Naik, Sameer V.
Fall 2009
1000
Solution for Special Problem 3
Given:
- A double U-tube connecting two horizontal pipelines
- Density of sea water = 1035 kg/m
3
Find:
- Pressure difference between the pipelines
- Effect of air column
- Effect of an oil column instead of the air column
System:
Assumptions:
- Liquids are incompressible
Basic Equation(s):
atm
P
P
gL
ρ
=
+
Solution:
(a) Let the pressure in the fresh water pipeline be
P
1
and the pressure in the sea water
pipeline be
P
5
; the different points are as shown in the figure above.
As we move along
the manometer connecting the two pipelines, pressure increases when moving in the
downward direction while pressure decreases when moving in the upward direction.
We
can write:
1
5
freshwater
freshwater
mercury
mercury
air
air
seawater
seawater
P
gh
gh
gh
gh
P
ρ
ρ
ρ
ρ
+
−
−
+
=
Using Table A-19, we have:
3
kg
996
m
freshwater
ρ
=
;
3
kg
13,529
m
mercury
ρ
=
For STP conditions:
3
kg
1.2
m
air
ρ
=
Sea Water
Mercury
Air
60 cm
10 cm
70 cm
40 cm
1
2
3
4
5
Fresh Water

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