Vertical hydrostatic force acting upwards on a curved surface?

In summary, the equation F_y = ρghcA is used to analyze the forces on a specific region of water, treated as a block. The hc value of 5m is taken from the bottom of the region, as it is bounded by a vertical line through point A and a quadrant of the cylinder. The Fy value represents the vertically upward force on the block from the floor of the chamber, which must be equal and opposite to the force exerted by the block on the floor. This pressure is equivalent to the pressure at a depth of 5m.
  • #1
theBEAST
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Homework Statement


I am only confused about F_y.

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The Attempt at a Solution


I don't understand why in the equation F_y = ρghcA, the hc is 5m. Why do they take the centroid distance to be the very bottom?
 
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  • #2
They're analysing the forces on a particular region of the water, treated as a block. It's the region lying 'under' the cylinder, i.e. it's bounded by a vertical line through point A, the floor of the chamber, and a quadrant of the cylinder. Fy is the vertically upward force on this block from the floor of the chamber. It must be equal and opposite to the force the block exerts on the floor. The pressure there is the pressure at 5m depth.
 

FAQ: Vertical hydrostatic force acting upwards on a curved surface?

1. What is vertical hydrostatic force?

Vertical hydrostatic force is the force exerted by a fluid, such as water, on an object or surface in a vertical direction due to the pressure of the fluid.

2. How is the vertical hydrostatic force calculated?

The vertical hydrostatic force is calculated by multiplying the density of the fluid by the acceleration due to gravity and the height of the fluid column above the object or surface.

3. How does the curved surface affect the vertical hydrostatic force?

The curved surface creates a varying pressure distribution, causing the vertical hydrostatic force to also vary along the surface. This force is typically highest at the lowest point of the curve and decreases towards the edges.

4. What factors can affect the vertical hydrostatic force on a curved surface?

The factors that can affect the vertical hydrostatic force on a curved surface include the shape and curvature of the surface, the density and depth of the fluid, and the acceleration due to gravity.

5. How is the vertical hydrostatic force used in practical applications?

The vertical hydrostatic force is used in various engineering and scientific applications, such as designing dams and levees, calculating buoyant forces on ships, and understanding the mechanics of fluid flow in pipelines and channels.

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