Lesson: The Bernoulli Equation

## Overview of this Lesson

In fluid mechanics, the Bernoulli equation is foundational for conceptual understanding of pressure variation in flowing fluids. Also, the Bernoulli equation is used in advanced topics such as turbomachinery, boundary layer flow, and aerodynamics.

In addition, the Bernoulli equation is often used in application; it is one of the 5 most widely used eqns in fluid mechanics.

Thus, this lesson introduces the Bernoulli equation and also introduces the concepts that are used to describe flowing fluids.

## Benefits of this Lesson

• Learn how to describe flow (laminar flow, turbulent flow, streamlines, flow separation, etc.)
• Learn how to derive Euler's equation (precursor to Navier Stokes eqn.).
• Learn how to derive the Bernoulli equation.
• Learn how to use a static tube and a Pitot-Static Tube to measure pressure and velocity
• Learn how to apply the Bernoulli equation

## Goals (results we intend to create)

1. Essential Concepts. Learners know these concepts:
* velocity
* acceleration
* streamlines (include subconcepts "streak line" and "path lines")
* laminar-flow
* turbulent-flow
* pressure (include subconcepts of kinetic pressure, stagnation pressure, static pressure)
* flow separation

2 Seminal Eqns.
* Learners derive Euler's Eqn (4.8) with quality and from memory.
* Learners derive the Bernoulli Eqn with quality and from memory.
* Learners know The Bernoulli Equation. (4.18).

## Resources (sources of knowledge for reaching goals)

• Euler's Equation
• Instruments
• Active Learning
• Problem How do we explain the Bernoulli effect as it applies to flow out of a coffee pot.

## Plan (steps to reach the goals)

1. Goal Setting.
Recommend: Write down personal goals for this lesson. Ask yourself, what do I want? What are my motivations for studying engineering? Make your goals specific (i.e. measurable) and challenging. For more information, see "how to write goals."

2. Concepts for Describing Flow (p. 77 to 85. Read p. 111 to 112.)
a. Make sure you know "essential concepts" (see goals).

3. Euler's Equation (p. 86 to 89).
a. Make sure you can derive Eulers Eqn from memory1. Resources: Derivation Handout. A video example of the derivation is planned (9/24/10).
c. Re. fig 4.12, make sure you can prove that pressure variation normal to streamlines is hydrostatic.

4. The Bernoulli Equation. (p. 92 to 99)
a. Make sure you know the Bernoulli Eqn. Recommend: Create a NETMAD. Resource: The Bernoulli Equation netmad.
b. Practice doing problems such as 4.57, 4.59, 4.60, 4.61, 4.64, 4.65, 4.67 (all solns posted).
Recommend: Practice Wale/Woods & GENI. Do yourself and correct in red.

Classroom: Applying Bernoulli Eqn. to Coffee Pot.

5. How Things Work
a. Make sure you understand2 the stagnation tube. Recommend: Create a How things work document. Resource: How Pitot-static tube works
b. Make sure you understand the Pitot-static tube. Recommend: Create a How things work document.
c. Practice doing text problems such as 4.71, 4.73, & 4.75 (all solns posted).
Recommend: Practice Wale/Woods & GENI. Do yourself and correct in red.

6. Lesson Review (Reflective Thinking)
a. Assess your learning using this form. Print3 and staple the form to front of your homework. Resource: (How to write an SII).
b. Assess this lesson using this (form).