Hydro static forces on curved surfaces

This is because the weight of the column of water above the arc would balance out the pressure exerted by the liquid on the arc.In summary, the 'missing water' in the solution diagram refers to the hypothetical water that would need to be present in order for the pressure on the arc AB to be balanced. Without this water, there is a net pressure acting on the arc, which is why the diagram shows a different water level on the inside and outside of the tank.
  • #1
princejan7
93
0

Homework Statement


http://postimg.org/image/4fhu5k9r9/

Can someone explain what is meant by 'missing water' in this solution diagram
The original question diagram had no such water above the gate AB

Homework Equations


The Attempt at a Solution

 
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  • #2
princejan7 said:

Homework Statement


http://postimg.org/image/4fhu5k9r9/

Can someone explain what is meant by 'missing water' in this solution diagram
The original question diagram had no such water above the gate AB

Homework Equations


The Attempt at a Solution


By Pascal's Law, the hydrostatic pressure on the wetted portion of the arc AB at a given depth h from the free surface of the liquid is the same as the pressure exerted by a column of liquid of depth h placed on the outside of the arc.

If the region indicated by 'missing water' on the diagram was filled with water, there would be no net pressure acting on the arc AB, i.e., the pressure outside the arc would be the same as the pressure inside the tank.
 
Last edited by a moderator:

Related to Hydro static forces on curved surfaces

1. What is meant by hydrostatic forces on curved surfaces?

Hydrostatic forces on curved surfaces refer to the pressure exerted by a fluid at rest on a curved surface. This force is perpendicular to the surface and is a result of the weight of the fluid above the surface.

2. How do you calculate hydrostatic forces on a curved surface?

The hydrostatic force on a curved surface can be calculated using the formula F = ρgV, where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the fluid above the curved surface.

3. What factors affect the hydrostatic force on a curved surface?

The hydrostatic force on a curved surface is affected by the density and weight of the fluid, the shape and size of the curved surface, and the depth at which the surface is submerged in the fluid.

4. What is the significance of hydrostatic forces on curved surfaces in engineering?

Hydrostatic forces on curved surfaces play a crucial role in designing structures that are submerged in fluids, such as ships, dams, and underwater pipelines. Understanding and accurately calculating these forces is essential for ensuring the stability and safety of these structures.

5. How do hydrostatic forces on curved surfaces differ from those on flat surfaces?

Hydrostatic forces on curved surfaces are distributed over the entire surface, whereas on flat surfaces, they are concentrated at a single point. Additionally, the magnitude and direction of the hydrostatic force on a curved surface vary at different points, while on a flat surface, they are uniform.

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