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 Engine tested · Source checked · 15/15 tests · Production surface contract 3/3 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 15/15 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 5167-2 — Measurement of fluid flow by means of pressure differential devices — Orifice plates — Incompressible discharge with velocity-of-approach factor
Munson, B.R., Young, D.F., and Okiishi, T.H. Fundamentals of Fluid Mechanics — Orifice discharge; Torricelli
Sources
Evidence: 1 golden · 9 boundary · 5 property · Production surface contract 3/3 · 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; 163 CURRENT) @ 2026-09-17T03:09:03.307Z
Semantic contract: PASS

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

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.

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.

Optional C_d

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

Read Q (or inverted H / Δp)

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

Example calculations

Common configurations with formula and result.

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

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

Engine tested 15/15 tests · Production surface contract 3/3
Named expert review Not performed
Calculation version 1.0.0

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 3/3 · 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: ISO 5167-2 — Measurement of fluid flow by means of pressure differential devices — Orifice plates — Incompressible discharge with velocity-of-approach factor
Supports: Q = C E (π/4) d² √(2Δp/ρ); E = 1/√(1−β⁴); this page takes C as an input
Munson, B.R., Young, D.F., and Okiishi, T.H. Fundamentals of Fluid Mechanics — Orifice discharge; Torricelli
Supports: Free discharge Q = C_d A √(2gH) for a sharp-edged tank orifice
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: Weir discharge, Flow rate, Darcy–Weisbach, Pump power .

}

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 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.