Question $3$:

Consider the scale$-$up of fermentation from a $10L$ to $10000L$ vessel. The small fermenter has a high$-$to$-$diameter ratio of $3.$ The impeller diameter is $30\%$ of the tank diameter. Agitator speed is $500rpm$ and three Rushton impellers, are used. Assuming geometric similarity, determine the dimensions of the large fermenter and agitator speed for:

a$.$ constant $\frac{P}{V}$

b$.$ constant impeller tip speed

c$.$ constant Reynolds number

Question $4$:

Assuming dynamic similarity, can you determine the power consumption and impeller speed of a $1000L$ fermenter, based on the findings of the optimum conditions from a geometrically similar $1L$ vessel?

If not, can you scale$-$up by using a different fluid system?