Question

A square gate of size 1m × 1m is hinged at its mid-point. A fluid of density ρ fills the space to the left of the gate. The force F required to hold the gate stationary is 

• A. \( \dfrac{\rho g}{3} \)
• B. \( \dfrac{\rho g}{2} \)
• C. \( \dfrac{\rho g}{6} \)
• D. (ρ g)/(8)

Hint:

For vertical submerged plates: 
• Resultant force acts at centre of pressure. 
• Always take moments about hinge point.

Answer 1

The Correct Option is C

Step 1: Resultant hydrostatic force on the gate: FR = ρ g A hc = ρ g (1)(0.5) = (ρ g)/(2)
Step 2: Centre of pressure from top: h = (2)/(3)m Distance from hinge (mid-point): d = (2)/(3) - (1)/(2) = (1)/(6)
Step 3: Taking moments about hinge: F × (1)/(2) = (ρ g)/(2) × (1)/(6) ⟹ F = (ρ g)/(6)