Question

A rectangular gate of width 2 m and height 3 m lies in a vertical plane, the top of which is at the surface of water. If the unit weight of water is 10 kN/m$^3$, then the force exerted by the water in the gate is

• A. 20 kN
• B. 30 kN
• C. 60 kN
• D. 90 kN

Hint:

The formula for hydrostatic force is "Pressure at the centroid times the Area".
$F = P_{centroid} \times A = (w \bar{h}) \times A$.
Remember that $\bar{h}$ is the vertical depth to the centroid, not the slant distance.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Vertical rectangular gate 2m×3m, top at water surface. Find hydrostatic force.

Step 2: Key Formula (Alternate):
F = wAȟ. ȟ = depth to centroid = h/2 from surface. w=10 kN/m³.

Step 3: Detailed Explanation:
A=2×3=6m². ȟ=1.5m. F=10×6×1.5=90kN. Center of pressure at 2/3 depth from surface = 2m below surface.

Step 4: Final Answer:
90 kN.