Question

The upper edge of a gate in a dam runs along the water surface. The gate is 2 m high and 4m wide and is hinged along the horizontal line through its top. Find the torque due to the force from water.

• A. 10.67 × 10⁴ N – m
• B. 5.33 × 10⁴ N – m
• C. 2.66 × 10⁴ Nm
• D. None

Answer 1

Answer: (A)

10.67 × 10⁴ N – m

Answer 2

Consider a strip of (4m × dy) at a height y.

Force on the strip

dF = ρg (2 - y)4dy;

Torque dτ= ρg (2 - y)² 4 dy

τ = ρg4

= 10³ × 10 × 4$\left[ 8 + \frac { 8 } { 3 } - 8 \right]$

= 10.67 × 10⁴ N – m.