Contextualization

Theoretical Introduction

Bernoulli's Principle, formulated in 1738 by the Swiss mathematician Daniel Bernoulli, is a fundamental concept in fluid physics. It describes the behavior of fluids when they are in motion. According to this principle, the total energy of a flowing fluid - represented by the sum of kinetic energy, gravitational potential, and pressure - is constant along its trajectory. The principle is often expressed by the following equation:

E = 1/2 ρv²+ ρgh + p = constant.

Where:

• E is the total energy per unit volume,
• ρ is the fluid density,
• v is the fluid velocity,
• g is the acceleration due to gravity,
• h is the height above a reference point, and
• p is the fluid pressure.

Bernoulli's Principle implies that if the velocity of a fluid increases, the pressure or the potential energy of the fluid decreases, and vice versa.

Importance and Applications of Bernoulli's Principle

Bernoulli's Principle has a wide range of real-life applications, from engineering and technology to biology and geography. In aircraft, for example, the pressure difference generated by Bernoulli's Principle is one of the forces responsible for the phenomenon of flight. In the human body, blood circulation also follows the same principle.

Practical Activity: Bernoulli Experiment

Project Objective

The objective of this project is for students to be able to prove and understand Bernoulli's Principle through a simple experiment, as well as to understand and apply the Bernoulli equation to analyze the results of the experiment.

Detailed Project Description

Students will conduct an experiment called 'The Ping-Pong Ball Levitator' that illustrates Bernoulli's Principle. They will observe the ping-pong ball floating in the airflow produced by a hairdryer and will be challenged to calculate the air velocity at the point where the ball stabilizes, using the Bernoulli equation.

Required Materials

• Ping-pong ball
• Hairdryer
• Ruler

Step by Step

1. Organize yourselves into groups of 3 to 5.
2. Turn on the hairdryer and place the ping-pong ball in the airflow. Observe how the ball floats in the air.
3. Measure the height h at which the ball stabilizes in the air. Use the ruler for this measurement.
4. Using the Bernoulli equation, calculate the air velocity (v) at the point where the ping-pong ball stabilizes. Consider the air density (ρ) as 1.225 kg/m³ and the acceleration due to gravity (g) as 9.8 m/s².

Project Deliverables

At the conclusion of the project, each group must submit a written report containing the following sections:

1. Introduction: In this section, students should contextualize Bernoulli's Principle, its importance, and real-life applications. It is also essential to explain the project's objective and the steps taken to achieve this objective.

2. Development: Here, students should explain the details of the experiment conducted: the materials used, a detailed description of the step-by-step process, observations made during the experiment, and calculations of air velocity using the Bernoulli Equation. This section should also include a discussion on the obtained result.

3. Conclusion: Students should revisit the main points of the work, comment on what they learned from the project, and draw conclusions based on practical experience and the theory of Bernoulli's Principle.

4. Bibliography: Should contain all the sources that students consulted for the project: books, websites, videos, etc.

Remember: the goal of this activity is to prove and understand Bernoulli's Principle in a playful and engaging way. Have fun learning!