Need help with understanding this solution (fluid pressure problem)

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In summary, the pressure is due to the oil and water mixture being at different levels, and the measurements are taken at the point where the oil meets the water.
  • #1
bigmike94
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I dont fully understand the solution
So here’s the question (I am only talking about the pressure at point B, the other 2 I can understand.)
94326FD6-597D-474F-94C3-9BCBC33DF58B.jpeg


And here is the solution
3C602BA6-4E95-403A-8973-BFE9E6853BB6.jpeg

B86A26B6-2AE9-4037-AB6F-1F0DF5EF36DD.jpeg


Here is what I am not understanding, why is the pressure due to the water negative and the oil positive, and why are all measurements only made from where the oil meets the water?

i must be missing something really obvious
 
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  • #2
bigmike94 said:
why are all measurements only made from where the oil meets the water?
Because that's how we find the difference between ##p_{atm}## and ##p_B##
Going down contributes a positive ##\Delta p## and up a negative ##\Delta p##.

One can just as well take the bottom as the turning point: the ##\Delta p## of the extra 1.25 m down is cancelled by ##\Delta p## going up the same 1.25 m

##\ ##
 
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  • #3
BvU said:
Because that's how we find the difference between ##p_{atm}## and ##p_B##
Going down contributes a positive ##\Delta p## and up a negative ##\Delta p##.

One can just as well take the bottom as the turning point: the ##\Delta p## of the extra 1.25 m down is cancelled by ##\Delta p## going up the same 1.25 m

##\ ##
Thank you that helped a lot. I attempt the problems quite a bit after I learnt about that method of finding the pressure. Hopefully I’ll remember it 😃
 
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  • #4
I think of the problem as moving along a path from the external reference surface to the destination, at point B.
1. Start at the surface with atmospheric pressure. Specify absolute or gauge pressure for the reference.
2. Compute the increasing hydrostatic pressure as you move down through the oil, to the oil-water interface surface.
3. Compute the reducing hydrostatic pressure as you move up through the oil to the destination at point B, on the water-air interface.
 
  • #5
bigmike94 said:
Here is what I am not understanding, why is the pressure due to the water negative and the oil positive, and why are all measurements only made from where the oil meets the water?

i must be missing something really obvious

This arrangement can be calculated like a U-shaped manometer, if you can imagine the bend located just underneath the central partition.

Please, see:
https://pressbooks.online.ucf.edu/osuniversityphysics/chapter/14-2-measuring-pressure/
 

Related to Need help with understanding this solution (fluid pressure problem)

1. What is fluid pressure?

Fluid pressure is defined as the force per unit area exerted by a fluid on its container or any object in contact with it. It is caused by the collisions of the fluid particles with the walls of the container or object.

2. How is fluid pressure calculated?

Fluid pressure can be calculated using the formula P = F/A, where P is the pressure, F is the force exerted by the fluid, and A is the area over which the force is applied. The SI unit for pressure is Pascal (Pa).

3. What is the difference between absolute and gauge pressure?

Absolute pressure is the total pressure exerted by a fluid, including atmospheric pressure. Gauge pressure, on the other hand, is the difference between the absolute pressure and the atmospheric pressure. It is often used to measure pressure changes in a system.

4. How does fluid pressure affect objects?

Fluid pressure can affect objects in different ways depending on their shape and orientation. For example, a flat surface will experience a greater force from fluid pressure compared to a curved surface. Additionally, objects will experience a net force in the direction of lower pressure.

5. How is fluid pressure used in real-world applications?

Fluid pressure has many practical applications in various industries, such as hydraulics, aerodynamics, and hydrology. It is used to design and operate systems like hydraulic lifts, aircraft wings, and dams. It is also important in understanding weather patterns and predicting natural disasters like hurricanes and floods.

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