#### Bernoulli's Equation : Interactive Simulations

The top simulation is browser-based and will work directly on this page. The bottom simulation was prepared using Mathematica. Download the free CDF player, and then download the simulation CDF file (link given below or click on figure to download). Try to predict the behavior when a parameter changes before using a slider to change that parameter. Screencasts below explain how to use these simulations.

##### Simulation: Bernoullli Equation and Pipe Flow

This simulates water flowing through a pipe with an inlet diameter of 5 cm. You can adjust the outlet height (i.e., change Δz), outlet pipe diameter, inlet pressure, and inlet velocity using the sliders. The pressure and velocity at the outlet are determined using Bernoulli’s equation. To learn more about Bernoulli’s equation, click the “Details” button.

Try to answer these questions before determining the answer with the simulation. We suggest that you write down the reasons for your answers.

1. It is possible for the outlet pressure to be higher than the inlet pressure for liquid flow through a pipe system? Why?
2. For liquid flow through a pipe whose outlet is higher than the inlet and whose diameter is half the inlet diameter, how does the outlet velocity compare to the inlet velocity? Why?
##### Simulation: Measuring Flow Rates with a Pitot Tube

A pitot tube determines the velocity of a fluid by measuring the fluid’s stagnation pressure. In this demonstration, stagnation pressure is measured with a manometer. The height differential in the manometer is a function of the manometer fluid density, and the flowing fluid’s kinetic energy. Bernoulli’s equation relates these terms, and is used to solve for velocity. Vary the manometer fluid (green) height or the velocity of the fluid in the pipe (blue) to see how each variable is related. Also, use a slider to vary the density of the fluid in the manometer.

Try to answer these questions before determining the answer with the simulation. We suggest that you write down the reasons for your answers.

1. As the velocity increases for fluid flowing in a pipe, how does the height of fluid in a pitot tube change? Why?