Animated Demonstration of Bernoulli's Principle

Introduction

A cutout view of a venturi tube is shown below, with flow markers that show the fluid traveling through the tube. The tube geometry can be changed by moving the yellow handles. Underneath, the cross-sectional area, pressure, flow rate and velocity profiles are graphed so you can see how they are affected by the tube geometry.

Directions

Click and drag the yellow handles to change the geometry. Java must be enabled in your browser to see this demonstration.

Java must be enabled to use the Venturi Tube Demonstration

Suggested Geometries

Geometry	Title	Comments
	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

Internal Pressure Versus Ram Pressure

This applet displays internal pressure, which is the pressure felt by an object or person suspended in the fluid and moving with it. Internal pressure should not be confused with ram pressure, which is the pressure felt by an object because it is moving relative to the fluid.

The ram pressure varies as the square of the velocity. This explains the stronger force felt by your hand when it is held in the faster moving current.

Background Theory

We assume that the fluid is irrotational, incompressible, nonviscous and with steady streamlines. We ignore hydrostatic pressure.

The venturi tube has a rectangular cross-section, so the area is linearly proportional to the tube height.

We use the equation of continuity to get the velocity as a function of cross-sectional area. We use the Bernoulli equation to get the pressure once we have the velocity.

With our simple model for the fluid behavior, we can use the work-energy theorem to relate the kinetic energy of the moving fluid to the ram pressure felt by a fixed object.

More theory information may be found elsewhere.