Step 1: Understanding Scale-up Criteria
When scaling up a process, the criteria used must ensure that similar flow conditions and mixing behaviors are achieved between the lab and industrial scales.
Step 2: Evaluating Options
- Mixing time: Dependent on several factors, not a primary scale-up criterion.
- Reynolds No.: Helps compare flow types, but doesn't always predict mixing efficiency.
- Power number: Relates to the power required for mixing in different scales and is preferred for scale-up since it ensures similar flow and mixing characteristics.
- Power/volume of fermenter: Useful for scaling but doesn’t directly address flow similarity.
Step 3: Conclusion
The power number is the most effective criterion for scale-up, as it directly impacts the mixing efficiency across different scales.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.