Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Hydrostatic pressure and its measurement
Question Statement:
A vertical rectangular irrigation sluice gate of width $2.0\text{ m}$ and height $3.0\text{ m}$ retains water up to its top edge. Taking water density $\rho = 1000\text{ kg/m}^3$ and acceleration due to gravity $g = 9.81\text{ m/s}^2$, the total hydrostatic pressure force acting on the face of the gate in $\text{kN}$ is ________ (round off to 2 decimal places).
Answer Key:
88.29
Step-by-Step Solution & Explanation
1. Area of the submerged gate face:
$A = B \times H = 2.0 \times 3.0 = 6.0\text{ m}^2$
2. Depth to centroid of the gate:
$\bar{h} = \frac{H}{2} = \frac{3.0}{2} = 1.5\text{ m}$
3. Total hydrostatic force:
$F = \rho \cdot g \cdot \bar{h} \cdot A = 1000 \times 9.81 \times 1.5 \times 6.0 = 88290\text{ N} = 88.29\text{ kN}$