Bernoulli's Equation

• Introduction
• Venturi effect
• Stagnation pressure
  • Pitot tubes
  • Sources

Introduction

Bernoulli’s equation – based on conservation of energy:

Venturi effect

The Venturi effect is the drop of fluid pressure when a fluid flows through a constricted section of pipe – velocity increases, so static pressure decreases.

A version of the Venturi effect that applies to air is commonly known as Bernoulli’s principle.

Stagnation pressure

Take a fluid initially flowing at velocity $v_1$ at point 1. At Point $P_2$, the fluid has nowhere to go, so it’s stagnant (does not move).

$V_2 = 0$ because fluid is stagnant, and assume height diff. is negligible. Then by Bernoulli’s equation:

$P_2$ is known as the stagnation pressure.

Pitot tubes

Pitot tubes make use of stagnation pressure to measure velocity. When stagnation pressure and $P_1$ are measured, you can calculate the initial velocity (v).

Sources

• https://www.khanacademy.org/test-prep/mcat/physical-processes/fluids-in-motion/v/venturi-effect-and-pitot-tubes
• http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html
• https://en.wikipedia.org/wiki/Venturi_effect