Problem $1(60\%)$:

It is desired to form an emulsion by mixing two liquids, such as oil and water using a Rushton

turbine. For this example, assume that the emulsion is successfully formed if the average size of

oil droplets is less than $100$ microns. Assume furthermore that the dimension of the tank is $2,500$

$m^3,$ that the maximum diameter of the impeller is $2\mathrm{.}5m,$ and the maximum rotation speed is $800$

$rpm.$

$(10\%)$

Provide a description of a Rushton turbine as supplied by a manufacturer $($i$.$e$.,$ use the internet

and$/$or call a manufacturer$).$ Provide schematics, figures, tables, etc..

$(50\%)$

The power supplied by a Rushton turbine to the surrounding water body is given by the formula:

$P=K_T{n}^3{d}^3$

where KT is an "impeller constant" varying between $0\mathrm{.}32$ and $1\mathrm{.}6$ in general. Use the values $0\mathrm{.}3$

and $1\mathrm{.}2$ herein.

$n=$ rotational speed, revolution$/$second$.$

$d=$ Impeller diameter $(m)$

$=$ density of fluid $(k\frac{g}{m^3})$

Design a Rushton turbine that provides the minimum requirement for emulsion formation.

Namely, find the combinations' values of $d$ and $n$ that achieve emulsion. Also compute the

velocity gradient $G=(\frac{P}{V}{)}^{\frac{1}{2}}$ for these combinations, where $V$ is the volume of the tank.

Plot and discuss all results.

Problem $2$: $30\%$

Explain the role of the Komogorov scale in terms of the cascade of energy AND in terms of the

size of particles in a "smoothie". Provide the equation. $10\%$

Comment on how the Kolmogorov scale changes when the energy dissipation rate increases by

$10,100,$ and $1000$ folds. Do you need to increase the power need by a lot to reduce the

Kolmogorov scale to half its value?$20\%$

Problem $4$: $10\%$

Compute the energy dissipation rate and the Kolmogorov scale due to a static mixer of diameter

$0\mathrm{.}05m$ and length $2\mathrm{.}5m$ with a water flow rate of $Q=0\mathrm{.}005\frac{m^3}{s}.$ Assume $f=5\mathrm{.}0$ in the Darcy

Weisbach equation for pipe flow.