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Elbow Flow Meter Calculator

Compute 90° elbow-tap discharge from inner/outer Δp. C=√((R/D)/2). Runs locally. Not pipe-bend K, not Pitot C=1, not venturi, not ISO 5167-6 wedge, not given C_d.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = C A √(2Δp/ρ) with C=√((R/D)/2), A=(π/4)D²; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Q = C A √(2Δp/ρ) with C=√((R/D)/2), A=(π/4)D²; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not pipe-bend K, not Pitot C=1, not venturi/orifice β, not Q=Av, and not Darcy.
Numerical scope
O2: elbow meter Q=C A √(2Δp/ρ), C=√((R/D)/2) vs a separate-module identity (≤2 ULP). Not pipe-bend K, not Pitot C=1, not venturi/orifice, not Q=Av, and not Darcy. ≤2 ULP vs O3 applies only to the published tabulated elbow-meter vectors. Not pipe-bend K, not Pitot C=1, not venturi/orifice, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
90° elbow-tap discharge from D, R or rd, and inner/outer Δp. Invert Δp. Report C=√((R/D)/2).
Scope
90° elbow tap meter: Q = C A √(2Δp/ρ); C=√((R/D)/2); A=(π/4)D²; inner/outer radius taps; incompressible; C is reported, not an input
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = C A √(2Δp/ρ) with C=√((R/D)/2), A=(π/4)D²; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-27.o2-o3
Verification revision
2026-09-27.o2-o3 · 1/1 property · digest 958679d30c6a
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 · 2/2 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 · 2/2 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 A √(2Δp / ρ)
Elbow CC = √((R/D) / 2)
AreaA = (π/4) D²
iSI. Incompressible. C is reported; do not send C, C_d, or Pitot C=1. Do not send query v — that is calculation_version. Mean speed is result v. 90° only; variable θ is pipe-bend loss.

How to use

1

Enter D and R

Pipe ID D and bend centerline radius R. REST may send D+rd instead of R. rd is R/D, not Chezy hydraulic radius.

2

Enter Δp and ρ

Inner-to-outer tap differential pressure. Invert on the Δp tab. Read C on the C tab without Δp.

Example calculations

Common configurations with formula and result.

ϟ

D=0.1 m, R=0.15 m, 10 kPa

Long-radius R/D=1.5, Δp=10 kPa, ρ=1000 kg/m³

C=√(1.5/2), Q=C A √(2Δp/ρ)
C≈0.86603 · Q≈0.030418 m³/s
ϟ

Same R/D via D+rd

D=0.1 m, rd=1.5

R = rd·D
R=0.15 m · same Q

Elbow Flow Meter calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
90° elbow tap flow meter. Incompressible Q = C A √(2Δp/ρ) with A=(π/4)D² and C=√((R/D)/2) from inner/outer radius taps. R/D∈[1.0,3.0], D∈[25 mm, 600 mm], 90° only. C is reported. Not pipe-bend K=0.21 (θ/90)/√(R/D), not Pitot v=C√(2Δp/ρ) with C=1, not venturi, not ISO 5167-6 wedge.
What it calculates
90° elbow-tap discharge from D, R or rd, and inner/outer Δp. Invert Δp. Report C=√((R/D)/2).
Inputs
  • mode?
  • D
  • R|rd
  • dP?
  • rho?
  • Q?
Outputs
  • Q?
  • D
  • R
  • rd
  • A
  • C
  • Cd
  • v?
  • rho?
  • dP?
  • mode
  • model
Formula
Q = C A √(2Δp/ρ); C = √((R/D)/2); A = (π/4) D²
Assumptions
  • 90° elbow tap meter: Q = C A √(2Δp/ρ); C=√((R/D)/2); A=(π/4)D²; inner/outer radius taps; incompressible; C is reported, not an input
  • R/D∈[1.0, 3.0]; D∈[25 mm, 600 mm]; 90° only; C from R/D, not a given Pitot C=1
  • Not pipe-bend K=0.21 (θ/90)/√(R/D), not Pitot v=C√(2Δp/ρ), not venturi, not ISO 5167-6 wedge, not Q=Av, not Darcy f
Units
  • SI; D, R in m; Q in m³/s; Δp in Pa; ρ in kg/m³
Boundary conditions
  • missing D, R/rd, Δp, Q, or ρ when required → MISSING_REQUIRED_INPUT
  • D outside [25 mm, 600 mm] or R/D outside [1.0, 3.0] → VALUE_OUT_OF_RANGE
  • K, θ, C/C_d, A or v, Darcy f, tank H, wedge h, n_miters, β, kind=pitot or kind=bend → MIXED_INPUT_ENCODING
  • mode=Cd or unknown mode → INVALID_MODE
Example
D=0.1 R=0.15 dP=10000 rho=1000 → C≈0.86603 Q≈0.030418
Validation cases

