Question

With reference to the gate shown in the figure, the gate will start opening automatically when the water level 'h' above the hinge is ________ m (rounded off to 2 decimal places).

Answer 1

Correct Answer: 3.4

Step 1: Calculate the hydrostatic pressure at depth \( y \). \[ P(y) = \rho g y \] Step 2: Compute the torque due to hydrostatic pressure. \[ \tau = \frac{\rho g h^3}{3} \] \[ \text{Substitute \( h = 3.40 \) m into the formula:} \] \[ \tau = \frac{1000 \times 9.81 \times (3.40)^3}{3} = 128702.648 \, \text{N} \cdot \text{m} \]