 In this module we will talk about fermentor design with the multi impeller as we have seen in our previous module that when we have to design the fermentor with the single impellers that is only depend upon the fermentor height as well at the width of the fermentor. But when there is a situation of very deep fermentors we have to need a multi impellers fermentors. In such case we have to follow there are we have to follow the three different model reported first one reported in 1958 by Jackson and the second one that was reported by Iba et al in 1973 and the third one that was reported by Paka et al 1976 actually in these three models there are the detail of geometrical ratios having more impellers with multi blades impellers. You can see in this slide having the different geometrical ratios as concerned the operating volume that was only reported by Paka et al and Iba et al Iba et al reported 1 lakh liter capacity fermentor and Paka et al reported the fermentor with 170 liter fermentor. But in case of working volume height that was only reported by Paka et al that was 150 centimeter and Paka et al only reported the ratio between L over D mean the ratio between the working height volume with respect to the diameter of the fermentor that is only 1.7 very critical dimension. So, as concerned the ratio between P over D as we know that P is the width of the impeller and the D is the diameter of the fermentor that was reported by all three models. So, in case Jackson 1958 that range from 0.34 to 0.5 but in Iba et al that is 0.4 but in case of point Paka et al that is 0.33. So, as concerned that how much will be the height and the baffle width the ratio between as with compared to the diameter of the fermentor that is mostly range from 0.08 to 0.1 and 0.095 and 0.098. I mean there is a little difference among these three models but as concerned the ratio of impeller height over D that is 0.5, 0.25 and 0.37 respectively in Jackson in Iba et al and Paka et al. So, as we have seen that the impeller height that first impeller the height of the first impeller from the bottom of the fermentor. But as we know that when we are talking about with multi impellers then there is a gradually one and then second and then third and then fourth. So, what is the distance between the two impellers? So, that is you can see the ratio between P over V, P over W, P over Y and P over Z and then in the last in the latest slide I will show you that what will be the V, what will be the W, what will be the Y and what will be the Z. But here the most important geometric ratio that is H over D H is the total height of the fermentor and D we know that that is the diameter of the fermentor. So, in case of Jackson et al he reported that there should be a ratio between height with the diameter that should be 1 to 1.6 but Iba et al say that that should be 2.2. But in case of Paka et al that have a elevated that goes up to 2.95. So, here in all these three models we say that Paka et al reported all kind of the geometrical ratios that is very comprehensive report. So, by using these different geometrical ratio for multi impellers we can design our fermentor with any capacity. So, we can design the fermentor with 2 lakh litre capacity we can design either 100 litre capacity with the multi impellers. So, if we take an example if we want to have a fermentor with 500 litre capacity and we want to follow the Paka et al. So, first of all decide that what should be our diameter. So, if we decide that our diameter should be a specific this having the width. So, by using the last dimension so just by putting the value of the d. So, H over d is equal to 2.95 by the same if we put the value of d we can calculate the actual height of the fermentor. So, if first we calculate the total height of the fermentor and the d then we calculate the volume as we have seen our previous module by using the geometrical ratio and formulas which we can use for the calculation of the volume in that shape. So, you can see in this diagram as I have mentioned that I will told you in a later slide that what will be the V what will be the W what will be the Y and Z. So, Z basically is you can see that the height of the first impeller from the bottom and the Y is the height of the impeller from the first to the second and then W is from the second to the third and V is the height and we can say the depth of the last impeller from the surface of the working volume. Two impellers adjustment is very critical has concern that the last one and the first one. But all other impellers in a fermentor have almost the same height. You have seen in the previous slide that almost all other ratio between P over W, P over Y that almost have the same. But the below impeller and the top impeller is very critical. Just an example if we put our impeller just in a wrong geometrical ratio that will be the top of the surface that will create some such kind of the turbulence that can be sprinkle the fermentation media to the wall of the fermentor. Mean we can say that the headspace exists on the fermentor that can be effected. So, by the same way if we cannot fix properly the Z mean the height of the impeller from the bottom then we know that below the last mean the depth of the impeller. Then we can say then there should be the sparger. So, it is very critical while keeping the height of different impellers with respect to the diameter and the height of the fermentor.