How to Solve Hydrostatics Problems with Curved Surfaces?

In summary, the conversation discusses a problem with a curved dam and how to find the force and area using integration. The force at each point of the dam is normal to the surface and the pressure is the same in every direction. The angle on strut BC may be missing and it is suggested to draw a free-body diagram and set up an applicable integral.
  • #1
Fionn00
12
0
Hi I am really stuck on this problem and would greatly appreciate some help.

Homework Statement



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Homework Equations


The Attempt at a Solution



I would be able to solve this if the dam wasn't curved. I would just use integration to find the magnitude of the force f = pghA. I would express a in h and integrate from 0 to 3. and then the direction would be at right angles to the wall but this is curved so I don't know how to find the force or how to express the area in h.

Thanks for help.
I know hot to calculate the moments and get the solution once I have the magnitude and position of the force.
 
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  • #2
Hi Fionn00! :smile:

The force at each point of the dam is normal to the surface, and the force per area is pressure (which of course is the same in every direction at any particular point). :wink:
 
  • #3
Can I postulate that the overturning moment about A is independent of the shape of the dam cross-section? In other words use pressure distribution as if the dam was vertical and use the projected (vertical) area.
 
  • #4
but the pressure is always perpendicular to the dam, so surely the angle does matter?
 
  • #5
Isn't the angle on strut BC missing?

Fionn00: Because you know how to do an integration, try drawing a free-body diagram (FBD), and set up an integral that is applicable to the situation at hand.
 
  • #6
Sorry for post #3. I stand corrected.
 

Related to How to Solve Hydrostatics Problems with Curved Surfaces?

1. What is hydrostatics?

Hydrostatics is the study of fluids at rest and the forces that act on them. It is a branch of fluid mechanics that deals with the properties and behavior of fluids under the influence of gravity or other external forces.

2. What is a hydrostatics problem?

A hydrostatics problem is a mathematical or physical problem that involves analyzing the forces and pressures exerted by fluids at rest. These problems often involve calculating the buoyant force, pressure at a given depth, or the equilibrium of an object submerged in a fluid.

3. How do you solve a hydrostatics problem?

To solve a hydrostatics problem, you will need to apply the principles of hydrostatics, such as Pascal's law and Archimedes' principle, to the given situation. This usually involves setting up and solving equations that describe the balance of forces and pressures acting on the fluid and any submerged objects.

4. What are some real-world applications of hydrostatics?

Hydrostatics has many practical applications, such as in the design of ships, submarines, and other marine vessels. It is also used in the construction of dams, bridges, and other structures that interact with water. Additionally, hydrostatics is important in understanding the behavior of fluids in the human body and can be applied in medical fields, such as cardiology and respiratory therapy.

5. What are some common mistakes when solving hydrostatics problems?

Some common mistakes when solving hydrostatics problems include not properly considering all the forces and pressures acting on the fluid, using incorrect units or conversion factors, and not properly setting up the equations to solve for the desired variable. It is also important to be careful with assumptions and to double-check calculations for accuracy.

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