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

  • D=0.1 R=0.15 dP=10000 rho=1000 → C≈0.86603 Q≈0.030418
  • D=0.1 R=0.15 dP=10000 rho=1000 K=0.3 → MIXED_INPUT_ENCODING
  • D=0.1 R=0.15 dP=10000 rho=1000 C=1 → MIXED_INPUT_ENCODING
  • mode=Cd D=0.1 R=0.15 → INVALID_MODE
Sources
  • ISO 80000-4 — Mechanics — Length, speed, pressure
    Supports: D and R are lengths; Q is a volume flow; Δp is a pressure
  • Elbow tap meter — centrifugal Δp — C=√((R/D)/2) from inner/outer taps
    Supports: Q=C A √(2Δp/ρ) with C=√((R/D)/2); 90° only. Not pipe-bend K, not Pitot C=1, not venturi, not ISO 5167-6 wedge
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute 90° elbow-tap discharge from D, R, and inner/outer Δp. C is √((R/D)/2), not supplied.

Supported and not supported

Supported — Q from D, R or rd, and Δp · invert Δp · C=√((R/D)/2) · API physics.fluid.elbow_meter

Not supported — pipe-bend K, Pitot C=1, venturi, ISO 5167-6 wedge, given C_d, Q=Av, Darcy f, variable θ

Agent / API notes

Capability id: physics.fluid.elbow_meter · tool id: elbow-meter · pin 1.0.0.

{ "D": 0.1, "R": 0.15, "dP": 10000, "rho": 1000 }

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 same as circular-arc pipe-bend loss?

No. Pipe-bend reports K=0.21 (θ/90)/√(R/D) and h=K v²/(2g) from a given speed. This page is a 90° inner/outer tap Δp flow meter. Sending K or θ is MIXED_INPUT_ENCODING and points at /calc/physics/pipe-bend.

Is this a Pitot tube with C=1?

No. Pitot is v=C √(2Δp/ρ) with default C=1 and no R/D. Elbow C=√((R/D)/2)≈0.866 at R/D=1.5. Sending Pitot C or omitting R is not this page. Sending rd on /calc/physics/pitot-tube is MIXED_INPUT_ENCODING.

Can I send a given C_d or K?

No. C is reported from R/D. A given C_d is venturi or orifice. K is /calc/physics/pipe-bend or /calc/physics/minor-loss. Sending C, C_d, or K is MIXED_INPUT_ENCODING.

Does θ vary?

No. The seed is 90° only. Variable deflection is /calc/physics/pipe-bend. Sending theta_deg is MIXED_INPUT_ENCODING.

Is centerline R the same as Chezy R?

No. R is the bend centerline radius. Chezy hydraulic radius is /calc/physics/chezy-formula. Sending Manning n or Chezy S is MIXED_INPUT_ENCODING.

Is this an ISO 5167-6 wedge?

No. Wedge C=0.77−0.09β from gap h/D is /calc/physics/iso-wedge. Sending h or kind=wedge is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending A or input v is MIXED_INPUT_ENCODING.

Where does this run?

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