Question

4 of 4 3. The formation of a bubble indicates that there is excess pressure AP inside the bubble above the atmospheric pressure. For a bubble of radius R having a surface tension Os, the excess pressure AP is given by: ΔΡ = 205 R a. Draw a free-body diagram of half a bubble indicating the force balance (4 marks) b. Derive the above equation (4 marks) C. Everything else being the same, do you expect the air bubble to be larger when formed at the top or base of a mountain (2 marks) Consider water in a tank is pressurized by air. A multifluid manometer as shown in the figure below measures the pressure. The tank is located on a mountain at an altitude of 1400 m where the atmospheric pressure is 85.6 kPa. Determine the air pressure in the tank if he = 0.1 m, h = 0.2 m and hz = 0.35 m. Assume the densities of water, oil, and mercury to be 1000 kg/m”, 850 kg/m®, and 13,600 kg/m", respectively. (10 marks) Ou AIR WATER Mercury

Answer 1

ds. 6X10²-1000 x g. 8ixo. - 850X9.81X 0.2 water PL Apr equal to latm sonce the tribe is open to the 3 Part @ Consider on a link respectively, hizo. Im harco.2m h = 0.35m Sw = 1000kg/m3 850 kg/m3 Atmospheric pressure Parton = 85.6 Kf = 95.68103 / starting with the Pressure at pornt 1 at the air-water interface , moving along the tube addling or substracting Igh from until We reach porut 2 setting atmospheric. Soz 850 Im = 13600 kg/m3 the and the result -and P Pressure inside the tank P & Sw gh, et high - Inglez – Patom - P = Pation - Sogh, a loghat Singhz + 13600X9, 81X0.35 Pi 129 64619 Pa Il = 129,65 kla

FBD of half surface Pension Drive the equation. cero However, this result still gives the difference between a bubble force due to prepun Projected Area inside FAR? force due to for equilitnum sum of resultant forces are nero. & EF20 og (QAR) + P: ( 0R2) = 0 force due to surface tension R the inside force due to pressure inside bubble. Pia 2017 Ingeneral fase pressure Po outsicle the bubble is not and outside pressures so that we have Pe - Po R AP= 256 R

Part@ Yes, the at the top air bublole to be carger when formed or base of the mattade larger at the bottom side.