Writing Force equation in terms of pressure and area

In summary: If the pressure is constant, the force is also constant. Therefore, in summary, when calculating the force in a fluid system, it is important to consider the pressure difference and the area of the surface in order to accurately determine the force.
  • #1
Beth N
41
4

Homework Statement


Problem 16.39
[/B]
The viscous force of a liquid in laminar flow through length L is given by ##F_v=4\pi\etaL v_m## where ##\eta## is liquid viscosity and ##v_m## is maximum velocity of the fluid. Find an expression for ##v_m## in terms of p1, p2 (pressure at each end) and in terms of ##\eta , L, r## (r is radius of pipe)

*I'm not solving the whole problem, but I have a question about force.
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Homework Equations



##F=p*A##

The Attempt at a Solution


I look at the key and see that they are equating ##F_v## with the pressure difference. Can it just be one pressure?
Is there a difference between representing force as pressure times area as they are (##F=p * A##), versus when one or both of the variables is changing? ( ##F=\Delta p * A## or ##F=p* \Delta A ##). It makes sense to me if both variables are not changing. But if they changes, does it mean the force is changing as well, so we should write the equation as ##\Delta F##?

Thank you!
 

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  • #2
F is the frictional tangential force at the wall, acting opposite to the direction of the fluid velocity.
 
  • #3
Chestermiller said:
F is the frictional tangential force at the wall, acting opposite to the direction of the fluid velocity.
Thank you, but I was just wondering what would be the difference between the force represented by ##pA## versus ##\Delta pA## or ##p\Delta A## . I know that the unit remains the same regardless but still, what would happen if one of the variables is changing. My question is not specific to the problem posted above.
 
  • #4
Beth N said:
Thank you, but I was just wondering what would be the difference between the force represented by ##pA## versus ##\Delta pA## or ##p\Delta A## . I know that the unit remains the same regardless but still, what would happen if one of the variables is changing. My question is not specific to the problem posted above.
If you know the pressure at a surface and the area of that surface, do you know how to get the force on the surface? Also, do you know how to perform a force balance (on a section of the fluid in a pipe) using a free body diagram?
 
  • #5
Chestermiller said:
If you know the pressure at a surface and the area of that surface, do you know how to get the force on the surface? Also, do you know how to perform a force balance (on a section of the fluid in a pipe) using a free body diagram?

The force is pressure times area. I think the force balance, as indicated in the problem, is the force caused by the pressure difference between the two ends of the pipe, and the force caused by the fluid's viscosity.
Oh, so there must be a difference in pressure or area in order for a force to exist? So writing in terms of ##pA## is incorrect? (Sorry I'm doing Algebra-based Physics, I think this might be clearer for someone who studies Calc-based physics)
 
  • #6
Beth N said:
The force is pressure times area. I think the force balance, as indicated in the problem, is the force caused by the pressure difference between the two ends of the pipe, and the force caused by the fluid's viscosity.
Oh, so there must be a difference in pressure or area in order for a force to exist? So writing in terms of ##pA## is incorrect? (Sorry I'm doing Algebra-based Physics, I think this might be clearer for someone who studies Calc-based physics)
If A is constant, then the difference of forces is A times Delta p.
 

1. What is the formula for calculating force in terms of pressure and area?

The formula for calculating force in terms of pressure and area is F = P x A, where F is force in newtons, P is pressure in pascals, and A is area in square meters.

2. How do you determine the direction of the force in this equation?

The direction of the force can be determined by the direction of the pressure. If the pressure is applied perpendicular to the surface, the force will also be perpendicular. If the pressure is applied at an angle, the force will have both vertical and horizontal components.

3. Can this equation be used for any shape or surface?

Yes, this equation can be used for any shape or surface as long as the pressure and area are measured at the same point. However, for irregular shapes, the area must be calculated by breaking it down into smaller, simpler shapes.

4. How does this equation relate to the concept of pressure?

This equation demonstrates the direct relationship between force and pressure. As the pressure increases, the force also increases proportionally. This is because pressure is defined as the force exerted per unit area.

5. Can the equation be rearranged to solve for pressure or area?

Yes, the equation can be rearranged to solve for pressure or area. To solve for pressure, the equation becomes P = F/A, and to solve for area, the equation becomes A = F/P. This allows us to calculate the missing variable if the other two are known.

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