Bernoulli Equation Solver
Solve downstream pressure between two points from velocities, elevations and fluid density (ideal, lossless).
Ideal Bernoulli assumes steady, incompressible, frictionless flow along a streamline. Add Darcy friction losses separately for real pipework.
Formula
Note: Lossless idealization — actual pressure will be lower by the friction head between the two points.
Bernoulli Equation Solver is a free bernoulli equation for process, mechanical and water engineers — instant, accurate and 100% client-side, with the governing formula and reference shown next to the result so the number can be defended, not just quoted.
About Bernoulli Equation Solver
Solve downstream pressure between two points from velocities, elevations and fluid density (ideal, lossless). The calculation implements P₁ + ½ρV₁² + ρgz₁ = P₂ + ½ρV₂² + ρgz₂ (Çengel & Cimbala, Fluid Mechanics, §5-4). Ideal Bernoulli assumes steady, incompressible, frictionless flow along a streamline. Add Darcy friction losses separately for real pipework.
How to use Bernoulli Equation Solver
- 1Enter Upstream pressure P₁ in kPa.
- 2Enter Upstream velocity V₁ in m/s.
- 3Enter Downstream velocity V₂ in m/s.
- 4Enter Upstream elevation z₁ in m.
- 5Read Downstream pressure P₂, Total head instantly — no submit button needed.
- 6Need US units? Flip the SI/Imperial toggle and every field converts.
Why use Bernoulli Equation Solver?
- ✓Implements the standard formula — P₁ + ½ρV₁² + ρgz₁ = P₂ + ½ρV₂² + ρgz₂
- ✓Reference cited on-page: Çengel & Cimbala, Fluid Mechanics, §5-4
- ✓One-click SI ⇄ Imperial toggle — values convert in place, physics stays in SI
- ✓Live worked example: the substitution recomputes from your numbers
- ✓Runs entirely in your browser — nothing uploaded, free forever
Frequently asked questions
What formula does the Bernoulli Equation Solver use?+
It computes P₁ + ½ρV₁² + ρgz₁ = P₂ + ½ρV₂² + ρgz₂, per Çengel & Cimbala, Fluid Mechanics, §5-4. The formula is displayed under the result along with a worked example substituted with your own inputs.
What should I keep in mind when using this calculator?+
Ideal Bernoulli assumes steady, incompressible, frictionless flow along a streamline. Add Darcy friction losses separately for real pipework. Note: Lossless idealization — actual pressure will be lower by the friction head between the two points.
Does this work for any fluid?+
Yes — density and viscosity are inputs (with common fluids suggested in the field hints), so the same physics applies to water, oils, gases and process fluids. Compute always runs in SI internally, so unit mix-ups can't corrupt the result.
Is the Bernoulli Equation Solver free to use?+
Yes — completely free, no sign-up, no limits. It runs client-side in your browser, so inputs stay private and results are instant even on slow connections.
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