Bernoulli's Equation Calculator
Apply Bernoulli's principle to find the velocity or pressure at a second point along a streamline.
Pressure at Point 2 (P2)
238,550 Pa
Pressure at Point 2 (P2) vs Pressure at Point 1 (P1)
Formule
## Bernoulli's Equation For steady, incompressible, frictionless flow along a streamline, the total energy per unit volume remains constant. ### Formula **P1 + 0.5 rho V1^2 + rho g z1 = P2 + 0.5 rho V2^2 + rho g z2** Rearranging for P2: **P2 = P1 + 0.5 rho (V1^2 - V2^2) + rho g (z1 - z2)** This equation is the foundation of fluid mechanics, connecting pressure, velocity, and elevation energy.
Exemple Résolu
Water (1000 kg/m^3) flows from point 1 (P1=200 kPa, V1=2 m/s, z1=5 m) to point 2 (V2=5 m/s, z2=0 m).
- 01Velocity term: 0.5 x 1000 x (4 - 25) = -10,500 Pa
- 02Elevation term: 1000 x 9.81 x (5 - 0) = 49,050 Pa
- 03P2 = 200,000 - 10,500 + 49,050 = 238,550 Pa = 238.55 kPa
Questions Fréquentes
When can I use Bernoulli's equation?
Bernoulli's equation applies to steady, incompressible, inviscid flow along a streamline. For viscous flows, add a head-loss term. For compressible flows (high-speed gas), use the compressible form.
What is dynamic pressure?
Dynamic pressure is the kinetic energy term 0.5 rho V^2. It represents the pressure increase when a moving fluid is brought to rest. Static pressure + dynamic pressure = total (stagnation) pressure.
How does Bernoulli explain lift on a wing?
Faster airflow over the curved top surface creates lower static pressure than the slower flow underneath. This pressure difference produces a net upward force (lift). However, the full explanation also involves circulation and flow turning.
Apprendre