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Bernoulli's Principle Calculator

Conservation of energy in fluids.

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Total Pressure

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Overview

Bernoulli's Principle is a fundamental expression of the conservation of energy for flowing fluids, relating pressure, velocity, and elevation. It dictates that in a steady flow of an incompressible, frictionless fluid, an increase in speed occurs simultaneously with a decrease in static pressure or potential energy.

Symbols

Variables

H = Total Pressure, P = Static Pressure, = Density, v = Velocity, g = Gravity

Total Pressure
Pa
Static Pressure
Pa
Density
Velocity
m/s
Gravity
Height

Apply it well

When To Use

When to use: Apply this equation to steady, incompressible, and inviscid flows along a streamline where friction and heat transfer are negligible. It is primarily used to analyze fluid behavior in closed conduits, calculate flow through orifices, or determine lift on aerodynamic surfaces.

Why it matters: This principle is the cornerstone of aerodynamics and hydraulics, explaining how aircraft wings generate lift and how venturi meters measure flow rates. It allows engineers to predict pressure changes in complex piping networks and design efficient fluid transport systems.

Avoid these traps

Common Mistakes

  • Ignoring energy losses in real pipes.
  • Mixing m and cm for height.

One free problem

Practice Problem

A horizontal water pipe has a total energy head H of 200000 Pa. If the water (density 1000 kg/m³) flows at 4 m/s at an elevation of 5 meters, determine the static pressure P within the pipe using g = 9.81 m/s².

Total Pressure200000 Pa
Density1000 kg/m^3
Velocity4 m/s
Gravity9.81 m/s^2
Height5 m

Solve for:

Hint: Rearrange the formula to P = H - 0.5ρv² - ρgh.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Fundamentals of Fluid Mechanics by Bruce R. Munson, Donald F. Young, Theodore H. Okiishi, Wade W. Huebsch
  2. Fluid Mechanics by Frank M. White
  3. Wikipedia: Bernoulli's principle
  4. Britannica: Bernoulli's principle
  5. Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. Transport Phenomena. 2nd ed. John Wiley & Sons, 2002.
  6. Incropera, Frank P., DeWitt, David P., Bergman, Theodore L., Lavine, Adrienne S. Fundamentals of Heat and Mass Transfer. 7th ed.
  7. Halliday, David, Resnick, Robert, Walker, Jearl. Fundamentals of Physics. 10th ed. John Wiley & Sons, 2014.
  8. Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. Transport Phenomena, 2nd Edition. John Wiley & Sons, 2002.