Problem 3.35
[Difficulty: 3]
Given:
Utube manometer with tubes of different diameter and two liquids, as shown.
d
1
10 mm
⋅
=
d
2
15 mm
⋅
=
SG
oil
0.85
=
Find:
(a) the deflection, h, corresponding to
(b) the sensitivity of the manometer
Δ
p
250
N
m
2
⋅
=
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
dp
dz
ρ
−
g
⋅
=
(Hydrostatic Pressure  z is positive upwards)
ρ
SG
ρ
water
⋅
=
(Definition of Specific Gravity)
h
AB
l
1
p
atm
l
2
l
w
l
3
l
4
p
atm
p
atm
+
Δ
p
p
atm
Assumptions:
(1) Static liquid
(2) Incompressible liquid
Integrating the hydrostatic pressure equation we get:
pp
o
−
ρ
−
g
⋅
zz
o
−
()
⋅
=
ρ
g
⋅
z
o
z
−
⋅
=
From the left diagram:
p
A
p
atm
−
ρ
water
g
⋅
l
1
⋅
=
ρ
oil
g
⋅
l
2
⋅
=
1
From the right diagram:
p
B
p
atm
Δ
p
+
−
ρ
water
g
⋅
l
3
⋅
=
2
p
B
p
atm
−
ρ
water
g
⋅
l
4
⋅
ρ
oil
g
⋅
l
2
⋅
+
=
3
Combining these three equations:
Δ
p
ρ
water
g
⋅
l
4
l
3
−
⋅
ρ
oil
g
⋅
l
2
⋅
+
=
ρ
water
g
⋅
l
4
l
1
+
l
3
−
⋅
=
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 Fall '07
 Lear
 Fluid Mechanics

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