Which area should I use to calculate the force on a submerged surface?

In summary, when calculating the force applied by a liquid on a wall, you should only consider the area of the wall that is in contact with the liquid. This is because the pressure is not constant and increases with depth, requiring an integral to be done. However, an integral taken over the entire area will yield the same result as one taken over the area where the pressure is non-zero.
  • #1
rbmartel
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In order to find the resultant force applied to a submerged vertical wall, which area should I consider?
Let's say we have a tank filled with water only half way up. I want to calculate the force being applied by the liquid on one of the walls, that's F = P.A. For the area (A), should I consider the area of the entire wall (H.L), or only the area of the wall that's in contact with the liquid ((H/2).L).
I'm having a hard time trying to understand if I should or shouldn't include in the calculations the part of the wall that is not in contact with the water.
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  • #2
You should take area in contact with liquid. If the upper part is in contact with air, you may have to consider air pressure on that part.
 
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  • #3
You also need to consider that the total force is pressure times area only if the pressure is constant. Here the pressure is not constant because it increases with depth. You will have to do an integral.
 
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  • #4
kuruman said:
You also need to consider that the total force is pressure times area only if the pressure is constant. Here the pressure is not constant because it increases with depth. You will have to do an integral.
And, of course, an integral taken over the whole area will yield the same result as an integral taken over the area where the pressure is non-zero.
 

1. What is the formula for calculating the force on a submerged surface?

The formula for calculating the force on a submerged surface is F = ρghA, where F is the force in Newtons, ρ is the density of the fluid, g is the acceleration due to gravity, h is the depth of the submerged surface, and A is the area of the submerged surface.

2. How do I determine the area to use in the force calculation?

The area to use in the force calculation is the projected area of the submerged surface, which is the area that is perpendicular to the direction of the force. For example, if the submerged surface is a rectangle, the area to use would be the length multiplied by the width.

3. Is the force on a submerged surface always equal to the weight of the fluid above it?

No, the force on a submerged surface is not always equal to the weight of the fluid above it. This is because the weight of the fluid above the submerged surface is distributed over the entire surface area, while the force is only acting on the projected area.

4. Can I use the same formula for calculating the force on a submerged surface in any fluid?

Yes, the formula for calculating the force on a submerged surface can be used in any fluid as long as the density and acceleration due to gravity are known. However, the shape and orientation of the submerged surface may affect the calculation.

5. How does the depth of the submerged surface affect the force calculation?

The depth of the submerged surface directly affects the force calculation. As the depth increases, the force also increases due to the increased pressure of the fluid. This is reflected in the formula as h, the depth, is a factor in the calculation.

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