Electrospray devices $($such as inkjet printers and one type of electrostatic thruster$)$ use a strong electric eld to accelerate a thin stream of liquid until it breaks up into individual droplets. Consider a string of droplets whose diameter d $($SI units of m$)$ is set by the liquid properties of density $($SI units of kg$/$m$3),$ viscosity $($SI units of Pas$),$ and surface tension $($SI units of N$/$m$)$ as well as the initial stream diameter D $($SI units of m$)$ and the droplet kinetic energy E $($SI units of J$).($a$)[4$ pts$]$ How many dimensionless groups are necessary to describe this problem, and why? $($b$)[8$ pts$]$ Using $\{$rho$,$D$,$E$\}$ as your K$-$set, use a standard Buckingham$-$Pi dimensionless analysis to find the exponents for a surface tension$-$scaling coe cient of the form Pi$\_$sigma $=$ sigma$*$rho$^$alpha$*$D$^$beta$*$E$^$gamma Show your work for full credit! $($c$)[8$ pts$]$ Using the same K$-$set, use a standard Buckingham$-$Pi dimensionless analysis to find the exponents for a viscosity$-$scaling coe cient of the form Pi$\_$mu $=$ mu$*$rho$^$alpha$*$D$^$beta$*$E$^$gamma Again, show your work for full credit.