Notes

Our Bernoulli's Principle Concept Builder targets students' ability to combine the use of Bernoulli's principle with the principle of continuity in order to analyze situations involving fluid flow and make predictions about the relative fluid velocity and fluid pressure at specified locations. Students will need to use Bernoulli's principle to identify a high velocity region as being a low pressure region. In the first two activities of the Concept Builder. most questions involve the flow of fluid along a horizontal streamline. There is often a widening or narrowing of the flow tube; students must use the principle of continuity to associate a narrow region with a high velocity region. There are also two situations in the first activity that involve the flow of air around a spinning golf ball or baseball. Students will have to be able to identify the side of the ball along which air is traveling fastest if given the spin direction and the direction of air flow relative to the ball.

The last activity in the Concept Builder involves steady-state, laminar, fluid flow uphill or downhill. Students must use Bernoulli's equation as a guide to thinking about how velocity changes and height changes for a fluid affect the fluid pressure. There are six situations to be analyzed. Two of the situations involve a flow tube with a constant cross-sectional area. The other four situations involve flow tubes with a changing cross-sectional area.

The Bernoulli's Principle Concept Builder is comprised of 38 questions. The questions are divided into 16 different question groups. Questions in the same group are rather similar to one another. The Concept Builder is coded to select at random a question from each group until a student is successful with that group of questions. The questions and question groups are organized into three different activities. The activities are differentiated as follows:

• Bernoulli Effects Question Groups 1-6: Students analyze six common examples of the Bernoulli effect (airplane wing, spinning golf ball, spinning baseball, etc.) and use Bernoulli's principle to determine where the pressure is greatest and predict the effect that this has upon the object.
• Pressure Meters Question Groups 7-10: Students analyze fluid flow in a horizontal tube that narrows or widens in order to identify the location with the greatest speed and the location with the greatest pressure. They match their findings to a diagram displaying a set of attached Venturi tubes or a manometer.
• Bernoulli Thinking Question Groups 11-16: Students use Bernoulli's equation (and the continuity equation) to compare the velocity, height, and pressure at two locations along an ascending or descending flow tube.

The questions from each group are shown below. Teachers are encouraged to view the questions in order to judge which activity is most appropriate for their classes. We recommend doing all three activities.

Before using the Concept Builder with your classes, we recommend that teachers attempt each of the activities in order to determine which are most appropriate for your classes and what pre-requisite understanding a student must have in order to complete it. Alternatively, the Questions are provided in a separate file for preview purposes.

In order to complete an activity, a student must correctly analyze each question in that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar question twice in order to successfully complete the activity. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through an activity, a system of stars and other indicators are used to indicate progress on the level. A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the cue of questions to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question in an activity has been analyzed, the student earns a Trophy which is displayed on the Main Menu. This system of stars and trophies allows a teacher to easily check-off student progress or offer credit for completing assigned activities.

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each Question Group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.

We do not have a lot of resources on the topic of Fluids at The Physics Classroom website. What we do have is listed below. We hope to be adding more in the future.