Download Lecture 23

M E 433
Professor John M. Cimbala
Lecture 23
Today, we will:
•
Finish deriving the equation of motion for a particle in air flow
•
Show how to determine the direction of force (and acceleration) on a particle in air flow
•
Discuss drag coefficient and use it in the equation of motion for particle trajectories
•
Discuss the Cunningham correction factor (small particles; free molecular flow effects)
→
U
Example: Direction of drag force
Given: A small particle is moving through the air

at velocity v as sketched to the right. At the
location of the particle, and
 at a given instant in
time, the air velocity is U as also sketched.
→
v
Streamline
Particle
To do: Which is the correct direction of the drag
force on the particle? Text your answer as “a”,
“b”, or “c”, without the quotes.
→
U
→
U
(a)
→
→
U
(b)
→
v
v
→
(c)
Fdrag
→
Fdrag
Particle
Particle
Particle
→
Fdrag
Solution:
→
v
→
U
→ →
vr = v - U
→
→
Fdrag
Particle
Do a vector
summation. (a) is
the correct answer.
→
-U
→
v
Example: Direction of drag force
→
U
Given: A small particle is moving through the air

at velocity v as sketched to the right. At the
location of the particle, and
 at a given instant in
time, the air velocity is U as also sketched.
Streamline
Particle
To do: Which is the correct direction of the drag
force on the particle? Text your answer as “a”,
“b”, or “c”, without the quotes.
→
U
→
U
(a)
→
v
→
U
(b)
→
(c)
Fdrag
→
Fdrag
Particle
Particle
Particle
→
Fdrag
→
→
v
v
Solution:
→
U
→
Do a vector
summation. (c) is
the correct answer.
Fdrag
Particle
→
-U
→
v
→ →
vr = v - U
→
→
v