Bernoulli's Equation Calculator Formula
Understand the math behind the bernoulli's equation calculator. Each variable explained with a worked example.
Formulas Used
Pressure at Point 2 (P2)
p2 = p1 * 1000 + 0.5 * density * (pow(v1, 2) - pow(v2, 2)) + density * 9.81 * (h1 - h2)P2 in kPa
p2_kpa = (p1 * 1000 + 0.5 * density * (pow(v1, 2) - pow(v2, 2)) + density * 9.81 * (h1 - h2)) / 1000Variables
| Variable | Description | Default |
|---|---|---|
p1 | Pressure at Point 1 (P1)(kPa) | 200 |
v1 | Velocity at Point 1 (V1)(m/s) | 2 |
h1 | Elevation at Point 1 (z1)(m) | 5 |
h2 | Elevation at Point 2 (z2)(m) | 0 |
v2 | Velocity at Point 2 (V2)(m/s) | 5 |
density | Fluid Density (rho)(kg/m^3) | 1000 |
How It Works
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.
Worked Example
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
Frequently Asked Questions
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.
Learn More
Guide
Understanding Fluid Mechanics Basics: A Practical Introduction
Master the fundamentals of fluid mechanics including pressure, viscosity, Bernoulli's equation, Reynolds number, and flow types. Essential knowledge for engineers working with pipes, pumps, and hydraulic systems.
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