Question $1$

The optimum agitation speed for the cultivation of plant cells in a $3-$L fermenter equipped with four

baffles was found to be $150rpm$

$($a$)$ What should be the impeller speed of a geometrically similar $1000L$ fermenter if is scaled

up based on the same power consumption per unit volume?

$($b$)$ When the impeller speed suggested in $($a$)$ was used for the cultivation in the $1000L$

fermenter, the cells do not seem to grow well because of the high shear generated even though

the impeller speed is lower than $150rpm$ of the model system. This may be due to the higher

impeller tip speed which is proportional to ND$.$ Is this true? Justify your answer by

calculating the impeller tip speed for both systems.

$($c$)$ Using the impeller tip speed as the criteria for scale up$,$ determine the speed of the impeller to

be used in the $1000L$ fermenter.