Bernoulli Pressure Calculator Formula
Understand the math behind the bernoulli pressure calculator. Each variable explained with a worked example.
Formulas Used
Pressure at Point 2
p2 = p1 + 0.5 * density * (pow(v1, 2) - pow(v2, 2)) + density * 9.80665 * (h1 - h2)Dynamic Pressure at 1
dynamic_p1 = 0.5 * density * pow(v1, 2)Dynamic Pressure at 2
dynamic_p2 = 0.5 * density * pow(v2, 2)Variables
| Variable | Description | Default |
|---|---|---|
p1 | Pressure at Point 1(Pa) | 101325 |
v1 | Velocity at Point 1(m/s) | 2 |
v2 | Velocity at Point 2(m/s) | 5 |
h1 | Height at Point 1(m) | 0 |
h2 | Height at Point 2(m) | 0 |
density | Fluid Density(kg/m3) | 1000 |
How It Works
Bernoulli's Equation
For steady, incompressible, inviscid flow along a streamline, the total energy per unit volume is conserved.
Formula
P1 + 0.5 rho v1^2 + rho g h1 = P2 + 0.5 rho v2^2 + rho g h2
Solving for P2:
P2 = P1 + 0.5 rho (v1^2 - v2^2) + rho g (h1 - h2)
Faster flow means lower pressure (the Venturi effect).
Worked Example
Water in a horizontal pipe narrows from 2 m/s to 5 m/s. P1 = 101325 Pa.
- 01P2 = P1 + 0.5 * 1000 * (4 - 25) + 0
- 02P2 = 101325 + 500 * (-21)
- 03P2 = 101325 - 10500
- 04P2 = 90 825 Pa
Frequently Asked Questions
Why does faster flow mean lower pressure?
Energy is conserved along a streamline. If kinetic energy (flow speed) increases, the pressure energy must decrease to compensate.
When does Bernoulli fail?
It fails for viscous flows (high friction), compressible flows (high Mach number), and unsteady flows. Real pipes always have some viscous loss.
Does Bernoulli explain how aeroplane wings work?
Partially. The pressure difference is real, but the common explanation that air travels faster over the curved top because of longer path length is incorrect. Circulation and angle of attack are the primary factors.
Ready to run the numbers?
Open Bernoulli Pressure Calculator