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 $3.5\text{ m}$ 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:
Options:
(A) $90.13\text{ kN}$
(B) $135.19\text{ kN}$
(C) $60.39\text{ kN}$
(D) $180.26\text{ kN}$
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 $\bar{h} = \frac{d}{2} = \frac{3.5}{2} = 1.75\text{ m}$, and area $A = 1.5 \times 3.5 = 5.25\text{ m}^2$.
$F = 9.81 \times 1.75 \times 5.25 = 90.13\text{ kN}$