Chapter 1
Introductory remarks and starting
assumptions
Solids, liquids and gases
At macroscopic level, the most noticeable dierence between solids and uids lies in their dierent
deformation capability. Under the action of a small external force, solids r
1.1. lMany centuries ago, a mariner poured 100 cm3 of water into the ocean. As time
passed, the action of currents, tides, and weather mixed the liquid uniformly
1.3. The Maxwell probability distribution, v) = v1,vz,v3), of molecular velocities in a
[base
2.21. Use the vector integral theorems to prove that V- (V x u) = 0 for any twice-
differentiable vector function u regardless of the coordinate system.
2.22. Use Stokes' theorem to prove that V x (Vq) = 0 for any singlevalued twice-
differentiable scalar
3.19. For the ow eld 11 = U + n x x, where U and Q are constant linear- and
angular-velocity vectors, use Cartesian coordinates to a) show that 51-]- is zero,
and b) determine Rij. _ _
[U] I [)0
3.23. The velocity field of a certain ow is given by u = nyz
Math
I. First order differential equation
(y)dy = f(x)dx
dy f(x)
=
, with boundary condition y(x 0 ) = y 0 . Solution
dx (y)
y(x)
x
y0
x0
(y')dy' = f(x')dx'
d2y
= a 2 y and
II. Second order differential equations
2
dx
2
d y
= a 2 y y = C1e ax + C 2eax ;
4.20. A large wind turbine with diameter D extracts a fraction 11 of the kinetic energy from 4.24. 1An inviscid incompressible liquid with density p ows in a wide conduit of height
the airstream (density = p = constant) that impinges on it with velocity U
4.2.
4.3.
4.8.
Consider the one-dimensional Cartesian velocity eld: 11 = (ax/LO, 0) where a is a
constant.
a) Find a spatially uniform, time-dependent density eld, p = p(t), that renders this
ow eld mass conserving when p = pa at t = to.
b) What are the u
HOMEWORK #4, NANO 203
DUE MARCH 14
1) To the right is a body-centered-cubic (bcc) crystal. Assume that the length of
the side of the cube is a. Assume that this is a single molecule (not a crystal with
this structure) where each of the atoms if the same.
HOMEWORK #3, NANO 203
Due Feb. 26
1) Determine the wavelength of an electron in a 100 keV electron microscopy, x-rays that have
been tuned to Fe L3 absorption edge, Cu K x-rays and a He-Ne laser. Of these, which could be
used to determine the atomic spaci
MAE 210A FLUID MECHANICS I FALL 2015
HOMEWORK ASSIGNMENT # 3 (Due at 8AM on Oct 22, 2015)
Exercises 4.1 and 4.2 from Kundu (5th Edition), which correspond to exercises 4.1 and 4.2
(part a) in Kundu (6th Edition)
P1: Consider the steady planar ow of a liq
MAE 210A FLUID MECHANICS I FALL 2015
HOMEWORK ASSIGMENT # 1 (Due at 8AM on Oct 8, 2015)
Exercises 3.8, 3.11, 3.13, and 3.15 from Kundu (5th Edition), which correspond to exercises
3.9, 3.12, 3.14, and 3.16 in Kundu (6th Edition)
(adapted from 3.14 in Ku
1.27.
The oscillation frequency 0 of a simple pendulum depends on the acceleration of
gravity g, and the length L of the pendulum.
a. Using dimensional analysis, determine single dimensionless group involving (2, g
and L.
1.40. Consider dune formation in