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Thermodynamics -- Double U Tube Manometer with 2 Closed Ends
GIVEN:
Fresh water and sea water in parallel horizontal pipelines are connected to each other by a double U tube manometer.
Density of sea water is 1035 kg/m^3
Density of air is 1.2 kg/m^3
Standard temp and pressure
A link to the relevant diagram is here:
https://engineering.purdue.edu/ME200/Fall%202009/SpecialProblems/SpecialProblems3-5.pdf"
FIND:
a) Pressure difference between the pipelines
b) Can the air column be ignored in your analysis?
c) If the air is replaced with oil of specific gravity 0.72, then what is the pressure difference in kPa between the two pipelines? Can the oil column be neglected?
P-Patm = rho * g * h of liquid
The problem I am running into is that each end of the manometer is closed so I'm not sure how to find an initial pressure. If one end were open to atmospheric pressure I think I could find the pressure difference and work my way back, if that makes sense. However since both ends are closed "bulbs" of sea and fresh water, I'm not really sure where to start.
Right now I have labeled the point where the fresh water meets the mercury as point a, the point in the mercury at that same level as point b, the point where the air meets the sea water as point d, and the point at that same level as point c. I am thinking that I can then use the rho*g*l equation somehow, I'm just unclear as to how since Patm isn't evident. Pressure at point a and point be should be equal though, and pressure at point c and point d should be equal.
I am thinking that there is some sort of equivalency I can use or something... I have the entire manometer hookup as my system but perhaps that is where I am going wrong.
I am sorry I don't have much worked out, if anyone can even give me some hints as to a starting point I would appreciate it greatly.
Thanks!
Homework Statement
GIVEN:
Fresh water and sea water in parallel horizontal pipelines are connected to each other by a double U tube manometer.
Density of sea water is 1035 kg/m^3
Density of air is 1.2 kg/m^3
Standard temp and pressure
A link to the relevant diagram is here:
https://engineering.purdue.edu/ME200/Fall%202009/SpecialProblems/SpecialProblems3-5.pdf"
FIND:
a) Pressure difference between the pipelines
b) Can the air column be ignored in your analysis?
c) If the air is replaced with oil of specific gravity 0.72, then what is the pressure difference in kPa between the two pipelines? Can the oil column be neglected?
Homework Equations
P-Patm = rho * g * h of liquid
The Attempt at a Solution
The problem I am running into is that each end of the manometer is closed so I'm not sure how to find an initial pressure. If one end were open to atmospheric pressure I think I could find the pressure difference and work my way back, if that makes sense. However since both ends are closed "bulbs" of sea and fresh water, I'm not really sure where to start.
Right now I have labeled the point where the fresh water meets the mercury as point a, the point in the mercury at that same level as point b, the point where the air meets the sea water as point d, and the point at that same level as point c. I am thinking that I can then use the rho*g*l equation somehow, I'm just unclear as to how since Patm isn't evident. Pressure at point a and point be should be equal though, and pressure at point c and point d should be equal.
I am thinking that there is some sort of equivalency I can use or something... I have the entire manometer hookup as my system but perhaps that is where I am going wrong.
I am sorry I don't have much worked out, if anyone can even give me some hints as to a starting point I would appreciate it greatly.
Thanks!
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