Bernoulli's Equation Calculator
Bernoulli's equation relates pressure, flow velocity, and elevation for an ideal, incompressible, and steady fluid flow along a streamline.
Formula first
Overview
Derived from the principle of conservation of energy, the equation states that the sum of static pressure, dynamic pressure, and hydrostatic pressure remains constant along a streamline. It is foundational in fluid mechanics for determining how fluid flow characteristics change when piping geometry or elevation varies. This idealization assumes no friction losses and constant fluid density.
Symbols
Variables
P = Pressure, = Fluid Density, g = Gravity, h = Height
Apply it well
When To Use
When to use: Apply when analyzing steady, incompressible, frictionless (inviscid) flow along a streamline where fluid properties do not change over time.
Why it matters: It is essential for designing piping systems, aircraft wings, and hydraulic devices, allowing engineers to calculate velocity changes based on pressure differentials.
Avoid these traps
Common Mistakes
- Neglecting the hydrostatic pressure term (rho*g*h) when there is a significant elevation change.
- Attempting to apply the equation to systems with significant viscous losses (e.g., long pipes with friction) without using the Energy Equation extension.
- Confusing static pressure with stagnation pressure.
One free problem
Practice Problem
A horizontal pipe with a cross-sectional area of 0.02 m² narrows to 0.01 m². If water flows at 2 m/s in the wider section with a pressure of 200 kPa, what is the pressure in the narrow section (density = 1000 kg/m³)?
Solve for:
Hint: Use the continuity equation A1v1 = A2v2 to find the velocity in the second section, then apply Bernoulli's.
The full worked solution stays in the interactive walkthrough.
References
Sources
- White, F. M. (2011). Fluid Mechanics (7th ed.). McGraw-Hill Education.
- Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press.