This tool calculates the pressure or velocity of a fluid flow based on Bernoulli’s equation for you.

## How to Use the Bernoulli Equation Calculator

This calculator uses the Bernoulli equation to compute the relationship between pressure, velocity, and height at two different points in a fluid flow.

To use this calculator:

- Enter the pressure at point 1 (P1) in Pascals.
- Enter the velocity at point 1 (V1) in meters per second.
- Enter the height at point 1 (H1) in meters.
- Enter the pressure at point 2 (P2) in Pascals.
- Enter the velocity at point 2 (V2) in meters per second.
- Enter the height at point 2 (H2) in meters.
- Enter the fluid density (ρ) in kilograms per cubic meter.
- Click on the “Calculate” button to compute the results.

## How It Calculates the Results

The Bernoulli equation is given by:

`P1 + 0.5 * ρ * V1^2 + ρ * g * H1 = P2 + 0.5 * ρ * V2^2 + ρ * g * H2`

where:

`P1, P2`

are the pressures at points 1 and 2.`V1, V2`

are the velocities at points 1 and 2.`H1, H2`

are the heights at points 1 and 2.`ρ`

is the fluid density.`g`

is the acceleration due to gravity (9.81 m/s²).

The result output refers to the change in energy between the two points.

## Limitations

Please note that the Bernoulli equation assumes a number of ideal conditions, including incompressible, non-viscous fluid and steady flow. In real-world applications, these conditions may not always hold, thus limiting the accuracy of the results.

## Use Cases for This Calculator

### Calculate Pressure or Elevation Head

Enter the values for the velocity head, gravitational acceleration, pressure, and density to determine the pressure or elevation head using Bernoulli’s equation. This calculation is essential in fluid mechanics to analyze fluid flow characteristics in pipes or open channels.

### Find Velocity Head

Input the pressure head, elevation head, gravitational acceleration, pressure, and density to compute the velocity head with the Bernoulli equation. This helps in determining the kinetic energy of the flowing fluid and is crucial for understanding fluid dynamics.

### Determine Total Pressure

By entering the values for the velocity head, pressure head, elevation head, density, and gravitational acceleration, you can calculate the total pressure. Total pressure is the sum of all energies in a fluid system and is vital in various engineering applications.

### Compute Flow Velocity

Provide the values for pressure head, elevation head, gravitational acceleration, pressure, and density to find the flow velocity using Bernoulli’s equation. Flow velocity calculation helps in predicting the behavior of fluid flow in different scenarios.

### Estimate Elevation Difference

Enter the velocity head, pressure head, gravitational acceleration, pressure, and density to estimate the elevation difference. This calculation is useful in determining the height variation in a fluid system based on energy considerations.

### Calculate Pressure Difference

Input the velocity head, elevation head, gravitational acceleration, pressure, and density values to calculate the pressure difference. Understanding pressure variation is crucial in analyzing fluid flow behaviors in pipelines or hydraulic systems.

### Determine Velocity Pressure

By providing the velocity head, pressure head, gravitational acceleration, pressure, and density, you can compute the velocity pressure using Bernoulli’s equation. Velocity pressure is a key parameter in analyzing fluid flow characteristics in different engineering applications.

### Verify Energy Conservation

Check the conservation of energy in a fluid system by entering the values for pressure head, velocity head, elevation head, pressure, density, and gravitational acceleration. Bernoulli’s equation helps in ensuring that energy is conserved throughout the fluid flow process.

### Analyze Pump Performance

Input the necessary parameters such as elevation head, pressure head, velocity head, density, pressure, and gravitational acceleration to analyze the performance of a pump using Bernoulli’s equation. This analysis aids in optimizing pump efficiency and system design.

### Optimize Pipe Diameter

By entering the flow velocity, pressure, density, and gravitational acceleration, you can optimize the pipe diameter based on energy considerations using the Bernoulli equation. Proper pipe sizing is crucial for efficient fluid transportation and system performance.