A circular plate 2 m diameter is placed vertically in water such that the centre of plate is at a distance of 3 m below free surface of water. Taking unit weight of water as 10 kN/m³, the total pressure force on the plate will be
- A20 π kN
- B30 π kNCorrect
- C35 π kN
- D40 π kN
Solution
Concept
Total pressure on a submerged plane surface
Formula
F = γ · x̄ · A
Step-by-step solution
1. A = π d²/4 = π × 2²/4 = π m². 2. x̄ = 3 m, γ = 10 kN/m³. 3. F = 10 × 3 × π = 30π kN.
Explanation
Hydrostatic force equals the intensity of pressure at the centroid times the area of the surface: F = γ x̄ A. The orientation of the plate does not change this expression.
Shortcut
F = γ × (depth of centroid) × area.
Common mistake
Using the area πd² instead of πd²/4 (this would give 120π).
Correct answer: B) 30 π kN