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Problem 3.36
[Difficulty: 3]
Given:
Water column standin in glass tube
Δ
h5
0
m
m
⋅
=
D
2.5 mm
⋅
=
σ
72.8
10
3
−
×
N
m
=
(From Table A.4, App. A)
Find:
(a) Column height if surface tension were zero.
(b) Column height in 1 mm diameter tube
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
dp
dh
ρ
g
⋅
=
(Hydrostatic Pressure  h is positive downwards)
Δ
h
p
Δ
h
c
Δ
h
Δ
h
c
π
D
δ
θ
Mg
=
ρ
gV
Σ
F
z
0
=
(Static Equilibrium)
Assumptions:
(1) Static, incompressible liquid
(2) Neglect volume under meniscus
(3) Applied pressure remains constant
(4) Column height is sum of capillary rise and pressure
difference
Assumption #4 can be written as:
Δ
h
Δ
h
c
Δ
h
p
+
=
Choose a freebody diagram of the capillary rise portion of the column for analysis:
Σ
F
z
π
D
⋅
σ
⋅
cos
θ
()
⋅
π
4
D
2
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 Fall '07
 Lear
 Fluid Mechanics

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