Equação de Bernoulli (P + ½ρv² + ρgh)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P + ½ρv² + ρgh = const
About this calculator
The Bernoulli Equation Calculator solves the equation P + ½ρv² + ρgh = constant along a streamline in an ideal fluid. It allows calculating pressure, velocity, or height at different points of a flow, provided the other variables are known. The tool is useful for students and professionals in engineering, physics, and related fields who need to analyze the behavior of incompressible, inviscid fluids.
The operation is based on conservation of mechanical energy per unit volume. The user inputs values for pressure (P), density (ρ), velocity (v), gravitational acceleration (g), and height (h) at two points (1 and 2). The calculator checks if the sum is constant and, if a value is missing, solves for the unknown automatically. The result is displayed with appropriate units, considering the International System.
The equation is applied in situations such as flow in pipes, airplane wings, ventilation systems, siphons, and flow meters (Venturi, Pitot). For example, it can determine water velocity in a pipe based on pressure difference or calculate the height of a reservoir to achieve a certain flow rate. It is important to remember that the formula assumes ideal fluid, without friction and incompressible.
Cautions: do not use the equation in flows with significant head losses (valves, bends) or compressible fluids (gases with density variation). The tool provides theoretical results; in practice, consider correction factors. Check units: pressure in Pascals, density in kg/m³, velocity in m/s, height in meters. Standard gravity is 9.81 m/s², but can be adjusted if needed.
Frequently asked questions
Can I use the Bernoulli equation for gases?
The equation is valid for incompressible fluids. For gases, use it only if density variation is negligible (low speed, small height difference). Otherwise, use the Bernoulli equation for compressible fluids.
What if there is head loss in the system?
The Bernoulli equation does not consider friction losses. For real systems with losses, use the modified Bernoulli equation with a head loss term (hf) or apply the energy equation.
What is the unit of the constant in the equation?
The constant has units of pressure (Pascal in SI). Each term (P, ½ρv², ρgh) is expressed in Pascals. Ensure all units are consistent.
Does the calculator solve for more than two points?
No. The tool compares only two points. For multiple points, apply the equation sequentially between pairs of points along the streamline.
Can I use the calculator for open channel flow?
Yes, provided the fluid is considered ideal and the flow is gradually varied. The Bernoulli equation is applicable to free-surface flows, but note that the pressure at the surface is atmospheric.