Q5. Water is filled into a column and oil at 40 C is passed through it in drops. The oil goes into the water in drops from a perforated plate on the column, as seen in Fig. Q5.1. The height of the column is 2 m and the diameter of the holes on the plate is 5 mm.

a) What is the flow direction of the oil droplets? Can the oil droplets be considered as spherical droplets? Give the answers, considering the viscosities of phases physical and transport properties of the phases.

b) Show the forces effective on a droplet

Write a force balance and derive an equation for drop diameter as a function of interfacial tension for free flow.

c) If the oil droplets move in free flow regime, calculate droplet diameter.

d) Decide the flow regime of the oil droplet and calculate the terminal velocity of the oil droplets.

e) What is the retention time of oil droplets in the column? (how long does the oil stay in the water?).

f) (BONUS) If jet flow of oil droplets exists from the perforated plate holes, how can you calculate oil droplet diameter? Calculate drop diameter, flow regime, terminal velocity of the droplet and the retention time of the droplets in the column ?

Q5. Water is filled into a column and oil at 40C is passed through it in drops. The oil goes into the water in drops from a perforated plate on the column, as seen in Fig. Q5.1. The height of the column is 2m and the diameter of the holes on the plate is 5mm. a) What is the flow direction of the oil droplets? Can the oil droplets be considered as spherical droplets? Give the answers, considering the viscosities of phases physical and transport properties of the phases. [5 pts] b) Show the forces effective on a droplet Write a force balance and derive an equation for drop diameter as a function of interfacial tension for free flow. [7 pts] c) If the oil droplets move in free flow regime, calculate droplet diameter. Fig. Q5.1 d) Decide the flow regime of the oil Water phase: droplet and calculate the terminal Density: 992kgm3; Viscosity: 0.65cP velocity of the oil droplets. [4 pts] e) What is the retention time of oil Oil Phase: Density: 850kgm3; Viscosity: 35cP droplets in the column? (how long does the oil stay in the water?). [2 pts] f) (BONUS) If jet flow of oil droplets exists from the perforated plate holes, how can you calculate oil droplet diameter? Calculate drop diameter, flow regime, terminal velocity of the droplet and the retention time of the droplets in the column? [10 pts]