Bernoulli Equation Calculator
Find the pressure terms in Bernoulli's equation.
Results update as you type.
How it works
Bernoulli's equation is a cornerstone of fluid dynamics, expressing conservation of energy in a flowing fluid, and this calculator breaks it into its component pressures. You enter the static pressure, fluid density, flow velocity, and elevation, and it returns the dynamic pressure, the hydrostatic pressure, and the total pressure. The equation states that along a streamline, the sum of three terms stays constant: the static pressure, the dynamic pressure equal to half the density times velocity squared, and the hydrostatic pressure equal to density times gravitational acceleration times height. This constant total is why a fluid speeding up must lose static pressure, the principle behind how airplane wings generate lift, how a carburetor or atomizer draws fluid, and why pressure drops where a pipe narrows and the flow accelerates. The dynamic pressure represents the kinetic energy of the moving fluid per unit volume, and the hydrostatic term represents its gravitational potential energy per unit volume. By computing each term, you can see how energy shifts between pressure, motion, and elevation as a fluid flows. Bernoulli's principle applies to idealized, incompressible, non-viscous, steady flow, so real flows with friction or turbulence deviate somewhat, but it remains a powerful and widely used approximation. Density must be non-negative. Enter the pressure, density, velocity, and height to compute the Bernoulli pressure terms.
P + ½ρv² + ρgh = constant
Bernoulli's equation states that along a streamline the sum of static pressure, dynamic pressure (half the density times velocity squared), and hydrostatic pressure (density times gravity times height) is constant. The calculator computes each term and their total, which stays the same as a fluid speeds up, slows down, or changes elevation.
Source:Fluid dynamics
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Worked example
How to use this calculator
- 1
Enter your values
Enter static pressure (p), fluid density (ρ), flow velocity (v) and elevation (h).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Total pressure 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, frictionless flow, the sum of static pressure, dynamic pressure, and hydrostatic pressure is constant. It expresses conservation of energy for a fluid, showing that as one term changes, the others must adjust to keep the total the same.
What is dynamic pressure?
Dynamic pressure is the pressure associated with a fluid's motion, equal to half the fluid density times the velocity squared. It represents the kinetic energy of the flow per unit volume. When a fluid speeds up, its dynamic pressure rises, which by Bernoulli's principle means its static pressure must fall to keep the total constant.
How does Bernoulli's principle explain lift?
Air moving faster over the curved top of a wing has higher dynamic pressure and therefore lower static pressure than the slower air beneath. This pressure difference produces a net upward force, lift. While a complete explanation of lift involves more than Bernoulli alone, the equation captures the key relationship between speed and pressure.
What are the assumptions of Bernoulli's equation?
The equation assumes steady flow, incompressible fluid, negligible viscosity or friction, and that measurements are taken along the same streamline. Real flows have some friction, turbulence, and compressibility, so Bernoulli is an idealization. Despite this, it is remarkably accurate for many practical situations and is a standard tool in fluid mechanics and engineering.
What is hydrostatic pressure?
Hydrostatic pressure is the pressure due to a fluid's elevation in a gravitational field, equal to density times gravitational acceleration times height. It represents gravitational potential energy per unit volume. In Bernoulli's equation, raising a fluid increases its hydrostatic pressure, which must be offset by a decrease in static or dynamic pressure.