Notes:
The Bernoulli's Equation is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Interactive can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.
Teaching Ideas and Suggestions:
Activities on the topic of Fluids have traditionally been absent from our website. We began adding CalcPad problem sets and Concept Builders in 2023. And now we have some simulations. This simulation provides an environment by which students can investigate the role of a pipe's cross-sectional area and height upon the speed of fluid within the pipe. The interface has two distinct regions whose properties can be modified. By default, the fluid flows from left to right through the pipe - from region 1 to region 2. The green and gold circles are hot spots that can be dragged to change the height, the length, and the cross-sectional area of the two regions.
There are a variety of controls on the right side of the simulation that allow a user to alter other properties of the environment. These controls include:
- the fluid density
- the acceleration due to gravity
- the segment volume (which affects the horizontal distance between the cross-sections)
- the volumetric flow rate (which can be + or - and thus determines the direction of flow), and
- the baseline pressure for either region 1 or region 2.
Here are at least a few of the many questions that students can explore with this simulation.
- If regions 1 and 2 have equal cross-sectional area, what affect (if any) does the height of region 2 (relative to region 1) have upon the speed of fluid?
- If regions 1 and 2 have equal cross-sectional area, what affect (if any) does the height of region 2 (relative to region 1) have upon the pressure of fluid?
- Assuming a left-to-right flow direction, what are two changes that can be made to region 2 to make the pressure change more positive?
- And assuming a left-to-right flow direction, what are two changes that can be made to region 2 to make the pressure change more negative?
- How do increases and decreases in the fluid density affect the pressure in region 2?
- How do increases and decreases in the acceleration of gravity affect the pressure in region 2?
- If regions 1 and 2 have equal cross-sectional area and gravity is turned off, how does the pressure of region 2 compare to the pressure of region 1?
As of this time, we do not have a student activity sheet for this simulation. When inspiration strikes and time frees up, we will likely create an activity sheet and accompanying Concept Checker.
Related Resources
There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Bernoulli's Equation simulation. These include:
- The Calculator Pad
Our Calculator Pad tool is sourced with more than 2500 ready-to-use Physics word problems. Each problem contains randomized numbers, an answer field for inputting an answer, immediate feedback, and (often) problem-specific help. Our Fluids section has two particularly applicable problem sets associated with the Bernoulli's Equation. See Problem Set FM4 and Problem Set FM5 on the topic of mass and energy conservation in fluid flow.
Credits
We owe a special thanks to Physics teacher Martin Kirby for donating the Bernoulli's Equation Simulation to our Interactives collection. Martin has contributed many other simulations to our Interactives collection. You can view them all by visiting our page listing all
Martin Kirby Simulations. Or visit Martin's website (
kirbyx.com) to learn more.