3 Favorites
 0 Times Used
Classroom Card #3891
EM Case Study - Bernoulli at Work: Fluid Dynamics and EM in an iFLY Wind Tunnel
Updated: 4/5/2024 1:10 PM by Sid G
Reviewed: 4/5/2024 8:45 AM by Becky Benishek
"Bernoulli's equation is probably the most famous equation in all of fluid dynamics." - John Anderson

This module is specially designed for the following courses - Fluid Mechanics, Introduction to Flight, Aerodynamics, and Thermodynamics. In this card we discuss two approaches for delivering the module. 

One week
All the resources and supplemental materials required to implement this module are included in the resources tab below.


1. Introduction

Bernoulli's principle is one of the most foundational concepts in fluid dynamics, profoundly influencing the design and operation of a wide range of applications. It represents a simplified form of the Navier-Stokes equation and is derived by applying key assumptions. Despite what may seem like an unrealistic set of assumptions, it establishes the fundamental relationship between three critical variables in fluid flow: Pressure, Velocity, and Height. This principle is applicable in designing and operating systems ranging from small-scale ones like beer flowing from a beer keg through a tap and into a glass, to large-scale systems like a closed loop iFLY wind tunnel.

2. EM Infusion

In this module, we use the expertise of iFLY engineers regarding the use of Bernoulli's principle in their daily work to derive, apply, and evaluate this principle. We hear from the engineers about how they have used this fundamental principle to solve technical problems to significantly benefit their customers. This is why they can use glass walls in their test section to allow friends and family of the flyer to watch while the air inside flows at up to 120 mph. We hope that students will see the engineers' Entrepreneurial Mindset (EM) at work and learn how this mindset can not only solve problems, but also add tremendous value.

3. Approach

Much of this module consists of high-quality videos created at the iFLY tunnel and headquarters in Austin, TX, featuring the iFLY engineers. However, videos alone won't make an impact without a structured approach. We propose two alternate approaches to module delivery, where the videos are integrated into the process of deriving, applying, and evaluating Bernoulli's principle. Each approach uses different active learning techniques and structures while incorporating elements of EM throughout the module. 

Approach 1: 

In this approach, the module starts with a summary of the Governing Equations of Fluid Dynamics. The derivation of Bernoulli's principle begins with the context of the iFLY wind tunnel. Initially, students are asked a set of questions to establish the context for the iFLY wind tunnel, its purpose, and its target customers. Then, a series of videos are shown where iFLY engineers explain the reason for the tunnel's existence and overall mission. 

Then, the students are guided through the derivation of Bernoulli's principle from the Conservation of Energy by applying a series of assumptions. During this process, videos are shown in which engineers describe Bernoulli's principle and its inherent assumptions. Once Bernoulli's equation is derived, students use the iFLY wind tunnel schematic to calculate the pressure and velocity at various locations within the tunnel. 

Two technical questions are strategically introduced to enable students to discover the "FORCE" exerted on the walls of the test section while air flows at 120 mph. After calculating this significant force value, students brainstorm various methods to mitigate the pressure difference between the test section and ambient pressure. Then, the solution implemented by iFLY engineers is revealed in the videos, helping students understand the role of "reference" pressure in Bernoulli's equation. 

The module then walks the students through a design problem to reduce the footprint of the overall wind tunnel (implemented if time permits) and ends with a collection of advice and insights from iFLY engineers.

Use of Guided Notes:

The approach strongly leverages guided notes (pre-prepared, typed notes with key information purposefully missing), the benefits for which are described below.

In classes heavy on math and derivation, guided notes provide a platform for students to engage their curiosity and establish connections between various concepts. These instructor-prepared handouts include essential background information and prompts, with spaces left blank for students to fill in key facts, equations, concepts, and assumptions during lectures. The guided notes we prepared are included in the Resources below, and instructors can adapt them as necessary for their classes. Critical assumptions, derivation steps, and equations are intentionally omitted from the notes, encouraging students to collaborate and complete them. This method allows students to fully engage with the content, prompting them to ask significant questions. Surprisingly, guided notes expedite the derivation process compared to writing equations on the board. They also reduce the likelihood of students misinterpreting mathematical symbols and variables, a common issue with board-written notes. By focusing on understanding of the concepts rather than mere copying, students are compelled to pay attention to their work, fostering deeper retention, and understanding, and also fostering their curiosity. A brief video on the use of guided notes is available in the resources section below.

All the resources for Approach 1 are included in the resources tab below the card.

Approach 2: 

In this approach, the origins of the Bernoulli equation are discussed in reference to the previously established Navier Stokes equations for the first 50-minute lecture. The limiting assumptions for the Bernoulli equation are discussed. See supporting resources for this lecture.

The next 50-minute lecture focuses on the iFLY case study. Introductory videos are shown to the students at the beginning of class to provide an idea of what iFLY is all about. Next, videos of iFLY engineers discussing the advantages/disadvantages of the Bernoulli equation. During this, discussion surrounds how we as engineers use class-based knowledge to tackle real-world problems.

After this, one of the iFLY logistical design problems is introduced. This problem revolves around the high pressures experienced in the test section. The students are asked to spend 5-10 minutes to talk with their neighbor(s) about this problem, and how they might address it utilizing the Bernoulli equation (and previously learned Continuity equation). Before showing the videos of how the iFLY engineers solved the problem, the students are first asked to describe what solutions they may have come up with and to explain why they think their solution will work. Next, the video of the iFLY engineer describing their solution is showed. Follow-up discussion and working out of quantitative values is worked at the board together. 

Lastly, some of the closing remarks/advice videos from the iFLY engineers are shown, and the students are asked if they have any further questions. Between this lecture and the following, the students write a brief discussion forum about their experience, and post it to our online learning platform to be graded. Because the instructor writes live on the computer screen, the completed and recorded lecture is posted to the student's online learning platform for reference.

The iFLY wind tunnel is then discussed qualitatively throughout the rest of the lecture (specifically when talking about pipe flow and pipe-flow losses).


  • Demonstrate constant curiosity about our changing world
  • Explore a contrarian view of accepted solution
  • Integrate information from many sources to gain insight
Creating Value
  • Identify unexpected opportunities to create extraordinary value
Log In to View More