Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Hydrostatic pressure and its measurement
Question Statement:
A vertical rectangular sluice gate of width $2.0\text{ m}$ and height $3.0\text{ m}$ is submerged in water such that its upper edge is $1.0\text{ m}$ below the free water surface. Taking density of water $\rho = 1000\text{ kg/m}^3$ and $g = 9.81\text{ m/s}^2$, the total hydrostatic thrust acting on one face of the gate in $\text{kN}$ is ________ (round off to 1 decimal place).
Answer Key:
147.2
Step-by-Step Solution & Explanation
1. Area of the sluice gate $A = 2.0\text{ m} \times 3.0\text{ m} = 6.0\text{ m}^2$.
2. Depth to the centroid $\bar{h}$:
$\bar{h} = 1.0 + \frac{3.0}{2} = 2.50\text{ m}$
3. Total hydrostatic force $F$:
$F = \rho g A \bar{h} = 1000 \times 9.81 \times 6.0 \times 2.50 = 147,150\text{ N} = 147.15\text{ kN} \approx 147.2\text{ kN}$