Advanced Fluid Mechanics

Winter Quarter 2020

Stefan LLEWELLYN SMITH
EBUII 574
x23475
http://mae.ucsd.edu/~sgls

Homework I

Due

Friday January 17, 2020, in class (or before).

Problems (MYO is the textbook, 8th edition)

  1. MYO 1.73
  2. MYO 2.54
  3. MYO 3.74
  4. MYO 4.55
  5. MYO 5.63
  6. MYO 6.94
  7. Fluid mechanics provides the opportunity for beautiful visualizations. Find a striking image or video on the Internet and write a paragraph about it, including the origin of the image or video, why it was made, its scientific or technological relevance, and why you think it is interesting and/or beautiful and/or educational. One good resource is the Gallery of Fluid Motion, but Google Search will provide many other examples. There are no right or wrong answers to this question. However, you should aim to write a coherent paragraph. I will read these, and then rather than assign points for this question, I'll include a -/0/+ note for my records that could come into play during borderline decisions about final grades. This is a chance for you to express yourselves and develop a personal connection with fluids. (A colleague in Visual Arts provided the following link: labocine.com, which appears to include short scientific/arts films. Some might involve fluids.)

Comments

We have been reviewing a quarter's worth of fluid mechanics in 5 lectures or so, so there hasn't been time to cover everything. The book's treatment is good, but the chapters are fairly long, so I would recommend you try and focus on which equations or discussions are most important. One good approach is to work back from the Chapter Summaries and Study Guides. Topics that will be particularly relevant for the new material in this class are Bernoulli's equation, particularly Sections 3.5–3.7, control volume analysis for the momentum and energy equations (Sections 5.2 and 5.3), Poiseuille flow (Section 6.9) and Dimensional analysis (in particular Sections 7.2, 7.6 and 7.7). In the homework I have assigned one representative question from each chapter up to Chapter 6. Usually there will be 8 questions; this week there are 7.

The last question in each homework is a chance for you to learn something about fluid mechanics beyond the lectures and textbook. Please use appropriate citations. Last time, students were not going a good job with this and were essentially plagiarizing, so we ended up using turnitin.com, which was a hassle for everyone.

We will next start to look at viscous flow through pipes (Chapter 8 of the book). You have already encountered laminar flow in pipes: this is Poiseuille (or Hagen–Poiseuille) flow. However, if the Reynolds number is large enough, the flow may be turbulent. The instantaneous prediction of turbulent flow is usually a futile task. What we want is to understand the relation between the properties of the pipe and fluid (diameter, length, viscosity), the pressure drop and the flow rate. Even though the flow is turbulent, there is a well-defined relation between these if we consider  mean quantities.

We will first look at the general characteristics of pipe flow (Section 8.1). This might be a good time to review the Reynolds pipe experiment: there are plenty of YouTube videos that feature it, with diverse soundtracks. Then we will review laminar flow (Section 8.2), and examine the corresponding force and energy balance.

Homework policy and academic integrity

Please see main class webpage.