A glass tube of cross-sectional area 0.00013 m2 is partially filled with water. An oil with a density of 790 [cg/m3 is slowly poured into the tube so that it does not mix with the water and floats on top of it. The height of the oil above the water's surface is 3 cm. (a) By how much does the pressure change at a depth of 10 cm below the water's surface after the oil is added? (On the side where the oil is sitting)? Pa (b) Would the pressure at this depth (1) increase or (2) decrease if you added more oil to the tube? (input either 1 or 2 into the answer box) GIVEN: Area of cross-section of tube A = 0.00013 m2 Density of oil Poil = 790 kg/m Height of oil coloumn above water surface hoil = 3 cm = hoil = 0.03 m Depth below water surface dwater = 10 cm = dwater = 0.1 m Density of water Pwater = 1000 kg/m Accleratingue to gravity g = 9.81 m/s2 SOLUTION: (a) Initial pressure (before pouring oil) at the given depth below water surface is Pi = Pwater - Pi = Pwater gdwater Final pressure (after pouring oil) at the given depth below water surface is Pf = Pwater + Poil Pf = Pwatergdwater + Poilghoil Hence, change in pressure at given depth after pouring of oil is AP = Pf - Pi AP = Pwater gdwater + Poilghoil - Pwater gdwater - AP = Poilghoil - AP = 790 kg x 9.81- x 0.03 m m3 AP = 232.5 Pa (b) From the equation for pressure due to oil coloumn Poil = Poilghoil If more oil is added to the tube, the height of the oil coloumn will rise. As Poil and g are constant then the pressure due to oil at the given depth will increase with increase in the height of the oil coloumn in tube. Thus, if more oil is added to the tube then the pressure at the depth will increase. Calculations: 790 . (9.81) . 0.03 X = 232.497