Calculating the pressure on a surface exerted by opposing forces?

  • #1

Main Question or Discussion Point

Suppose there is a circle with area 'A' and on one of the faces of the circle a force of 100N is applied and on the other face a 30N force is applied (since all 2D surfaces have 2 faces) such that these forces are opposite to each other, perpendicular to the faces, and forces are equally distributed on the surface, then what will be the pressure on any point of the surface? Will it be 100/A or (100-30)/A=70/A or (100+30)/A=130/A and why?
 

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  • #2
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The pressure will be 100/A on one side and 30/A on the other side. The different pressure on each side will lead to acceleration.
 
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  • #3
CWatters
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You didn't say anything about the disc being constrained so it will accelerate as Dale says.

Is the disc constrained? Perhaps its a rigid window in the wall between two tanks of water at different pressures?
 
  • #4
The pressure will be 100/A on one side and 30/A on the other side. The different pressure on each side will lead to acceleration.
thank you for replying, but are you saying that each point on the surface will have 2 values of pressure ? In hydrostatics I was told that each point of the liquid will have only one pressure value by Pascal's law(P=p+xdg, where p is pressure at free surface, g is g effective(resultant of pseudo acceleration and g) and x is the distance of the point from free surface along the direction of g effective), if the container accelerates
 
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  • #5
LURCH
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When working with pressurized systems in most applications, we nearly always refer to pressure in the term “gauge pressure “. Gauge pressure is the difference between pressure on one side of a surface and that on the other side. For most applications, this is the pressure that matters. In fact, if you have an air compressor nearby, you can look at the pressure gauge and it probably says “”PSIG”, which stands for the pressure in units “per square inch; gauge”.

It is this pressure differential that makes fluid-powered systems go, or tells us how close we are getting to the maximum pressure a vessel can handle. For example; if a pressure vessel is rated to hold 20 lbs psi, what that really means is that it can hold 20 psi more than the pressure on the outside. If the vessel has 30 lbs of absolute pressure inside, and 14 lbs on the outside, it will be fine. Similarly, if the vessel is under water, with 50 lbs of absolute pressure on the outside and 60 lbs absolute on the inside, we’re still ok. However, if you fill it to 60 when it’s down deep, and then bring it up to the surface, it’s going to burst.

An instrument that only shows you the absolute pressure would give no warning, because the absolute pressure doesn’t change. But a gauge that shows pressure differential , or Gauge Pressure, will start to climb as soon as external pressure begins to drop.

There are some practical applications for which absolute pressure is important, like chemistry and biology, but most of the time, gauge pressure is the important value.
 
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  • #6
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are you saying that each point on the surface will have 2 values of pressure ?
Perhaps you should provide more detail about your scenario. I was envisioning a metal disk with pressure applied on both sides of the disk.
 
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  • #7
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If your circle is truly 2D and flat, it has no mass, and you can't sustain a pressure difference across it. If you try, you will have an infinite rate of acceleration. In systems involving a massless frictionless piston, the pressures on both faces of the piston must always match irrespective of how rapidly the gas is expanding or compressing.
 
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  • #8
If your circle is truly 2D and flat, it has no mass, and you can't sustain a pressure difference across it. If you try, you will have an infinite rate of acceleration. In systems involving a massless frictionless piston, the pressures on both faces of the piston must always match irrespective of how rapidly the gas is expanding or compressing.
I was talking about theoretical case like those involving calculations on moment of inertia of circles, rectangles about a axis etc, assuming they have weight and dealing with 1 dimensional objects (points) in force and laws of motion.
 
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  • #9
Perhaps you should provide more detail about your scenario. I was envisioning a metal disk with pressure applied on both sides of the disk.
Yes the disk is a metal one. Its just that a single point on disk having two pressure 100/A on one side and 30/A on the other was something unusal because i have mostly calculated only one pressure value for a point.
 
  • #10
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Yes the disk is a metal one. Its just that a single point on disk having two pressure 100/A on one side and 30/A on the other was something unusal because i have mostly calculated only one pressure value for a point.
Think about the hull of a submarine. It has a huge pressure outside and a low pressure inside.
 
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  • #11
CWatters
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Think about the hull of a submarine. It has a huge pressure outside and a low pressure inside.
And if you wonder why the walls of a sub don't accelerate due to the huge pressure difference its because there are other forces acting on the walls so the net force on any bit of wall is zero (assuming the sub is stationary).
 
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