Ch. 3 | Flow Computation based on Kinematics
3.1
Velocity Potential
For an irrotational ow, the velocity potential in integral form is dened at any point P
as
P
u dx
O
where O is some arbitrary xed point. Partial dierentiation of this equation gives u =
N
Ch. 1 | Introduction
1.1
Some background on uids
Before we begin, let me go over some of the restrictions that govern this class. First, we
will limit ourselves to classical mechanics. Relativity and quantum mechanics are ignored.
Also, electromagnetic ee
Ch. 5 | Hydrostatic Fluids
In the previous chapter, we learned that, for a
the diagonal form
P
0
0 P
=
0
0
uid at rest, the stress tensor reduces to
0
0 .
P
This is equivalent to saying that all viscous stresses within the uid go to zero. In this
chapter
Ch. 4 | Forces and Stresses in a Fluid
It is possible to distinguish two kinds of forces which act on matter in bulk: 1) longrange forces, which decrease slowly with increasing distance; and 2) short-range forces, which
decrease rapidly with increasing di
Ch. 2 | Kinematics
2.1
Particle velocity and acceleration
In dynamics, the position of a test particle often changes with time. Therefore, the
coordinates of the particle must be functions of time, denoted as
x1 = X1 (t),
x2 = X2 (t),
x3 = X3 (t) .
Simila