# Bernoulli Principle Animation

 Bernoulli's Principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases.

## Introduction

The Bernoulli's Principle animation on this page explores the behavior of an ideal fluid passing through a pipe. You can interact with the animation, and immediately see the effects on the fluid velocity and pressure. The animation is accompanied by two discussions - an introductory discussion without any math, and a more advanced discussion involving algebra and calculus.

The fluid can be either a liquid or a gas. For Bernoulli's Principle to apply, the fluid is assumed to have these qualities:

• fluid flows smoothly
• fluid flows without any swirls (which are called "eddies")
• fluid flows everywhere through the pipe (which means there is no "flow separation")
• fluid has the same density everywhere (it is "incompressible" like water)

As a fluid passes through a pipe that narrows or widens, the velocity and pressure of the fluid vary. As the pipe narrows, the fluid flows more quickly. Surprisingly, Bernoulli's Principle tells us that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases!

## Demonstration

A cutout view of a rectangular pipe is shown below, with fluid flowing through it from left to right. This pipe demonstrates the physics of fluid flow and Bernoulli's Principle.

In this pipe, you can change the shape of the pipe by clicking and dragging the yellow handles (). Underneath, the cross-sectional area, pressure, flow rate and velocity curves are graphed so you can see how they are affected by the pipe shape. In the fluid, there are flow markers () that show how the fluid travels through the pipe. A flow marker may be thought of as a small bit of fluid that has been given a different color, but is otherwise identical to the surrounding fluid.

Suggested Shapes
Narrow pipe widens As cross-sectional area increases, velocity drops and pressure slightly increases
Rocket nozzle Exhaust is shot at high speed out of narrow opening
Drifting Rafters drift in lazy current between rapids

## Discussions

Two discussions are available:

The meaning of the flow separation flag () is explained in the more advanced discussion. Simply put, this flag is telling you when the demonstration should be modeling flow separation, so the displayed pressure and velocity values are not quite right because the demonstration ignores flow separation effects. Since flow separation is an advanced topic, beginners should just ignore it.

There are other useful resources for Bernoulli's Principle and the Bernoulli Equation:

This demonstration of Bernoulli's Principle has to be seen to be believed! While blowing through the narrow part, remove your finger that is holding the ball inside the inverted funnel. The ball will hover in the funnel until your breath runs out.

When describing why curve balls curve, Bernoulli's Principle is sometimes invoked. However, the Magnus Effect (which is not discussed here) is more appropriate for explaining curve balls, as explained at:

When describing how airplane wings work, many textbooks claim that the air traveling above the wing must travel faster over the wing so it can "catch up" with the air that went under the wing, so there is less air pressure above according to Bernoulli's Principle. This "catch up" explanation of airplane lift is seriously flawed. For clear and thorough explanations of airplane wings, start with the following links: