Chapter 7.1-7.6
1
Thought Experiment
Lets say we want to know how the drag force
(F) on a sphere moving through a fluid is
affected by the other flow variables (v, , d, ,
etc.)
How can we figure this out?
d
v
2
Thought Experiment
Experimentally:
Vary ea
Chapter 2.1-2.6
1
Pressure
What is pressure?
Force divided by area
More specifically,
dF PdA
dF
P
dA
Scalar quantity (only component of force
normal to surface is important)
SI units: Pascals (Pa)
2
Atmospheric Pressure
Patm = 101.3 kPa or 14.7 psi or 221
Chapter 6.1-6.3
1
Conservation of Mass
Consider the control volume composed of an
infinitesimal cube with side lengths dx, dy and
dz
The density of the center of the cube is , and
the velocity
y
v ui there
vj wis
k
x
z
2
Conservation of Mass
To evaluate t
Chapter 6.8-6.9
1
Navier-Stokes Equation
Remember the Navier-Stokes equation is
Dv
v
v v P 2 v g F
Dt
t
Continuity
Pressure
Gradient
Shear/Friction
Other Body
Forces
Gravity
We saw a few examples on how to use it last
class
We will see a few more today
Day 1
Introductions and Basic Concepts
1
Introductions
Go over syllabus
Ch. 1.1 1.4
3
Math Review
What do we need?
Definition of derivative?
Easy derivatives / integrals?
Chain rule (changing variables in derivatives)
Vector calculus?
4
Differentiation
Ev