GATE 2026 CE (CE2) – Question 53
The cross section of a 0.5 m wide vertical gate holding water and oil is shown in the figure. The unit weights of water and oil are 10 kN/m$^3$ and 7.5 kN/m$^3$, respectively.
[Figure: A vertical gate on the right of a tank holding a layer of oil 0.5 m deep on top of a layer of water 1.0 m deep. The figure is not to scale.]
The horizontal hydrostatic force (in kN) acting on the vertical gate is _________ (*rounded off to two decimal places*).
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Correct answer: 4.82 to 4.86
Explanation
The pressure at the oil-water interface is $7.5 \times 0.5 = 3.75$ kPa and at the bottom it is $3.75 + 10 \times 1.0 = 13.75$ kPa. The force per metre width is the area of the pressure diagram: oil triangle $\frac{1}{2} \times 3.75 \times 0.5 = 0.9375$ kN/m, water rectangle $3.75 \times 1.0 = 3.75$ kN/m and water triangle $\frac{1}{2} \times 10 \times 1.0 = 5$ kN/m. The total is $9.6875$ kN/m. For the 0.5 m width, $F = 9.6875 \times 0.5 = 4.84$ kN.