The thickness of the oil is 0.327 m.
The bottom pressure of the tank is given by atmospheric pressure, pressure given by oil and pressure of water. It is mathematically given as,
P = Patm + ρoil g* t + ρwater g * h
Making 't' as subject, we have,
ρoil g* t = P - Patm - ρwater g * h
t = (P - Patm - ρwater g * h)/ρoil g -------(1)
Given that, Height of the tank h = 0.9 m
Pressure at the bottom of the tank P = 113 kPa
Patm = 1.013 * 10⁵ Pa
g = 9.8 m/s²
ρwater = 1000 kg/m³
ρoil = 900 kg/m³
Placing the values in the above equation,
t = (P - Patm - ρwater g * h)/ρoil g
t = (113* 10³ - 1.013 * 10⁵ - 10³* 9.8* 0.9 )/(900* 9.8)
⇒ (113* 10³ - 101.3* 10³ - 8.82* 10³)/(900* 9.8) = 2.88 * 10³/(900* 9.8)
⇒ 0.327 m
Thus, the thickness of the oil is found to be 0.327 m.
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