GATE 2024 CE (CE1) – Question 59
A 5 m × 5 m closed tank of 10 m height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use $\gamma_w = 10$ kN/m$^3$ and Specific gravity of oil = 0.8.
[Figure: a closed tank PQR of 10 m height. P is the bottom, Q is the oil-water interface, 6 m above P, and R is the top. Oil fills the 4 m between R and Q and water fills the 6 m between Q and P. A pipe enters the tank at 2 m above P and comes from the base of an overhead reservoir whose base is at the level of Q. The pipe leaves the reservoir 2 m above its base, and the water surface of the reservoir is 8 m above the pipe.]
The total force (in kN) due to pressure on the side PQR of the tank is ______________ (rounded off to the nearest integer).
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Correct answer: 5580
Explanation
The reservoir water surface is $6 + 2 + 8 = 16$ m above P. The water in the tank is connected to the reservoir, so the pressure at a level $z$ above P is $\gamma_w(16 - z)$. At P it is 160 kPa and at Q ($z = 6$) it is 100 kPa. The oil above Q has the unit weight $0.8 \times 10 = 8$ kN/m³, so at R the pressure is $100 - 8 \times 4 = 68$ kPa. Over the 5 m wide side the force on the water part is $\frac{160 + 100}{2} \times 6 \times 5 = 3900$ kN, and on the oil part $\frac{100 + 68}{2} \times 4 \times 5 = 1680$ kN. The total is $3900 + 1680 = 5580$ kN.