QUESTION $5$

A fermentation conditions were optimised on a laboratory fermenter of

diameter and liquid height of $15cm.$ The fermenter is equipped with a $5cm$

diameter Rushton turbine operated at $800rpm.$ The fermentation was run

at turbulent conditions during agitation with a turbine impeller and

therefore, the Reynolds number had to be maintained at the value of $1{10}^4.$

Assuming that the density of the broth is close to that of water.

The laboratory fermenter is then scaled up so the tank and impeller are $15$

times the diameter of the laboratory equipment. The stirrer in the large

vessel is operated at the same impeller tip speed as in the laboratory

fermenter.

a$)$ What is the upper limit for the broth viscosity for the laboratory

fermenter?

$[8\%]$

b$)$ How does scale$-$up affect the maximum viscosity allowable for

maintenance of turbulent conditions?