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1354
CHAPTER 10. VORTICITY, VISCOSITY, LIFT AND DRAG
10.28
Chapter 10, Problem 28
Problem:
The horizontal speed,
u
, of a baseball thrown by a professional baseball
pitcher is accurately approximated by the equation
mdu/dt
=
−
π
8
ρ
D
2
C
D
u
2
,whe
re
m
,
D
and
C
D
are the ball’s mass, diameter and drag coefficient, respectively. Also,
ρ
is
the density of air.
(a) If
C
D
is constant, the distance from the pitcher’s mound to home plate is
f
and
the pitcher releases the ball with a speed
u
o
, verify that the time for a baseball
to travel from pitcher to batter is
t
=
8
m
πρ
D
2
C
D
u
o
±
e
πρ
D
2
C
D
f
/
(8
m
)
−
1
=
(b) Consider two pitchers, one with a 90mph fastball and the other with a 100mph
fastball. Referring to Figure 10.9, convince yourself that
C
D
≈
0
.
40
and
0
.
20
for 90mph and 100mph fastballs, respectively.
D
=3
inches and the kinematic
viscosity of air is
ν
=1
.
62
·
10
−
4
ft
2
/sec.
NOTE:
The rapid drop in
C
D
occurs
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This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.
 Spring '06
 Phares

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