Bernoulli Equation Calculator
Find downstream pressure in a flowing fluid.
Results update as you type.
How it works
Bernoulli's equation is one of the most important results in fluid dynamics, describing how pressure, velocity, and height trade off along a streamline in a flowing fluid. This calculator applies it to find the pressure at a downstream point when you know the conditions upstream. You enter the pressure, velocity, and height at the first point, the velocity and height at the second point, and the fluid density, and it returns the pressure at the second point. The principle behind it is conservation of energy: as a fluid speeds up, its pressure drops, and as it rises in height, pressure drops too, because the total of pressure energy, kinetic energy, and potential energy stays constant. This counter-intuitive link between fast flow and low pressure explains a huge range of phenomena, from the lift generated by an aircraft wing and the curve of a spinning ball, to how a carburettor draws fuel, how a Venturi meter measures flow rate, and why a shower curtain billows inward. The equation assumes steady, incompressible, frictionless flow along a single streamline, which is a good approximation for many practical situations. Engineers designing pipes, pumps, and aerofoils rely on it. Enter the six values to compute the downstream pressure.
P₂ = P₁ + ½ρ(v₁² − v₂²) + ρg(h₁ − h₂)
Bernoulli's equation expresses conservation of energy along a streamline in a steady, incompressible flow: the sum of static pressure, dynamic pressure (half density times velocity squared), and hydrostatic pressure (density times gravity times height) is constant. Solving for the pressure at the second point takes the first point's pressure and adds the change in dynamic pressure and the change in hydrostatic pressure between the two points, so faster or higher flow trades off against pressure.
Source:Fluid dynamics (Bernoulli's equation)
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Worked example
How to use this calculator
- 1
Enter your values
Enter pressure at point 1 (p₁), velocity at point 1 (v₁), height at point 1 (h₁), velocity at point 2 (v₂), height at point 2 (h₂) and fluid density (ρ).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Pressure at point 2 (P₂) updates instantly as you type — no button to press.
Frequently asked questions
What is Bernoulli's equation?
Bernoulli's equation states that along a streamline in a steady, incompressible fluid, the sum of the static pressure, the dynamic pressure from the fluid's motion, and the hydrostatic pressure from its height is constant. It expresses the conservation of energy for flowing fluids, showing how pressure, speed, and elevation trade off against one another as the fluid moves.
Why does faster flow mean lower pressure?
Because the total energy along a streamline is conserved, when a fluid speeds up its kinetic energy increases, and that energy has to come from somewhere. It comes from the pressure energy, so the static pressure falls. This inverse relationship between velocity and pressure is the heart of Bernoulli's principle and underlies lift, Venturi effects, and many other fluid phenomena.
What are real applications of Bernoulli's principle?
Aircraft wings generate lift partly because air moves faster over the curved top surface, lowering the pressure there. Venturi meters and carburettors use constrictions that speed up flow to create suction. Atomisers, spray guns, and even the curve of a spinning ball all exploit the pressure drop that accompanies faster flow. Pipe and pump design relies on Bernoulli's equation too.
What assumptions does the equation make?
Bernoulli's equation assumes the flow is steady, meaning conditions do not change over time; incompressible, meaning the density is constant; and frictionless, meaning viscosity is negligible. It also applies along a single streamline. Real flows have some friction and turbulence, so the equation is an approximation, but a very useful one for many engineering and physics problems.
What units should I use?
Use consistent SI units for a correct result in pascals: pressure in pascals, velocity in metres per second, height in metres, and density in kilograms per cubic metre. Gravity is taken as 9.81 metres per second squared. Mixing units, such as entering velocity in kilometres per hour, would give a wrong answer, so convert everything to base SI units first.