Question about Hydrostatic Force?

In summary: That way you can integrate and find the total force by summing the forces on each triangle.In summary, the conversation discusses dealing with hydrostatic force in Calculus 2 and the use of integration to solve word problems. The main focus is on finding the width formula with respect to x and the similarities in solving for forces on equilateral triangles. The key is to set up a relation between depth and width to integrate and find the total force.
  • #1
Virang807
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Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I want to know the differences in solving both of them and trying to find the width formula with respect to x. Thank you!
 

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  • #2
Virang807 said:
Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I want to know the differences in solving both of them and trying to find the width formula with respect to x. Thank you!
There are no substantial differences in solving these problems; the regions are slightly different is all. If you can solve for the hydrostatic force on one triangle, you can solve for the force on the other.

The key here is you know that both triangles are equilateral, so you can figure their altitudes. What you want to do is set up a relation between the depth of the triangle below the attachment point and the width of the triangle at that depth.
 

Related to Question about Hydrostatic Force?

1. What is hydrostatic force?

Hydrostatic force refers to the force exerted by a fluid, such as water, on a submerged object or surface. It is caused by the weight of the fluid above the object or surface and is dependent on the density and depth of the fluid.

2. How is hydrostatic force calculated?

The formula for calculating hydrostatic force is F = ρghA, where F is the force in Newtons, ρ is the fluid density in kilograms per cubic meter, g is the acceleration due to gravity in meters per second squared, h is the depth of the fluid in meters, and A is the area of the surface in contact with the fluid in square meters.

3. What factors affect hydrostatic force?

The main factors that affect hydrostatic force include the density and depth of the fluid, as well as the surface area of the object or surface in contact with the fluid. Other factors that may impact hydrostatic force include the shape and orientation of the object or surface, as well as any external forces acting on it.

4. How is hydrostatic force used in real life?

Hydrostatic force has many practical applications in engineering and physics, such as in the design of dams, ships, and other structures that come into contact with water. It is also used in hydraulic systems, where fluids are used to generate and transmit power.

5. How does hydrostatic force differ from hydrodynamic force?

Hydrostatic force is caused by the weight of a fluid on a submerged object or surface, while hydrodynamic force is caused by the movement of a fluid past an object. Hydrodynamic force is typically larger and more complex to calculate, as it takes into account factors such as fluid velocity and viscosity.

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