Unit Plan – Fluid Dynamics

This unit is composed of three lessons that can be used independently or as a series of activities throughout the year to explore the theme of fluid dynamics. Fluid dynamics is a field of mathematics and science that describes how fluids move in and around objects. Fluid dynamics is a complex subject, but these lessons are designed to promote critical thinking, creativity, problem solving, and innovation. These are key components of the 21st Century Learning Skills. These lessons will also incorporate goals and objectives from the North Carolina Standard Course of Study for eighth grade mathematics and science. This unit is designed for students in an eighth grade pre-algebra or algebra course. Each lesson will offer the students a real life application to the mathematics and science, as well as a glimpse of topics, including fluid mechanics, for future study in high school physics. The lessons will relate to real and irrational numbers, cubic functions, density and viscosity, and scale models. For each lesson in the unit, the goals and objectives from the North Carolina Standard Course of Study are listed below.

Lesson 1:

Irrational numbers: Application to natural frequency and resonance

Lesson Theme:

The study of natural frequency and resonance and its effect on natural vegetation and trees, agriculture, and man-made constructions is an important and practical application of the fluid dynamics discipline. Natural frequency is the frequency at which an object vibrates once it has been set in motion. Resonance is the tendency of an object to oscillate at its maximum amplitude at certain frequencies. Resonance also has applications in acoustics. After a facilitated discussion about the effects of natural phenomena such as wind on an object’s natural frequency, pairs or groups of students will conduct an experiment to model resonance in plant stems and an activity to measure the natural frequency of pine trees. Through these activities, the students will gain an understanding of frequency, natural frequency, resonance, oscillations and square roots.

Curriculum Alignment for Lesson 1:

Grade 8 Mathematics

• Goal 1, Objective 1.01 – develop number sense for the real
  • Define and use irrational numbers
  • Use estimates of irrational numbers in appropriate situations
• Goal 1, Objective 1.02 – develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
• Goal 3, Objective 3.01 – represent problem situations with geometric models

Lesson 2:

Cubic Expressions: Application to Fluid Transport Systems through Murray’s Law

Lesson Theme:

Mathematics can be used to describe the flow of fluid through closed circulatory systems in living organisms such as plants and mammals. The students will view a schematic image of a leaf and the veins of the plant that circulate fluid throughout the leaf. Using a simplified version of Murray’s law, the students will be able to mathematically model the fluid transport system of some plants and animals.

Curriculum Alignment: Grade 8 Mathematics for Lesson 2:

• Goal 3, Objective 3.02 – apply geometric properties and relationships, including the Pythagorean theorem, to solve problems
  • Use estimates of irrational numbers in appropriate situations
• Goal 5, Objective 5.04 – solve equations using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots

Lesson 3:

Fluid Properties and Scale Models: Applying the Reynolds Number

Lesson Theme:

The study of scaling and scale modeling is extended from general proportions and similar figures to the actual conditions that must be present in order for a scale model to function as the actual object. During this lesson, students will gain a more realistic understanding of the use of scale models and understand that conditions beyond similarity of the objects are necessary for a scale model to function in the same manner as the actual object. The students will gain knowledge of how the properties of fluids, specifically density and viscosity, affect the movement of fluid around objects.

Curriculum Alignment:

Grade 8 Mathematics

• Goal 2, Objective 2.02 – apply and use concepts of indirect measurement

Grade 8 Science

• Goal 4, Objective 4.05 – identify substances based on characteristic physical properties:
  • Density