Problem 1.12
[Difficulty: 3]
mg
kV
t
Given:
Data on sphere and terminal speed.
Find:
Drag constant
k
, and time to reach 99% of terminal speed.
Solution:
Use given data; integrate equation of motion by separating variables.
The data provided are:
M
1
10
13
−
×
slug
⋅
=
V
t
0.2
ft
s
⋅
=
Newton's 2nd law for the general motion is (ignoring buoyancy effects)
M
dV
dt
⋅
M g
⋅
k V
⋅
−
=
(1)
Newton's 2nd law for the steady state motion becomes (ignoring buoyancy effects)
M g
⋅
k V
t
⋅
=
so
k
M g
⋅
V
t
=
k
1
10
13
−
×
slug
⋅
32.2
×
ft
s
2
⋅
s
0.2 ft
⋅
×
lbf s
2
⋅
slug ft
⋅
×
=
k
1.61
10
11
−
×
lbf s
⋅
ft
⋅
=
dV
g
k
M
V
⋅
−
dt
=
To find the time to reach 99% of
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 Fall '07
 Lear
 Fluid Mechanics

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