Notes

This Concept Builder is designed to target student understanding of the equation of continuity and the relationship between the cross-sectional area (or diameter) of a flow tube and the flow velocity of the fluid within the tube. There are three activities that target this understanding from a slightly different perspective. Each activity presents a diagram of a flow tube (e.g., pipe) with either a widening or a narrowing section. Information about cross-sectional area or diameter before and after the widening or narrowing is provided. The flow velocity at the entrance to this area is also provided. Depending on the activity, additional information may be given. Students must use the law of conservation of mass and the relation v₁•A₁ = v₂•A₂ in order to answer the questions. Calculations are involved; but each question extends beyond the calculation to some form of meaning-making. In most cases the numbers will afford the option of doing the calculations with head math. The numerical givens also invite students to use their proportional reasoning skills.

This Concept Builder consists of 44 different questions that are organized into 12 different Question Groups and spread across three different activities.The activities are differentiated as follows:

• Case Studies Question Groups 1-4: Students must compare the volumetric flow rate (m^₃/s) and the flow velocity at a location after a widening or narrowing of a flow tube to a location before the change.
• Ranking Tasks Question Groups 5-8: Students must rank three situations involving the widening or narrowing of a flow tube according to the output velocity. Information about the input velocity, the initial cross-sectional area (or diameter), and the final cross-sectional area (or diameter) are given.
• Law Breakers Question Groups 9-12: Students are presented with three situations. The input velocity, output velocity, and initial and final cross-sectional areas are given. Students must identify any situation in which the law of conservation of mass is broken.

Before using the Concept Builder with 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 (accessible by Task Tracker teachers only).

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 (displayed for Task Tracker users). A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the queue 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.

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.