Stefan LLEWELLYN SMITH
EBUII 574
x23475
http://mae.ucsd.edu/~sgls
Homework II
Due
Friday January 24, 2020, in class (or before).
Problems (MYO is the textbook, 8th edition)
MYO 5.106
MYO 6.96
MYO 7.16
MYO 7.45
MYO 7.83
MYO 8.2
MYO 8.5
Write a paragraph about an application of dimensional
analysis. Less credit will be given to discussions of Taylor's
work on the atomic bomb yield or other examples in the documents
linked to in the slides).
Comments
Monday is a holiday and I will not start Chapter 8 until Wednesday
or Friday. As a result, this homework covers just the beginning of
Chapter 8, as well as some question from Chapters 5 and 6 relevant
to pipes and questions on dimensional analysis from Chapter 7.
Section 8.1 is introductory. Pipe flow was a critical factor in the
development of ideas about laminar (smooth), transitional and
turbulent flows. There are many videos corresponding to Figure 8.2.
We will take the flow to be laminar if Re < 2100 and turbulent if
Re > 4000, where the Reynolds number is based on the diameter of
the pipe. (We will discuss how to define the Reynolds number for
ducts with non-circular cross-sections later.) Researchers still
don't fully understand the transition to turbulence in pipes, which
is a much more difficult problem than the transition to turbulence
in other systems. e.g. Rayleigh-Bénard convection (a layer of fluid
heated from below). We will limit ourselves mostly to
fully-developed flow, i.e. flows in which we neglect variations
along the pipe (remember that the pressure can change along a pipe,
although its gradient does not). This means we neglect the entrance
region, the region directly after a fluid enters a pipe e.g. from a
reservoir; there are empirical scalings for how long this region is.
The higher Re, the longer it is.
Homework III will cover Section 8.1 and then move to turbulent flow
in pipes, which is definitely more complicated.