Bernoulli Pressure Calculator
Find downstream pressure from upstream pressure, velocity, elevation, pump head and head loss using an extended Bernoulli balance.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Write pressure head, velocity head and elevation head at each station. Add externally supplied pump head, subtract entered head loss, and rearrange the energy balance for downstream pressure.
p₁/(ρg)+v₁²/(2g)+z₁+hadded = p₂/(ρg)+v₂²/(2g)+z₂+hloss
Worked example
For water-like density 998 kg/m³, p₁=250 kPa, v₁=1.5 m/s, v₂=3 m/s, z₂−z₁=4 m, added head 10 m and loss 2 m gives p₂ about 285.8 kPa.
Assumptions and input details
Both pressures must use the same basis: both gauge or both absolute. This steady, incompressible, one-dimensional energy balance uses mean section velocities and standard gravity. Added head and loss are user inputs; the calculator does not derive pump performance, friction or fittings. Bernoulli’s ideal relation is applied between the stated stations, and a negative gauge result can be mathematically valid but does not by itself establish cavitation safety or absolute pressure.
References: NASA Glenn: Bernoulli equation
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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