Problem 3.24
[Difficulty: 2]
c
d
e
Given:
Data on manometer
Find:
Gage pressure at point a
Assumption:
Water, liquids A and B are static and incompressible
Solution:
Basic equation
dp
dy
ρ
−
g
⋅
=
or, for constant
ρ
Δ
p
ρ
g
⋅
Δ
h
⋅
=
where
Δ
h is height difference
Starting at point a
p
1
p
a
ρ
H2O
g
⋅
h
1
⋅
−
=
where
h
1
0.125 m
⋅
0.25 m
⋅
+
=
h
1
0.375m
=
Next, in liquid A
p
2
p
1
SG
A
ρ
H2O
⋅
g
⋅
h
2
⋅
+
=
where
h
2
0.25 m
⋅
=
Finally, in liquid B
p
atm
p
2
SG
B
ρ
H2O
⋅
g
⋅
h
3
⋅
−
=
where
h
3
0.9 m
⋅
0.4 m
⋅
−
=
h
3
0.5m
=
Combining the three equations
p
atm
p
1
SG
A
ρ
H2O
⋅
g
⋅
h
2
⋅
+
()
SG
B
ρ
H2O
⋅
g
⋅
h
3
⋅
−
=
p
a
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 Fall '07
 Lear
 Fluid Mechanics, SGA⋅ ρH2O⋅ g⋅, SGB⋅ ρH2O⋅ g⋅, ρH2O⋅ g⋅, ρH2O⋅ g⋅ h3

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