Can you determine the power consumption and impeller speed of a 1000 gallon fermenter based on the findings of the optimum condition from a geometrically similar one gallon vessel? If you cannot, can you scale up by using a different fluid system? Solution Since vv=1000. the scale ratio is (D) P=100013 =10 (9.12) (D) To achieve dynamic similarity, the three . ionless numbers for the prototype and the model must be equal as follows P VD)=( nmo nmo ON (9.13)Can you determine the power consumption and impeller speed of a 1000 gallon fermenter based on the findings of the optimum condition from a geometrically similar one￾gallon vessel? If you cannot, can you scale up by using a different fluid system? Solution: Since Vp /Vm=1000, the scale ratio is, = 1000 1/3 = 10 (9.12) To achieve dynamic similarity, the three dimensionless numbers for the prototype and the model must be equal, as follows: = (9.13) I m I P D D ( ) ( ) P I mo N D P ( ) 3 5  m I mo N D P ( ) 3 5 