Solving Plane Pressure Problem: Finding the Line of Action

In summary, the conversation is about understanding equation 15.16 in the context of pressure on a plane. The person is requesting help in understanding how the equation was derived and the other person suggests finding the centroid as a possible explanation.
  • #1
Phys5
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Homework Statement


I am trying to study for an exam and a section in the book on pressure on a plane is shown in the attached picture. I am trying to understand how equation15.16 was derived. I know normally the line of action is found using moments so this seems to be a short cut but I can'tunderstand how the book got to this equation. Any help would be muchappreciated. Thanks![/B]

Homework Equations

The Attempt at a Solution

 

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  • #2
Equation 15.16 is illegible. Please post it with a better picture. Also post the relevant equations and your bet attempt at solving or understanding what is going on.
 
  • #3
I don't believe the issue is that they took some clever shortcut as it is that they plain just didn't say anything about how they got there. I am sure they just found the centroid as the that is pretty easy and I can't imagine there being anything shorter.

Write the pressure as a function of depth h and integrate

∫ h P(h) / ∫ P(h)

from h1 to h2.
 
  • #4
Cutter Ketch said:
∫ h P(h) / ∫ P(h)
This is not an equation. An equation has two sides. Which side is this, what is the other side and what is the equation supoosed to represent?
 
  • #5
Cutter Ketch said:
I am sure they just found the centroid
Or even just looked it up... Centroid of a trapezoid.
 

1. What is the definition of line of action in plane pressure problems?

The line of action in plane pressure problems refers to the imaginary line along which the total force acting on a surface is assumed to act. This line is perpendicular to the surface and passes through the centroid of the surface.

2. How do you find the line of action in a plane pressure problem?

To find the line of action in a plane pressure problem, you must first determine the total force acting on the surface. This can be done by calculating the pressure force on each individual element of the surface and then summing them together. Once the total force is known, the line of action can be found by drawing a vector diagram and finding the resultant force, which will pass through the centroid of the surface.

3. What is the importance of finding the line of action in a plane pressure problem?

The line of action is important because it helps to determine the stability and equilibrium of a structure. If the line of action falls outside of the base of the structure, it can cause the structure to topple or collapse. It is also important for calculating the bending moments and shear forces acting on the structure.

4. How does the shape of the surface affect the line of action in a plane pressure problem?

The shape of the surface can greatly affect the line of action in a plane pressure problem. The line of action is always perpendicular to the surface, so if the surface is curved, the line of action will also be curved. Additionally, the centroid of the surface will also change, which will impact the location of the line of action.

5. Can the line of action change in a plane pressure problem?

Yes, the line of action can change in a plane pressure problem. It depends on the direction and magnitude of the applied forces, as well as the shape and orientation of the surface. If any of these factors change, the line of action will also change. It is important to re-calculate the line of action if any of these factors change to ensure the stability and equilibrium of the structure.

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