Q$4.$ Density of milk composed of $80\%($by volume$)$ water and $20\%($by volume$)$ of liquid fat is $1012k\frac{g}{m^3}$ at $20C($https:$/$hypertextbook$.$com$/$facts$/2002/$Aliciallollevores$.$shtml$)$ and its viscosity is $2cP($https:$/$www$.$engineeringtoolbox.com$/$absolute$-$viscosity$-$foods$-$d$-1827.$Ktml$).$ At this temperature density and viscosity of water are $1000k\frac{g}{m^3}$ and $1cP,$ respectively. Diameter of spherical fat globule changes between $8$ and $20m.$

a$)$ Calculate density and viscosity of fat globules in the milk. $[5$ pts$]$

b$)$ Draw a fat globule and show forces effective on the fat globule. Show the flow direction of the globules. $[5$ pts$]$

c$)$ Calculate the terminal velocities of $8$ and $20m$ fat globules by deciding the flow regime. $[10$ pts$]$

d$)$ If $2$ liter milk exists in a cylindrical tank of which diameter is equal to the height of the milk, calculate the time required for the formation of a layer of fat globules in $20m$ in size. $[5$ pts$]$