where: F, = initial volume before orifice (ft3)
Pl = initial pressure (absolute)
P2 = (absolute) pressure after expansion k = C/Cv
Assuming that k= 1.50, then:
Figure 9 illustrates the adiabatic hp/1000 scfm in fermenters. Important features of using high velocity aeration are the following:
1. Increasing the liquid volume in the fermenter, such as feeding, reduces the horsepower. Conversely, removal of portions of broth will increase the horsepower.
2. The curves show the horsepower range at the air orifice from zero to sonic velocity which can be obtained by knowing the ungassed liquid height (differential pressure cell), the air pressure upstream of the orifice, and the scfm of air used.
3. Increasing the air pressure above the liquid reduces the horsepower (see Fig. 10).
The total theoretical horsepower of mixing by aeration alone is the sum of the isothermal and isentropic horsepower. At normal operating conditions, it is possible to double the agitation (P/V) by increasing the velocity of the air without increasing the scfm. It is easy to calculate the size of the orifices to give any desired velocity (up to sonic velocity), and the mixing horsepower. Conversely, one can scaleup aeration by horsepower per unit volume and determine the air required, i.e., it is possible to scaleup mechanical horsepower used in a pilot scale fermenter to a production vessel which is not mechanically agitated.
Figure 9. Isentropic horsepower/1000; scfm.
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