meter β=0.5

d=0.05 m, D=0.1 m, Δp=10 kPa, ρ=1000 kg/m³

Q = 0.61 E (π d²/4) √(2Δp/ρ)
Q≈0.005532 m³/s

Orifice Discharge calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Tank: Q = C_d A √(2gH). Meter: Q = C_d E A_t √(2Δp/ρ), E = 1/√(1−β⁴), β = d/D.
What it calculates
Sharp-edged orifice discharge. Tank free discharge or incompressible meter with velocity-of-approach E.
Inputs
  • mode?
  • d|A
  • H|Q (tank)
  • D, rho, dP|Q (meter)
  • Cd?
  • g?
Outputs
  • Q
  • Cd
  • mode
  • H? | dP?
  • A
  • beta?
  • E?
Formula
Q = C_d A √(2gH) | Q = C_d E A_t √(2Δp/ρ)
Assumptions
  • Sharp-edged orifice; SI; default C_d=0.61; C_d in (0, 1]
  • Tank: Q=C_d A √(2gH); not a weir H^{3/2}
  • Meter: Q=C_d E A_t √(2Δp/ρ), E=1/√(1−β⁴); incompressible; user C_d
  • Not weir, not Q=Av, not Darcy, not Manning, not compressible ISO ε(Re)
Units
  • SI; d, D, H in m; Q in m³/s; Δp in Pa; ρ in kg/m³
Boundary conditions
  • missing H, Q, d/A, D, Δp, or ρ when required → MISSING_REQUIRED_INPUT
  • H, Q, d, D, A, Δp, ρ, or C_d ≤ 0 → VALUE_MUST_BE_POSITIVE
  • d ≥ D → VALUE_OUT_OF_RANGE
  • C_d > 1 → VALUE_OUT_OF_RANGE
  • H and Q, Δp and Q, A and d, tank with D/Δp, meter with H, or crest L → MIXED_INPUT_ENCODING
  • weir, rectangular, Manning, Darcy, or Q=Av as mode → INVALID_MODE
Example
d=0.05 H=2 → Q=0.61 (πd²/4) √(2gH)
Validation cases

3 published on this page · 15/15 tests · Production surface contract 5/5 · View evidence

  • d=0.05 H=2 → Q≈0.007502
  • mode=meter d=0.05 D=0.1 dP=10000 rho=1000 → Q≈0.005532
  • mode=weir d=0.05 H=2 → INVALID_MODE
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute sharp-edged orifice discharge.

Supported and not supported

Supported — tank free discharge · incompressible meter with E=1/√(1−β⁴) · invert H or Δp · API physics.fluid.orifice

Not supported — weir overflow, Q=Av identities, Darcy–Weisbach, Manning, compressible ISO ε(Re), Reader–Harris/Gallagher C(Re), pump curves

Agent / API notes

Capability id: physics.fluid.orifice · tool id: orifice-discharge · pin 1.0.0.

{ "mode": "tank", "d": 0.05, "H": 2 }

Meter: { "mode": "meter", "d": 0.05, "D": 0.1, "dP": 10000, "rho": 1000 }. Optional "Cd". Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/orifice-discharge. 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 weir?

No. A weir is a thin-plate overflow with H^{3/2} or H^{5/2} at /calc/physics/weir-discharge. An orifice is a hole. Sending crest length L 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 kind=sluice here is MIXED_INPUT_ENCODING. An orifice is a hole with given C_d.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. This page uses C_d and either head or differential pressure.

Does the meter mode solve ISO 5167 C(Re)?

No. You supply C_d. Compressible expansion factor ε and Reader–Harris/Gallagher C(Re) are out of scope.

Where does this run?

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