Question

A sealed tank contains oil (SG 0.83) for a height of 2 m and air at an absolute pressure of 136.3 kPa above the oil. If a piezometer is attached to the side of the tank at the bottom, what will be the height of oil column within the piezometer?

Answer 1

Answer:

The height of oil column will be 6.298 meters.

Explanation:

The oil in the piezometer will rise until the pressure of the oil column formed balances the pressure at the bottom of tank.

Using the equation for pressure in a fluid at rest we have

$P_{bottom}=P_{top}+\rho _{oil}\times gh\\\\P_{bottom}=P_{top}+G\times \rho _{water}\times gh$

Applying values we obtain value of pressure at bottom of tank as

$P_{bottom}=136.3kPa+1000\times 0.83\times 9.81\times 2\\\\P_{bottom}=152.584kPa$

Now the pressure at the bottom of the oil column in the piezometer equals

$P_{bottom}=P_{air}+\rho _{oil}\times gh\\\\P_{bottom}=101.3kPa+0.83\times 1000\times 9.81\times h$

Equating the 2 pressures and solving for 'h' we get

$P_{bottom}=P_{air}+\rho _{oil}\times gh\\\\152.584kPa=101.3kPa+0.83\times 1000\times 9.81\times h\\\\\therefore h=\frac{152.584-101.3}{0.83\times 1000\times 9.81}\\\\h=6.29meters$