Advanced Bernoulli Equation Calculator

Compare energy heads across two flow points. Solve unknown variables using extended Bernoulli relationships instantly. Download results, inspect formulas, and visualize system head clearly.

Calculator Inputs

Pick the target variable, then enter the remaining engineering values below.

The selected field becomes auto-calculated.
Use 1000 for water at standard conditions.

Plotly Graph

This grouped chart compares pressure head, velocity head, and elevation head at both points.

Formula Used

The extended Bernoulli relation used here is:

P₁/(ρg) + V₁²/(2g) + z₁ + hp - ht - hL = P₂/(ρg) + V₂²/(2g) + z₂

Where P is pressure, ρ is density, g is gravitational acceleration, V is velocity, z is elevation, hp is pump head added, ht is turbine head removed, and hL is friction or minor head loss.

The calculator rearranges the same equation to solve for one unknown variable at a time. Pressure values are entered in kPa, while the internal equation converts them into Pascals before computing pressure head.

How to Use This Calculator

  1. Select the variable you want the calculator to solve.
  2. Enter the fluid density in kg/m³.
  3. Provide the known pressure, velocity, and elevation values for both points.
  4. Add pump head, turbine head, and total head loss when relevant.
  5. Press the calculate button to show the result above the form.
  6. Review the solved value, head comparison table, and Plotly graph.
  7. Export the completed result set as CSV or PDF.

Example Data Table

Scenario Solve For ρ (kg/m³) P1 (kPa) V1 (m/s) z1 (m) V2 (m/s) z2 (m) hp (m) ht (m) hL (m) Result
Water transfer line Pressure at Point 2 1000 220.00 2.50 12.00 4.20 5.00 0.00 0.00 1.20 271.19 kPa

Frequently Asked Questions

1. What does this Bernoulli calculator solve?

It solves one unknown among pressure, velocity, or elevation between two points in a flowing fluid system. It also accounts for pump head, turbine head, and total head loss.

2. Which units should I enter?

Enter density in kg/m³, pressure in kPa, velocity in m/s, and elevation or head terms in meters. The computation then stays consistent in SI form.

3. Can this tool handle head loss?

Yes. You can add total head loss directly as meters of fluid head. This is useful when piping friction and minor losses are already known or estimated.

4. What is pump head in this calculator?

Pump head represents energy added to the fluid. A positive pump head increases the available total head on the upstream side of the Bernoulli balance.

5. What is turbine head?

Turbine head represents energy removed from the flowing fluid. It reduces the total head available between the two points in the equation.

6. Why might I get no real velocity solution?

That usually means the entered pressures, elevations, and losses do not leave enough remaining energy head for the selected velocity term. Review the consistency of your inputs.

7. Does the result section include export options?

Yes. After calculation, the page shows buttons for CSV and PDF downloads. They export the solved result and the major Bernoulli head values.

8. When should I avoid Bernoulli assumptions?

Avoid it when compressibility, strong viscosity effects, major turbulence modeling limits, transient conditions, or significant heat transfer make a simple energy balance unreliable.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.