Hydrostatic forces on a curved surface

In summary, the forces acting on the cylinder are: -Horizontal: Fx = FH = ρghcA = (1000 kg/m3) (9.81 m/s2) [4.2 m + (0.8 m/2)] (0.8 m*1 m)-Vertical: Fy = -Fz
  • #1
rcummings89
19
0
Hello,

I'm trying to go through an example problem in a fluid dynamics textbook, and I'm having trouble understanding some of their logic. The problem deals with a solid cylinder of radius 0.8 m hinged at its midpoint that opens when the water it holds back reaches 5 m, and it is asking for the hydro-static forces acting on the cylinder, where the center of the cylinder is 4.2 m below the surface (see attached picture).

Their solution...

For the horizontal force: Fx = FH = ρghcA = (1000 kg/m3) (9.81 m/s2) [4.2 m + (0.8 m/2)] (0.8 m*1 m)

Now, I understand it up until the last part that deals with the area. Firstly, the 1 m length is never mentioned, is this just a typical assumption? Also (probably me missing something very basic here) but what area is radius * length?

For Fy they use the same area component, but when they calculate the weight they use the formula:

W = ρgV = ρg(R2 - πR2/4)(1) = (1000 kg/m3) (9.81 m/s2) (0.8 m)2 (1-π/4) (1 m)

And again, my question is, what area are they using (multiplied by 1 m) to calculate the volume?

Thanks in advance!
 

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  • #2
1. If you are not told the length of the apparatus, then a per meter basis (or L = 1 m) is reasonable, assuming no changes in the shape of the apparatus.
2. The Area = R * L is the projected area at the bottom of the outlet (see the inset figure in the lower right hand corner of your attachment.
3. Again, see the lower right hand corner of your attachment. The weight they are calculating is that of the lightly shaded portion where the letter 'W' is located.
 
  • #3
Ok, I think I understand. When they say "R" I kept thinking of circles and kept trying to find area formulas related to circles. I didn't realize they were just using R as the length of the side...

Thanks SteamKing!
 

1. What is the definition of hydrostatic forces on a curved surface?

Hydrostatic forces on a curved surface refer to the pressure exerted by a fluid on a curved surface due to the weight of the fluid above it.

2. How are hydrostatic forces on a curved surface calculated?

Hydrostatic forces on a curved surface can be calculated using the formula F = ρghA, where F is the total force, ρ is the density of the fluid, g is the acceleration due to gravity, h is the depth of the fluid, and A is the area of the curved surface.

3. What is the difference between hydrostatic forces on a flat surface and a curved surface?

Hydrostatic forces on a flat surface are calculated using the formula F = ρghA, where A is the area of the flat surface. On the other hand, hydrostatic forces on a curved surface take into account the curvature of the surface and use the formula F = ρghAcosθ, where θ is the angle between the normal vector to the surface and the vertical direction.

4. How do hydrostatic forces on a curved surface affect the stability of an object?

Hydrostatic forces on a curved surface can either provide stability or cause instability depending on the shape of the object and the direction of the forces. Objects with a lower center of mass and a wider base are more stable against hydrostatic forces.

5. What are some real-world applications of hydrostatic forces on a curved surface?

Hydrostatic forces on a curved surface are commonly used in engineering and design, such as in the design of dams, ships, and submarines. They are also important in understanding fluid dynamics and the behavior of fluids in various systems, such as in weather patterns and ocean currents.

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