# Is the pressure equal everywhere here?

• anonymous99
In summary: The pressure at the bottom depends only on the height of the water column on that side.So, if you add more water to one side of the manometer, the pressure on the other side will increase?If you add more water to one side of the manometer, the pressure on the other side will increase.
anonymous99
Homework Statement
Consider the picture below. I know the pressure is constant across the green line because pressure is fixed at a given depth. However, assume the red lines are physical boundaries. Would the pressure still be constant across the green line? My reasoning is no because inside the two red line boundaries, there is a smaller layer of water above so less pressure from the weight of thee water above whereas at the left/right sides there is a larger layer so more pressure. But if the pressure is unequal at either side of the red line, then the boundary should move until pressure equalizes so is my reasoning incorrect?
Relevant Equations
s

what kind of physical boundaries? You imply they can move but that's not much of a description.

I was thinking like a piston in a cylinder.

anonymous99 said:
I was thinking like a piston in a cylinder.
Well, if it's completely moveable (no friction) then it is irrelevant to the description of pressure and can be left out of the discussion.

Chestermiller
phinds said:
Well, if it's completely moveable (no friction) then it is irrelevant to the description of pressure and can be left out of the discussion.
I see. Is that because it would just end up moving until pressure is equalized? What if it was a fixed boundary. Then pressure must be unequal on both sidies right?

If the system is in static equilibrium, the pressure does not vary horizontally, irrespective of any boundaries.

Chestermiller said:
If the system is in static equilibrium, the pressure does not vary horizontally, irrespective of any boundaries.
Hmm. But how would the pressure be equal if the weight of water above is different inside and outside the boundary? Can they not be considered as two separate systems now.

@Anonymous 69 it may just be me but I find your question(s) ill formed. You seem to keep jumping from on scenario to another but considering them the same. Try to describe ONE scenario, and be VERY precise about the conditions and exactly what it is you are confused about.

PhDeezNutz and etotheipi
anonymous99 said:
Hmm. But how would the pressure be equal if the weight of water above is different inside and outside the boundary? Can they not be considered as two separate systems now.
Have you drawn a free body diagram of the water in the horizontal section, or do you feel that you’ve advanced beyond the need to use free body diagrams?

Chestermiller said:
Have you drawn a free body diagram of the water in the horizontal section, or do you feel that you’ve advanced beyond the need to use free body diagrams?
Yes and from my FBD it seems the pressure is different but I think I might be wrong. At a certain point on the green line inside the boundaries, the fluid particle experiences a force equal to the weight of the water above and this is balanced by an equal force from below. Since pressure is isotropic, forces in the x-direction on the particle are equal to this force too. Now, for a point on the same line at the left/right sides of the manometer, there is a larger weight of water above and thus more force = more presssure.

What does your horizontal force balance tell you?

Can we make this
anonymous99 said:
Now, for a point on the same line at the left/right sides of the manometer, there is a larger weight of water above and thus more force = more presssure.
Are the pressures on the tops of the columns of water on each side of the manometer equal?

If not, then why would you think that the pressure at the bottom depends only on the height of the water column on that side?

Chestermiller

## 1. What is pressure and how is it measured?

Pressure is the force per unit area exerted by a fluid or gas. It is typically measured in units of Pascals (Pa) or pounds per square inch (psi).

## 2. Why is it important to know if pressure is equal everywhere?

Knowing if pressure is equal everywhere is important in understanding the behavior of fluids and gases in a system. It can help determine if there are any imbalances or irregularities that could affect the performance of the system.

## 3. How can we determine if pressure is equal everywhere in a given space?

Pressure can be measured using pressure gauges or sensors placed at different points in the space. These readings can then be compared to determine if pressure is equal throughout.

## 4. What factors can cause pressure to be unequal in a space?

Unequal pressure can be caused by differences in temperature, elevation, or the presence of obstacles or barriers within the space. Changes in fluid or gas flow can also affect pressure distribution.

## 5. How does the concept of pressure relate to other scientific principles?

Pressure is closely related to other scientific principles such as fluid dynamics, thermodynamics, and atmospheric science. It is also a key factor in many engineering applications, including hydraulics, aerodynamics, and HVAC systems.

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