Calculating Hydrostatic Force of a Submerged Semicircle

In summary, the hydrostatic force of a circle is the pressure exerted by a liquid on the surface of a circle due to its weight. It can be calculated by multiplying the density of the liquid by the depth and area of the circle. The factors that affect it include the density, depth, and area, while the shape of the container indirectly influences it. The real-world applications of this force include use in engineering, physics, and oceanography to design structures and study fluid behavior.
  • #1
tylu234
2
0

Homework Statement



There is a semicircle submerged in the water. The distance between the surface and the top of the semicircle is 2 ft, and the radius is 5 ft. Find the hydrostatic force.

The answer is 1.2 * 10^4 N.

Homework Equations



y = sqrt(25 - x2)

The Attempt at a Solution



w = 62.5

dA = sqrt(25-x2)dx
dF = w(7-x)sqrt(25-x2)dx
F = w∫(7-x)sqrt(25-x2)dx, limits of integration: 0, 5

Calculated and got this answer:
F ≈ 1.4 * 10^4 N

I think the (7 - x) part is wrong, or maybe the limits of intg.
 
Physics news on Phys.org
  • #2
bump, test in 20 minutes
 

Related to Calculating Hydrostatic Force of a Submerged Semicircle

1. What is the hydrostatic force of a circle?

The hydrostatic force of a circle is the amount of pressure exerted on the surface of a circle by a liquid due to its weight.

2. How is the hydrostatic force of a circle calculated?

The hydrostatic force of a circle can be calculated by multiplying the density of the liquid by the depth of the liquid and the area of the circle.

3. What factors affect the hydrostatic force of a circle?

The hydrostatic force of a circle is affected by the density of the liquid, the depth of the liquid, and the area of the circle.

4. How does the shape of the container affect the hydrostatic force of a circle?

The shape of the container does not directly affect the hydrostatic force of a circle, but it can affect the depth of the liquid and the area of the circle, which in turn can affect the overall force.

5. What are some real-world applications of the hydrostatic force of a circle?

The hydrostatic force of a circle is relevant in many fields, including engineering, physics, and oceanography. It is used to calculate the stability of ships, design dams and water tanks, and study the behavior of fluids in different environments.

Similar threads

Calculate this Integral around the Circular Path using Green's Theorem
    • Calculus and Beyond Homework Help
Replies
3
Views
384
How to Find Hydrostatic Force on a Submerged Plate?
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Calculate Hydrostatic Force on 4x3 ft Triangle in 6 ft Tank
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
Moment of the Hydrostatic Force on a body
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Hydrostatic forces on a hinged gate
    • Mechanics
Replies
4
Views
3K
Hydrostatic Force (Out of my Calc book)
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
Hydrostatic Force on a Plate: Solving with Reimann Sums and Integrals
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
Gradient and tangent plane/normal line
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
Finding Hydrostatic Force on the Plate
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
How Does Centroid Affect Hydrostatic Pressure Calculation?
    • Calculus and Beyond Homework Help
Replies
3
Views
4K

Hot Threads

Recent Insights

Back
Top