Stefan LLEWELLYN SMITH
EBUII 574
x23475
http://mae.ucsd.edu/~sgls
Homework IV
Due
Friday February 7, 2020, in class (or before).
Problems (MYO is the textbook; 8th edition)
MYO 8.74
MYO 8.78
MYO 8.96
MYO 8.105
MYO 8.115
MYO 8.119
MYO 8.129
Write a paragraph about the engineering of pipeline design
(e.g. petroleum, crude oil). Try and find a specific example to
discuss. Cite your sources.
Comments
This homework covers Sections 8.5 and 8.6 of the book.
There isn't much to write about this homework, which is mostly
examples. The theoretical background was introduced earlier. The
applications here span quite a wide range. Remember that there are 3
basic types of problems: Type I in which you have to find the
pressure drop (or sometimes pump power which is related to pressure
drop), Type II in which you have have to find the velocity or flow
rate, and Type III in which you have to find the pipe diameter.
(There are other twists, such as finding viscosity or density, but
those are rare.)
Type I is straightforward: from V (sometimes from Q), D (which may
be the hydraulic diameter if the pipe is not circular in cross
section) and the fluid properties, find Re. That tells you if the
flow is laminar or turbulent. If the flow is laminar, use f = 64/Re
if it is circular or the appropriate formula if it is not. If the
flow is turbulent, use the roughness and Re to find f using the
Moody chart or one of the formulas. From f, you can find the major
losses. Compute the minor losses and then use the energy equation to
find the pressure drop (or shaft work).
For Types II and III, write down the equations you have, which are
usually the energy equation and the definition of the Reynolds
number in terms of your unknown, either V or D (for Type III the
nondimensional roughness is also unknown). Then seek a value for f
that satisfies all the equations, either iteratively using the Moody
diagram or finding the appropriate solution for f in the Colebrook
(or some other) formula, again using iteration or a numerical root
finder.
The next section of the class considers external flows. The
challenge here is that at high Reynolds numbers we know that the
viscous term is small. However, it can't be ignored next to
boundaries because of the no-slip condition. This leads to the
existence of boundary layers, which are narrow regions over which
the flow adjusts to match the free-stream velocity. We need to
understand these to obtain the drag due to shear stresses on the
boundary. There is also a second challenge: to compute the total
drag on a body, which depends on the overall flow field: bodies have
a wake behind them which has an important effect on the drag.
Turbulence is once again an important issue here. We will use
dimensional analysis again to obtain a non-dimensional measure of
drag, the drag coefficient.