Liquid pressure – U-tube manometer question

A U-tube with 30 cm of water is set up vertically and 12 cm of olive oil is poured carefully into the left-hand limb of the tube as shown below. It is observed that water will be pushed up in the other limb. The density of water and olive oil are 1000 kg m-3 and 920 kg m-3 respectively.

Given A is at same level as the boundary between olive oil and water.

a) What is the length of water column above point A?

b) A further 6 cm of olive oil is added into the left-hand limb. How much further will the water level rise in the right limb?

Solutions: View video tutorial for part (b)

a) Poil = Pwater above A

ρgh = ρgh920 x 10 x 12 = 1000 x 10 x h

h = 11.04 cm

b)         Pressure of water = pressure of olive oil

1000 x 10 x (2x + 11.04)/100  = 920 x 10 x 18/100

x = 2.76 cm