Bernoulli Equation Calculator
Pressure, velocity and height trade off along a streamline. Enter the flow at two points of a pipe and find the pressure at the second — or work backward from a pressure drop to the flow rate, the way a venturi meter does.
What Bernoulli’s Equation Tells You
Along a streamline in steady, frictionless flow, three things trade off and always add up to the same total: pressure, the energy of motion (velocity), and the energy of height. Speed the fluid up and pressure must fall; raise it and pressure falls again. That single balance explains carburettors, venturi meters, aerofoil lift and why a shower curtain pulls inward.
Pair it with continuity — the same flow rate passes every section, so a narrower pipe means faster flow — and you can solve a pipe that changes size or height for the pressure or the flow at the far end.
Why Pressure Drops Where Flow Speeds Up
Squeeze the flow into a smaller diameter and continuity forces it to accelerate. That extra kinetic energy has to come from somewhere, so the pressure drops. A venturi meter turns this around: measure the pressure drop across a known contraction and Bernoulli hands you the flow rate. This calculator runs it both ways — forward to a pressure, or backward to a flow.
Real Flow Has Losses
Pure Bernoulli assumes no friction. Real pipes lose head to wall friction, fittings and turbulence, so the downstream pressure is a little lower than the ideal. Enter a head loss to account for it, or estimate that loss with the Pressure Drop and Friction Factor tools. Bernoulli also assumes incompressible flow, so it is not valid for gases moving near the speed of sound.
Frequently Asked Questions
What does Bernoulli’s equation actually say?
That pressure energy, kinetic energy and elevation energy sum to a constant along a streamline in ideal flow. If one rises, another must fall.
Why does a narrowing pipe lower the pressure?
Continuity speeds the flow up through the narrow section; the added kinetic energy is paid for by a drop in pressure.
How does a venturi meter measure flow?
It reads the pressure drop across a contraction and uses Bernoulli plus continuity to back out the flow rate, times a discharge coefficient near 0.98.
When does Bernoulli stop working?
When friction is significant, when the fluid is compressible (high-speed gas), or when the flow is unsteady. Add head loss for friction; use other methods for the rest.
Related calculators
- Pipe Flow Calculator — velocity and flow in a full pipe.
- Pressure Drop Calculator — friction loss to use as head loss.
- Reynolds Number Calculator — is the flow laminar or turbulent?
- Orifice Flow Calculator — flow through a hole or plate.