Question 431: [Pressure] (Past Exam Paper – June 2013 Paper 11 Q21)
Bore-hole of depth 2000 m contains both oil and water as shown. Pressure due to the liquids at bottom of the bore-hole is 17.5 MPa. Density of the oil is 830 kg m–3 and density of the water is 1000 kg m–3.
What is depth x of the oil?
A 907 m B 1000 m C 1090 m D 1270 m
Solution 431:
Answer: D.
The pressure at the bottom of the bore-hole (= 17.5MPa) is the sum of pressures exerted by water and oil on the bottom.
Pressure at a point = hρg
where h is the length of the column of the liquid above that point.
For the column of water,
Pressure exerted by water = (2000 – x) (1000) (9.81)
Where x is the length of the column of oil
For the column of oil,
Pressure exerted by oil = x (830) (9.81)
The sum of pressures is 17.5MPa.
(2000 – x) (1000) (9.81) + x (830) (9.81) = 17.5x106
(1.96x107) – 9810x + 8142.3x = 17.5x106
Length x = 1260m
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