The size of liquid droplets produced by a spray nozzle depends upon the nozzle diameter, the fluid velocity, and the fluid properties (which may, under some circumstances, include surface tension).

(a) Determine an appropriate set of dimensionless groups for this system.

(b) You want to know what size droplets will be generated by a fuel oil nozzle with a diameter of $0.5 \mathrm{~mm}$ at an oil velocity of $10 \mathrm{~m} / \mathrm{s}$. The oil has a viscosity of $10 \mathrm{cP}$, a $\mathrm{SG}$ of 0.82 , and a surface tension of $35 \mathrm{dyn} / \mathrm{cm}$. You have a nozzle in the lab with a nozzle diameter of $0.2 \mathrm{~mm}$ that you want to use in a lab experiment to find the answer. Can you use the same fuel oil in the lab test as in the field? If not, why not?

(c) If the only fluid you have is water, tell how you would design the lab experiment. Note: water has a viscosity of $1 \mathrm{cP}$ and a $\mathrm{SG}$ of 1 , but its surface tension can be varied by adding small amounts of surfactant that does not affect the viscosity or density.

(d) Determine what conditions you would use in the lab, what you would measure, and the relationship between the measured and unknown droplet diameters.