How this calculator works
Bernoulli equation conserves mechanical energy along a streamline for ideal steady incompressible flow. Enter absolute pressures consistently and elevations above one datum. In pipe mode, continuity determines the two mean velocities from the same discharge. The model uses a uniform velocity-energy factor of one. Real pipes dissipate energy; pumps and turbines add or remove it, so those systems require an extended energy balance.
Formula
p1 + rho g z1 + rho v1^2/2 = p2 + rho g z2 + rho v2^2/2. Circular-pipe continuity: v = 4Q/(pi D^2). Mass flow = rho Q.
Worked example
With rho = 1000 kg/m3, equal elevations, p1 = 200000 Pa, v1 = 2 m/s and v2 = 4 m/s, p2 = 194000 Pa. If speeds are equal instead and point 2 is 1 m higher, p2 = 190193.35 Pa at standard gravity.
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Frequently asked questions
Can pressure become negative?
A calculated negative absolute pressure is rejected. Vaporization can invalidate liquid-flow assumptions even before pressure reaches zero.
Does faster flow always mean lower pressure?
That comparison also depends on elevation and energy additions or losses. The ideal same-elevation case isolates the speed-pressure exchange.
Can I apply it across a shock wave?
No. Shocks change density and dissipate mechanical energy; use the compressible shock relations.