Discussion
The gate is 1 m wide perpendicular to the plane of the paper. The force (in N) exerted on the gate is approximately
Answer: C
The force on the gate is about \(2.23 \times 10^{5}\) N.
For a plane vertical gate the resultant force is the pressure at its centroid times its area. The centroid is 1.5 m below the oil-water interface (1 m to the top of the gate plus half its 1 m height).
\[ \begin{aligned} p_{c} &= 2 \times 10^{5} + 800(10)(1) + 1000(10)(1.5) \\ &= 223000\ \text{Pa} \\ F &= p_{c}A = 223000 \times (1 \times 1) = 2.23 \times 10^{5}\ \text{N} \end{aligned} \]
The gas pressure dominates, which is why the answer is so large. The other options differ only by powers of ten, the result of dropping the gas pressure's 105 or mis-converting bar.
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