MENG 463 / ENAS 704
Fall 2010
Problem Set 10 Solutions
In class, we worked through the RayleighBnard instability for the case of two rigid boundaries,
e
and wound up with a transcendental equation that had to be solved numerically. Let us now change
thing

MENG 463 / ENAS 704
Fall 2010
Problem Set 1 Solutions
1. Suppose that Im oating in a boat on a lake carrying a brick. If I throw the brick overboard,
will the level of the lake change, and if so, how?
Solution:
When the brick is on the bottom of the lake,

MENG 463 / ENAS 704
Fall 2010
Problem Set 2 Solutions
1. (a) Consider two uid elements located at positions X(t) and X (t). Let the separation
vector between the two be s(t) = X (t)X(t). If the two uid elements are innitesimally
close together (i.e., s is

MENG 463 / ENAS 704
Fall 2010
Problem Set 3 Solutions
1. In class, we derived Cauchys equation as a general expression of the conservation of momentum for a continuum system. Lets now think about angular momentum.
(a) Without assuming anything about the s

MENG 463 / ENAS 704
Fall 2010
Problem Set 4 Solutions
1. In many cases, modern physics can be boiled down to a study of symmetries, since (by
Noethers theorem) symmetries imply conservation laws. Lets consider the known symmetries
of the NavierStokes equa

MENG 463 / ENAS 704
Fall 2010
Problem Set 5 Solutions
1. In class, we discussed the boundary conditions on the NavierStokes equations. Lets think
about the no-slip condition a bit more, so that we better understand its origin. Well use
some (admittedly cr

MENG 463 / ENAS 704
Fall 2010
Problem Set 6 Solutions
1. Several times in class, I have mentioned that the idea of a vortex is somewhat problematic.
Lets explore this idea a bit more with a few examples.
(a) Consider plane Couette ow between parallel plat

MENG 463 / ENAS 704
Fall 2010
Problem Set 7 Solutions
Consider a steady, high-Reynolds-number, laminar jet exiting from a small round orice. What
is the velocity eld?
1. State in words (or equations as appropriate) the simplifying assumptions that can be

MENG 463 / ENAS 704
Fall 2010
Problem Set 8 Solutions
Gravity currents are ows driven by horizontal density gradients. They are extremely common
in geophysical settings: examples include thunderstorm outows, mudslides, avalanches, and pyroclastic ow. Here

MENG 463 / ENAS 704
Fall 2010
Problem Set 9 Solutions
Each of the situations described below is potentially unstable. Here, we will consider the physics
of each instability. For each case, explain:
(a) What are the destabilizing eects? What are the stabil