Bernoulli Equation Calculator
Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser.
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Engineering
- Declared partition coverage
- PASS · 2/2 declared partitions (bernoulli, invalid-domain) · Matrix
- Known limitations
- Incompressible inviscid steady streamline
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Bernoulli solve for P2, v2, or h2.
- Scope
- Incompressible; inviscid; steady streamline
- Verification
- Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.0.0 · CVP protocol 1.0.0-proposed
- CVP identity
- 1/1 property · digest e5115f75bbb9
- Legacy regression
- 3/3 tests · Production surface contract 3/3
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Internal · Pass
- Named expert review
- Not performed
- CVP suite
- 1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
- Sources
- Fluid mechanics textbooks
- ISO 80000-4 / fluid mechanics practice
- Evidence
- 1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX physics review
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Choose what to solve for
Solve for P2, v2, or h2 along a streamline.
Enter density and known side states
Provide ρ plus P, v, and h on the known side, and the remaining unknowns as needed.
Read the solved value
Uses P/ρ + v²/2 + g h = constant (incompressible, steady, inviscid form).
Example calculations
Common configurations with formula and result.
Hydrostatic 10 m
v1=v2=0
Bernoulli Equation calculator specification
Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-09
- Engine tested 3/3 tests · Production surface contract 3/3
- Supplemental domain review Internal · Pass · 2026-08-09
- Named expert review Not performed
- Calculation version 1.0.0
Review policy · Evidence · Reviewed by CalculatorX physics review
- Definition
- P/ρ + v²/2 + g h = constant along a streamline (incompressible, inviscid, steady).
- What it calculates
- Bernoulli solve for P2, v2, or h2.
- Inputs
- mode P2|v2|h2
- rho
- P1,v1,h1
- remaining side
- Outputs
- P2_Pa|v2_m_s|h2_m
- Formula
P/ρ+v²/2+gh=const- Assumptions
- Incompressible; inviscid; steady streamline
- Units
- Pa, m/s, m
- Boundary conditions
- v2 radicand < 0 → VALUE_OUT_OF_RANGE
- Example
- h1=10 h2=0 v=0 → P2=P1+ρg·10
- Validation cases
1 published on this page · 3/3 tests · Production surface contract 3/3 · View evidence
- P2 rho=1000 P1=101325 v1=0 h1=10 v2=0 h2=0 → P2=199391.5
- Sources
- Fluid mechanics textbooks — Bernoulli equationSupports: P/ρ+v²/2+gh
- ISO 80000-4 / fluid mechanics practice — Bernoulli equationSupports: P/ρ + v²/2 + g h = const
- Fluid mechanics textbooks — Bernoulli equation
- Last reviewed
- 2026-08-09
- Reviewed by
- CalculatorX physics review
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Solve Bernoulli’s equation (ideal incompressible).
Supported and not supported
Supported — Solve P2|v2|h2 · API physics.fluid.bernoulli
Not supported — Viscous losses, compressible flow, unsteady terms
Agent / API notes
Capability id: physics.fluid.bernoulli · tool id: bernoulli · pin 1.0.0.
Related tools
Other calculators in this family: Reynolds, Specific Heat .
Frequently asked questions
Key distinctions behind the calculation.
Why can v2 fail?
If the radicand under the square root is negative, the state is physically inconsistent; API returns VALUE_OUT_OF_RANGE.