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 $3.0\text{ m}$ retains water up to its top edge on one side. Calculate the total hydrostatic force acting on the gate in $\text{kN}$. (Take $\rho = 1000\text{ kg/m}^3$ and $g = 9.81\text{ m/s}^2$)
Answer Key:
88.29
Step-by-Step Solution & Explanation
Area of the gate $A = 2.0 \times 3.0 = 6.0\text{ m}^2$.
Depth of centroid from free surface $\bar{h} = \frac{3.0}{2} = 1.5\text{ m}$.
Total hydrostatic force:
$F = \rho g A \bar{h} = 1000 \times 9.81 \times 6.0 \times 1.5 = 88290\text{ N} = 88.29\text{ kN}$