 As we discussed in our previous module that h t is a total height of a fermenter and l is the height of the working volume. So, while designing the body of a fermenter, so we should know different aspects because while talking about the 13 basic characteristics of a fermenter, so in those characteristics one character was that when we design a fermenter that should have identical geometrical shape. So, that is why that can facilitate the optimization process when we go from the lab scale to pilot scale and then to industrial scale. So, if these there is any identity or a similarity in geometrical shapes from the lab scale to pilot scale and then pilot scale to industrial scale then there will be a very easy to optimize the process and to control the process. As we have already seen that h is the total height of a fermenter and l is the height of the working volume, so just one more point that p is the width of the impeller. So, you can see here that schematic representation of a fermenter with one impeller having multi-blade mean sometimes there is a one impeller having three blades, four blades, six blades just like that when there is a ceiling fan having a three blades, sometimes we have a pedestal fan that have a four blades, so by the same case in fermenter impellers having different kind of the blades depending upon the type of the impellers. We will study in detail the different type of impellers later on, but here in this slide you can see that how a fermenter can be having a different dimensions and the parts, here you can see that baffles, so that is a drain point here and this is the d mean the diameter of a fermenter. So, if we know that H, L, P and D then before designing a fermenter in literature if we want to design a fermenter having single impellers then in the literature there are four three different models are reported, one model is reported by Steele and Maxon 1961 and the second that was reported by Wagerich and Sherton in 1963 and third that was very famous that is the fermenter with single impeller reported by Blackbarrow 1967. So, according to these three models they mentioned different geometrical ratios, you can see the operating volume, liquid height, the ratio between liquid height and the diameter very critical and then the impeller diameter and the diameter, so what will be the ratio of the impeller width and to the total diameter of the fermenter and by this ratio we can design the baffle width and then by the impeller height that this is basically that the height of the impeller from the base. So, these are the different ratios, so suppose if we want to design a 300 liter fermenter keep in mind the dimensions given by Steele and Maxon 1961 we can follow these lines. So, if we want to design a fermenter with a single impeller with keeping in mind and the Schetter, Wagerich and Schetter then we can use these the same the Blackbarrow is very critical because that given that has given the impeller height and d ratio, so that is 0.33. So, by using these geometrical ratio we can design any fermenter having single impeller. So, when we want to design a fermenter we have to calculate in detail that what is the total volume of the fermenter, so it is a very geometrical formulas. So, in case of this it is a very easy because if a fermenter is in a such shape we can just by using this formula v is equal to pi r square h by this formula we can calculate the total volume of that shape. But we know that sometime there is a long at a dome shape upper plate is not straight that is dome shape. So, in order to calculate the volume of the dome either on upper plate either but the round bottom then we have to follow this formula that v is equal to pi h over 6 into 3 a square plus h square. As you can see that h is basically the height of the dome and a is the distance of the periphery from the center. Sometimes it h and a are equal to r but all the time the h and the a are not equal to r. So, if we know the h and a of a fermenter then we can calculate the dome shape and the round bottom and then by plus in this addition of this two volumes we can have the calculations of the total volume of a fermenter vessel.