Bernoulli Equation Calculator
Bernoulli's equation is a fundamental principle of fluid mechanics that relates pressure, velocity, and elevation along a streamline in steady, incompressible, inviscid flow. The total mechanical energy per unit volume is conserved: P + 0.5 rho v^2 + rho g h = constant, where P is static pressure (Pa), rho is fluid density (kg/m^3), v is flow velocity (m/s), g is gravitational acceleration (9.80665 m/s^2), and h is elevation (m). This calculator finds the pressure at point 2 given conditions at point 1 and the velocity and height at point 2.
Bernoulli's equation
P2 = P1 + 0.5 rho (v1² - v2²) + rho g (h1 - h2)
g = 9.80665 m/s^2 (standard gravity, NIST). All pressures in Pascals. If the elevation terms are equal (h1 = h2), the equation simplifies to Venturi flow: P2 = P1 + 0.5 rho (v1^2 - v2^2), showing that higher velocity yields lower pressure.
Worked example: Venturi meter
- Water (rho = 1,000 kg/m^3) flows in a pipe. At the wide section: P1 = 101,325 Pa, v1 = 2 m/s. At the narrow throat: v2 = 4 m/s. Same elevation.
- P2 = 101,325 + 0.5 x 1,000 x (4 - 16) = 101,325 - 6,000 = 95,325 Pa.
- The pressure drops by 6,000 Pa (about 0.06 atm) as velocity doubles.
Frequently asked questions
What is Bernoulli's equation?
Bernoulli's equation states that for steady, incompressible, frictionless flow along a streamline, the sum P + 0.5 rho v^2 + rho g h is constant. P is static pressure, 0.5 rho v^2 is dynamic pressure, and rho g h is hydrostatic pressure.
What does this calculator solve?
This calculator takes the known conditions at point 1 (pressure P1, velocity v1, height h1) and solves for pressure at point 2 given the velocity v2 and height h2, using P2 = P1 + 0.5 rho (v1^2 - v2^2) + rho g (h1 - h2).
What assumptions does Bernoulli's equation make?
The equation assumes steady (time-independent) flow, incompressible fluid (constant density), inviscid (frictionless) flow, and that measurements are taken along the same streamline. Real-world applications require additional loss terms for viscous flow.
What units does this calculator use?
Pressure in Pascals (Pa), velocity in m/s, height in meters, and density in kg/m^3. The result P2 is in Pascals. Standard density of water = 1,000 kg/m^3; air at 20 degrees C = 1.204 kg/m^3.
What is a common application of Bernoulli's equation?
Applications include Venturi meters (flow measurement), airplane wing lift (pressure differential), pitot tubes (airspeed measurement), and carburetors. The equation explains why faster-moving fluid has lower pressure (the Bernoulli effect).
Official sources
- NIST: Standard Acceleration of Gravity (NIST CODATA).
- OpenStax University Physics: 14.6 Bernoulli's Equation.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.