Problem #$1(15$ pts$).$ A molten wax is pumped through a long capillary of diameter $0\mathrm{.}3$ cm at a volume flowrate of $10m\frac{l}{s}.$ The jet that issues from the capillary breaks down into a stream of droplets. The wax properties are:

$=900k\frac{g}{m^3}$

$=0\mathrm{.}005N*\frac{s}{m^2}$

$=0\mathrm{.}045\frac{N}{m}$

You want to model the drop breakup characteristics of this system using an aqueous solution of corn syrup. Assume that the aqueous solution has a density of $=1200k\frac{g}{m^3}$ and a surface tension of $=0\mathrm{.}065\frac{N}{m},$ independent of concentration.

a$.(5$ pts$)$ Select two dimensionless groups that must be equivalent between the prototype and model to achieve dynamic similarity. Hint: You will need to make assumptions about the effect of gravity on the flow.

Euler number, $Eu=\frac{p}{V^2}$

Reynolds number, $Re=\frac{Vl}{}$

$($