Contextualization

Physics provides us with an unparalleled understanding of our universe. One of its branches, Hydrodynamics, specifically deals with the movement of fluids. In this context, a key concept is conservation in fluids. In the physical world, conservation refers to the idea that something cannot change or disappear without a trace. In fluid physics, there are laws that explain how the quantity of fluid, its energy, and its movement are conserved.

For example, Bernoulli's Principle is a fundamental principle in hydrodynamics and is based on the law of conservation of energy. This principle reveals that for a steady flow of an incompressible fluid, the sum of potential energy, kinetic energy, and pressure energy is constant along the fluid flow line. That is, if a fluid flows horizontally and the velocity increases, then the pressure decreases, and vice versa.

The Principle of Continuity is another crucial concept in hydrodynamics. It is based on the law of conservation of mass, indicating that the amount of fluid passing through a point in a pipeline per unit of time is always the same. This implies that if the area of a tube decreases, the fluid velocity increases, and vice versa.

These concepts are not only theoretical but have important practical applications in our daily lives. For example, they explain the functioning of airplane wings, ships, turbines, irrigation systems, water distribution systems, among countless other applications. These principles are fundamental in engineering, infrastructure construction, and solving real and current problems.

They are also essential for us to understand how nature works, from the flight of birds and insects to the circulation of blood in our veins and arteries.

Now, to better understand these concepts, we suggest the following resources:

1. Explained Bernoulli's Principle - Khan Academy
2. Interactive Fluid Simulations - PhET
3. Video: What is the Principle of Continuity? - O Físico de Plantão
4. Book: Physics for Scientists and Engineers - Paul A. Tipler, Ralph A. Llewellyn

Practical Activity: Experimenting Conservation in Fluids

Project Objective

Each group must build a fluid siphon and a homemade wind tunnel to demonstrate and analyze Bernoulli's Principle and the Principle of Continuity, respectively. The project must be completed in 30 days, and each group member must dedicate between 5 to 10 hours of work.

Detailed Project Description

Part 1: Fluid Siphon (Principle of Continuity)

Required materials:

• Two empty plastic bottles (of the same size)
• One transparent plastic tube (sufficient length to connect the two bottles)
• Water
• Food coloring (optional)

Step by step:

1. Fill one of the bottles with water. If desired, add food coloring to the water for easier visualization.

2. Connect the tube to both bottles. Make sure the end of the tube in the empty bottle is near the bottom of the bottle.

3. Create a vacuum in the tube (using a syringe at the tube ends).

4. Lift the bottle with water above the empty bottle and observe what happens.

Part 2: Homemade Wind Tunnel (Bernoulli's Principle)

Required materials:

• Fan
• Transparent plastic tube
• Light papers (e.g., confetti)

Step by step:

1. Turn on the fan.

2. Throw the light papers in front of the fan.

3. Place the tube near the airflow.

4. Observe and take notes on what happens.

Project Deliverables

Report

Students must produce a written report containing the following topics:

1. Introduction: The theme of hydrodynamics should be contextualized, its relevance, the application of these principles in the real world, as well as the project's objective.

2. Development

   • Theory: Explain the theory behind Bernoulli's and Continuity principles.
   • Activity: Describe the activity in detail, indicate the step-by-step used, the materials used, and which experiments were performed.
   • Results: Present and discuss the results obtained.

3. Conclusion: Conclusions drawn from the project, pointing out the main learnings obtained and summarizing the key points.

4. Bibliography: Indicate the sources used for the project, including books, websites, videos, among others.

At the end of this practical project, students should be able to understand and explain Bernoulli's and Continuity Principles, how they apply in the real world, and how they can be demonstrated through experiments. In addition, students should have acquired skills in collaboration, time management, problem-solving, and communication, among others.