A rectangular plane surface 2 m wide and 3 m deep lies in a vertical plane in water. When its upper edge is horizontal and coincides with water surface, the distance of centre of pressure from free water surface will be
- A1 m
- B1.5 m
- C2 mCorrect
- D2.5 m
Solution
Concept
Centre of pressure on a vertical rectangle with top edge at the free surface
Formula
h* = x̄ + IG /(A x̄); for such a rectangle h* = 2d/3
Step-by-step solution
1. x̄ = d/2 = 1.5 m; A = 2 × 3 = 6 m². 2. IG = b d³ / 12 = 2 × 27 / 12 = 4.5 m⁴. 3. h* = 1.5 + 4.5 / (6 × 1.5) = 1.5 + 0.5 = 2.0 m.
Explanation
The centre of pressure always lies below the centroid. For a vertical rectangle whose upper edge is at the free surface it is at two-thirds of the depth: 2/3 × 3 = 2 m.
Shortcut
Vertical rectangle with top edge at the surface: centre of pressure at 2/3 of the depth.
Common mistake
Giving the centroid depth 1.5 m.
Correct answer: C) 2 m