Bernoulli's Principle Calculator
Conservation of energy in fluids.
Formula first
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
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.
Solve for:
Hint: Rearrange the formula to P = H - 0.5ρv² - ρgh.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Fundamentals of Fluid Mechanics by Bruce R. Munson, Donald F. Young, Theodore H. Okiishi, Wade W. Huebsch
- Fluid Mechanics by Frank M. White
- Wikipedia: Bernoulli's principle
- Britannica: Bernoulli's principle
- Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. Transport Phenomena. 2nd ed. John Wiley & Sons, 2002.
- Incropera, Frank P., DeWitt, David P., Bergman, Theodore L., Lavine, Adrienne S. Fundamentals of Heat and Mass Transfer. 7th ed.
- Halliday, David, Resnick, Robert, Walker, Jearl. Fundamentals of Physics. 10th ed. John Wiley & Sons, 2014.
- Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. Transport Phenomena, 2nd Edition. John Wiley & Sons, 2002.