Boneyard Tools

The Bernoulli principle and where the pressure goes

How energy conservation links speed, height and pressure in a moving fluid, plus the assumptions that make the simple equation work.

Open the Bernoulli Equation Calculator →

Three forms of energy in one balance

Bernoulli's equation is a statement about energy per unit volume. Static pressure is the flow work the fluid can do, the half rho v squared term is its kinetic energy of motion, and the rho g h term is its gravitational potential energy. Add the three together at any point on a streamline and, for an ideal flow, the sum is the same everywhere. When one term grows another must shrink to keep the total fixed, which is the whole content of the principle.

Why fast flow means low pressure

The most famous consequence is that speeding a fluid up at a constant height lowers its static pressure. In the first example above, doubling and then more than doubling the water speed from 2 to 5 m/s pulls the pressure down from 200000 to 189500 Pa. The same trade sits behind the lift on a wing, the pull of a carburettor throat and the way a shower curtain drifts inward when the water runs. The fluid has not lost energy, it has simply moved some of it out of the pressure term and into motion.

The assumptions you agree to

The clean equation only holds for steady flow that does not change with time, for an incompressible fluid whose density stays constant, and for a frictionless path along a single streamline. It also assumes no machine adds or removes energy between the two points. Real flows break these rules to some degree, so friction in a long pipe or a pump in the line will shift the true downstream pressure away from the ideal number this tool reports.

Reading the result sensibly

Because the calculator ignores losses, its answer is the best case pressure recovery for your geometry. Engineers often pair it with a separate head loss estimate, such as the Darcy Weisbach method, to subtract friction and get a realistic figure. Used that way, Bernoulli gives you the ideal baseline and the loss model tells you how far reality falls short of it.

Frequently asked questions

Is the Bernoulli principle the reason planes fly?

It is part of the story. The faster air over a wing does have lower pressure, which contributes to lift, but a full explanation also needs Newton's third law and the downward turning of the air. Bernoulli alone is a useful simplification rather than the complete cause.

What is a streamline?

A streamline is the path a tiny fluid particle follows through a steady flow. Bernoulli's equation only compares two points that lie on the same streamline, which is why the tool asks for conditions at two points rather than two random locations.