Calculating Hydrostatic Force of a Submerged Semicircle

Click For Summary
SUMMARY

The hydrostatic force acting on a submerged semicircle with a radius of 5 ft and a distance of 2 ft from the water surface is calculated to be approximately 1.2 x 10^4 N. The weight density of water used in the calculations is 62.5 lb/ft³. The integral setup for the force calculation is given by F = w∫(7-x)sqrt(25-x²)dx, with limits of integration from 0 to 5. A discrepancy in the calculated force of approximately 1.4 x 10^4 N suggests a potential error in the (7 - x) term or the integration limits.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of weight density of fluids, particularly water
  • Ability to interpret geometric shapes in fluid mechanics
NEXT STEPS
  • Review the derivation of hydrostatic force formulas for submerged shapes
  • Practice integration techniques involving square roots in calculus
  • Explore the concept of centroid in fluid mechanics
  • Investigate common mistakes in setting up limits of integration for area calculations
USEFUL FOR

Students in engineering or physics courses, particularly those studying fluid mechanics, as well as educators looking for examples of hydrostatic force calculations.

tylu234
Messages
2
Reaction score
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
bump, test in 20 minutes
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
3
Views
2K
Replies
9
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 5 ·
Replies
5
Views
12K
  • · Replies 2 ·
Replies
2
Views
5K
Replies
1
Views
8K
  • · Replies 3 ·
Replies
3
Views
4K