Bernoulli Equation Calculator

What is the Bernoulli equation?

The Bernoulli equation states that the sum of pressure energy, kinetic energy and potential energy of a flowing fluid is conserved along the flow. Written in head (metres): p1 / (ρ × g) + v1² / (2 × g) + z1 = p2 / (ρ × g) + v2² / (2 × g) + z2 + hL. The three terms on the left are the pressure head, velocity head and elevation at point 1. hL is the sum of friction and minor losses between the two points and is zero for ideal flow.

How to use it

Enter pressure, velocity and elevation at the first point. Give the two known quantities at the second point and the calculator finds the third. Velocity rises where the pipe narrows and pressure falls. Pressure also falls as the pipe climbs. The velocities at the two points can be found from continuity (Q = v × A).

Example

Water flows in a pipe at 200 kPa and 2 m/s. The pipe narrows so the velocity becomes 6 m/s while it rises 3 metres. With no loss the pressure at the second point is 200 000 + 1000 × (4 − 36) / 2 − 1000 × 9.80665 × 3 = 154 580 Pa, or 154.6 kPa. About 16 kPa of the drop comes from acceleration and 29.4 kPa from the climb.

Limits

The equation applies to steady incompressible flow. In real lines friction is rarely negligible, so work out the loss separately and type it into the head loss box. Lines with pumps or turbines, high speed gas flow and unsteady flow are outside this calculator.