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Bernoulli Equation Calculator

Bernoulli equation calculator helps you determine the speed and pressure, as well as the flow rate, of an incompressible fluid.

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Pressure at point 2240.687 kPa240.687 kPa, 34.909 psi
Velocity at point 28 m/sfrom continuity: 4× the inlet velocity
Pressure change-59.313 kPaa drop — the fluid traded pressure for speed and height
Static pressure at 1300 kPa
Dynamic pressure at 11.9964 kPa
Dynamic pressure at 231.9424 kPa
Elevation term29.367 kPa3 m of height costs this much pressure
Total head at 130.8506 mpressure, velocity and elevation head added — constant along the streamline in ideal flow
Total head at 230.8506 midentical to point 1, which is what Bernoulli asserts
Margin above vapour pressure238.348 kPawater boils at 2.339 kPa at 20 °C; below that the flow cavitates
Stagnation pressure at 1301.9964 kPawhat a pitot tube facing the flow would read
What this ignoresfriction, and any energy added or removedBernoulli is a statement of energy conservation for an ideal fluid — real pipes lose head to friction, so the total head at point 2 is always lower in practice

The formula

P + ½ρv² + ρgh is constant along a streamline

Energy conservation, wearing a disguise

Bernoulli's equation says pressure, kinetic and elevation energy per unit volume sum to a constant along a streamline. It is conservation of energy, and nothing more: where a fluid speeds up its pressure must fall, because the energy has to come from somewhere.

That is the source of most of the counter-intuitive results in fluids. Flow through a constriction is faster and at lower pressure, which is how a venturi, a carburettor and an atomiser all work. It is also why the pressure drops in the narrow part of a pipe rather than rising, which surprises people.

The practical limit is cavitation. If the pressure falls to the liquid's vapour pressure — about 2.34 kPa for water at 20 °C — it boils, forming bubbles that collapse violently downstream and erode metal. Any Bernoulli speed-up has to be checked against that floor.

What the equation omits is friction. Real flow loses head continuously, so measured pressure at the downstream point is always below the ideal figure. Bernoulli gives the best case; the Darcy–Weisbach calculation gives the loss to subtract from it.