Bernoulli Equation Calculator
Bernoulli’s equation trades pressure for speed and height: water at 200 kPa and 2 m/s reaching 6 m/s, 3 m higher, is at p₂ = 154.57 kPa.
154.57 kPa
Full answer, then cut to fewer decimals (not rounded):
- 154.57 kPa
- 154.5 kPa
- Total head at 1
- 20.5912 m
- Total head at 2
- 20.5912 m
- Pressure head at 2
- 15.7564 m
- Velocity head at 2
- 1.83486 m
Step-by-step solution
- p₁/ρg + V₁²/2g + z₁ = p₂/ρg + V₂²/2g + z₂ + hL
- p₂ = p₁ + ½ρ(V₁² − V₂²) + ρg(z₁ − z₂ − hL)
- = 200000 + -16000 + -29430 = 154570 Pa
Bernoulli Equation Formula
p₁/ρg + V₁²/2g + z₁ = p₂/ρg + V₂²/2g + z₂ + hL
p pressure, V velocity, z elevation, hL head loss
Worked Example
Water at 200 kPa and 2 m/s accelerating to 6 m/s while rising 3 m:
- p₁/ρg + V₁²/2g + z₁ = p₂/ρg + V₂²/2g + z₂ + hL
- p₂ = p₁ + ½ρ(V₁² − V₂²) + ρg(z₁ − z₂ − hL)
- = 200000 + -16000 + -29430 = 154570 Pa
Total head at 2: 20.5912 m · Pressure head at 2: 15.7564 m · Velocity head at 2: 1.83486 m
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Frequently asked questions
What are the assumptions of Bernoulli’s equation?
Steady, incompressible, inviscid flow along a streamline with no pump or turbine between the points; add hL for friction losses.
What is total head?
The sum of pressure head p/ρg, velocity head V²/2g and elevation z, in metres of the flowing fluid.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Bernoulli Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/bernoulli-equation-calculator/
IEEE
Scientific Converters, "Bernoulli Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/bernoulli-equation-calculator/