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Problem 1.7
[Difficulty: 3]
Given:
Small particle accelerating from rest in a fluid. Net weight is W, resisting force
F
D
= kV, where V
is speed.
Find:
Time required to reach 95 percent of terminal speed, V
t
.
Solution:
Consider the particle to be a system. Apply Newton's second law.
Basic equation:
∑
F
y
= ma
y
Assumptions:
1.
W is net weight
2.
Resisting force acts opposite to V
Then
F
yy
∑
=−
=
=
Wk
V
=m
a
dt
m
dV
W
g
dV
dt
or
dV
dt
g(1
k
W
V)
Separating variables,
dV
1V
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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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