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Problem 1.11
[Difficulty: 3]
Given:
Data on sphere and formula for drag.
Find:
Maximum speed, time to reach 95% of this speed, and plot speed as a function of time.
Solution:
Use given data and data in Appendices, and integrate equation of motion by separating variables.
The data provided, or available in the Appendices, are:
ρ
air
1.17
kg
m
3
⋅
=
μ
1.8
10
5
−
×
Ns
⋅
m
2
⋅
=
ρ
w
999
kg
m
3
⋅
=
SG
Sty
0.016
=
d
0.3 mm
⋅
=
Then the density of the sphere is
ρ
Sty
SG
Sty
ρ
w
⋅
=
ρ
Sty
16
kg
m
3
=
The sphere mass is
M
ρ
Sty
π
d
3
⋅
6
⋅
=
16
kg
m
3
⋅
π
×
0.0003 m
⋅
()
3
6
×
=
M
2.26
10
10
−
×
kg
=
Newton's 2nd law for the steady state motion becomes (ignoring buoyancy effects)
Mg
⋅
3
π
⋅
V
⋅
d
⋅
=
so
V
max
⋅
3
π
⋅
μ
⋅
d
⋅
=
1
3
π
⋅
2.26
10
10
−
×
×
kg
⋅
9.81
×
m
s
2
⋅
m
2
1.8
10
5
−
×
N
⋅
s
⋅
×
1
0.0003 m
⋅
×
=
V
max
0.0435
m
s
=
Newton's 2nd law for the general motion is (ignoring buoyancy effects)
M
dV
dt
⋅
⋅
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics

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