Question

A vertical tube 1.1cm in diameter and open at the top contains 4.8g of oil (density 0.82 g/cm3) floating on 4.8g of water.

A) Find the gauge pressure at the oil-water interface.

B) Find the gauge pressure at the bottom.

Answer 1

Area of tube = D²/4

mass =volume x density

mass =     D²/4xheight x density

for oil

H1=4.8x4/(3.14x1.1x1.1x0.82)

H1=6.16 cm

similarly for water

H2=5.05 cm

a) gauge presure at oil water interface =gH1                   (.82 g/cube cm 820 kg/cub m)

                                   =820x9.8x(6.1627/100)

                                  =495.2361 kg/m2

b) find the gauge pressure at bottom =(0il)gH1+(water)gH2

                                                      =495.0176+1000x9.8x5.053/100

                                                     =990.47 kg /m3

alternative simply gauge pressure can be calculated = weight/area

for interface weight is 4.8 x 9.8

at bottom weight = 2x4.8x 9.8

you will get same answer