Applications of Integrals · Work & Force
Hydrostatic Force
The force of fluid pressure on a submerged vertical surface, where d(y) is the depth and w(y) is the width at depth y.
- 0 variables
- 2 worked examples
- 14 in Applications of Integrals
Worked examples
Find the hydrostatic force on a vertical square plate (2m × 2m) with top edge at water surface (ρ = 1000 kg/m³).
- Width w(y) = 2 at all depths. Depth d(y) = y, y from 0 to 2.
- F = ∫₀² 1000(9.8)(y)(2) dy = 19600 ∫₀² y dy = 19600[y²/2]₀² = 19600(2) = 39200 N
Answer: 39,200 N = 39.2 kN
1 more worked examplePremium
A vertical rectangular plate is 3 m wide and 2 m tall, with its top edge 1 m below the surface of the water (ρ = 1000 kg/m³).
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Practice
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