Question Bank • QB_PARAMETRIC_SWCE_STA_016MCQ • 1 Mark
Section 4: Soil and Water Conservation Engineering
Fluid Statics, Pressure & Manometry
Subtopic: Hydrostatic pressure and center of pressure
Question Statement:
A vertical rectangular sluice gate of width $1.5\text{ m}$ and height $2.5\text{ m}$ is placed in a water reservoir with its top edge coinciding with the free water surface. Taking the unit weight of water $\gamma_w = 9.81\text{ kN/m}^3$, the total hydrostatic pressure force on the gate is: (Variation QB_PARAMETRIC_SWCE_STA_016)
Options:
(A) $45.98\text{ kN}$
(B) $68.97\text{ kN}$
(C) $30.81\text{ kN}$
(D) $91.96\text{ kN}$
Answer Key:
A
Step-by-Step Solution & Explanation
The total hydrostatic force on a submerged vertical plane area is:
$F = \rho g \bar{h} A = \gamma_w \bar{h} A$
Here $\bar{h} = \frac{d}{2} = \frac{2.5}{2} = 1.25\text{ m}$, and area $A = 1.5 \times 2.5 = 3.75\text{ m}^2$.
$F = 9.81 \times 1.25 \times 3.75 = 45.98\text{ kN}$