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

The height of oil column will be 6.298 meters.

Step-by-step 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)* gh\\\\P_(bottom)=P_(top)+G* \rho _(water)* gh`

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

`P_(bottom)=136.3kPa+1000* 0.83* 9.81* 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)* gh\\\\P_(bottom)=101.3kPa+0.83* 1000* 9.81* h`

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

`P_(bottom)=P_(air)+\rho _(oil)* gh\\\\152.584kPa=101.3kPa+0.83* 1000* 9.81* h\\\\\therefore h=(152.584-101.3)/(0.83* 1000* 9.81)\\\\h=6.29meters`