Stefan LLEWELLYN SMITH
EBUII 574
x23475
http://mae.ucsd.edu/~sgls
Homework V
Due
Friday February 21, 2019, in class (or before).
Problems (MYO is the textbook; 8th edition)
MYO 9.6
MYO 9.16
MYO 9.38
MYO 9.78
MYO 9.96
MYO 9.104
MYO 9.122
Write a paragraph about lift and drag and the role of fluid
mechnics on either automobiles or ships (but not aircraft for a
change). Cite your sources.
Comments
This homework covers Chapter 9 of the book (more material than usual
because there was no homework due last week).
Chapter 9 covers flows past bodies. It starts with a general
introduction, in which the overall geometry of these flows and their
dependence on Reynolds number, Re, is discussed. For small Re, the
influence of viscosity is felt far from the body. For high Re, it is
felt in a narrow layer close to the body and in the wake of the
body. The force on the body, which is conventionally decomposed into
drag along the direction of motion and lift perpendicular to motion,
can be obtained by integrating the stress over the body. The
tangential stress is directly due to friction and is important along
a flat plate for example. However, there is also pressure (or form)
drag, which arises from the fact that the pressure in the wake of a
body, especially a bluff body, is substantially different from the
pressure on its leading side. The result is an imbalance in the
integral of pressure, i.e. drag.
Section 9.2 examines boundary layers. It presents the Blasius
solution for the boundary layer over a flat plate, corresponding to
no pressure gradient along the boundary. This comes from solving an
ODE because of the existence of a similarity variable. The form of
the variable shows that the boundary layer thickness grows like the
square root of the distance along the surface. Approximate solution
methods (the momentum integral approach) are then presented. These
can be applied to situations in which the boundary layer becomes
turbulent or there is a pressure gradient. An adverse pressure
gradient (one in which the flow decelerates as it moves past the
boundary) leads to separation.
Section 9.3 treats drag. The approach is mostly empirical and based
on dimensional analysis. The relevant nondimensional parameter is
the drag coefficient, which is presented graphically as a function
of Reynolds number for different body shapes.
Section 9.4 on lift is quite similar. However, the important notion
of circulation (integral of velocity along a closed curve, mentioned
briefly in MAE 101A) is mentioned.