Bernoulli Equation Calculator
Calculate the fluid velocity ($v_2$) between two points.
Input Parameters
kg/m³
Pa (Pascals)
Pa (Pascals)
m (meters)
m (meters)
m/s
About the Bernoulli Equation
The Main Principle
The Bernoulli equation is a statement of the conservation of energy for a steady flow of an incompressible, non-viscous fluid. $$P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}$$
Where:
$P$ = pressure (Pa), $\rho$ = fluid density (kg/m³), $v$ = velocity of fluid (m/s), $g$ = gravitational acceleration (9.81 m/s²), and $h$ = height (m).
Usefulness of the Calculator
This Bernoulli Equation Calculator is an essential tool for students, engineers, and professionals involved in fluid dynamics, aerodynamics, and hydraulics.
- Students: Helps in visualizing the relationship between pressure, velocity, and elevation, making homework and complex problem-solving more manageable.
- Engineers: Quickly calculates necessary fluid velocities for designing piping systems, determining flow rates, and analyzing pressure drops in various mechanical systems.
- Professionals: Provides a reliable method for field checks and verification in civil, mechanical, and aerospace engineering applications, ensuring system efficiency and safety.
How to Use the Calculator
- Identify Inputs: Determine the six required values: Pressure 1 ($P_1$), Pressure 2 ($P_2$), Height 1 ($h_1$), Height 2 ($h_2$), Velocity 1 ($v_1$), and Fluid Density ($\rho$).
- Input Data: Enter these numerical values into the corresponding fields in the calculator section above. Ensure units are consistent (using SI units as specified).
- Calculate: Click the “Calculate Final Velocity ($v_2$)” button.
- Review Result: The final velocity $v_2$ will appear in the result section, calculated using the derived form of Bernoulli’s equation: $$v_2 = \sqrt{\frac{2}{\rho} \Big( (P_1 – P_2) + \rho g (h_1 – h_2) + \tfrac{1}{2}\rho v_1^2 \Big)}$$
- Troubleshooting: If an error message appears, check that all fields contain positive numerical values (especially Density $\rho$ must be greater than zero).
