Bernoulli Equation Calculator

Enter the conditions at two points along a streamline and get the static pressure at the second point — with each energy term shown separately, so you can see where the pressure actually went.

Worked example checked Frictionless assumed Incompressible only SI units

Solve for P₂

Steady, incompressible, frictionless flow along one streamline.

kg/m³

Point 1 — upstream

kPa
m/s
m

Point 2 — downstream

m/s
m

Elevations are measured from any datum you like — only the difference h₁ − h₂ affects the result.

datum P₁ , v₁ , A₁ P₂ , v₂ , A₂ h₁ h₂
Fluid speeds up as the pipe narrows and gains height. Both changes are paid for out of the static pressure.

The equation

Bernoulli’s equation says that along a streamline, the sum of three energy terms stays constant:

P₁ + ½ρv₁² + ρgh₁  =  P₂ + ½ρv₂² + ρgh₂

Rearranged for the pressure at point 2, which is what this tool solves:

P₂ = P₁ + ½ρ(v₁² − v₂²) + ρg(h₁ − h₂)

Read it as a budget. You start with P₁. Speeding the fluid up costs pressure. Lifting it costs pressure. Whatever is left is P₂.

Four assumptions — break any one and this is wrong

The flow must be steady (not changing with time), incompressible (fine for liquids, and for gases below about Mach 0.3), frictionless (no viscous losses), and both points must lie on the same streamline.

Friction is the one that catches people out. In a long pipe, a partly closed valve, or anything with a sharp bend, the losses are not small and the real P₂ will be lower than this calculator says. The full article works through a real example and shows how far off you get.

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