 Let us try and get a physical understanding of why centrifugal pump is not a good choice for the value of q and h that we had specified for this, it may be recalled that the value of q and h that was specified for this case was 5 meter head and 5 meter cube per second of water. So looking at the flow rates here and the head, it's apparent that the particular requirement calls for low head and high flow rate and that is actually the reason why a centrifugal pump is not a good choice and let us see why centrifugal pump is not a good choice for low head and high flow rate. So if you actually look at centrifugal pump, the impeller of which is shown here, the flow enters the eye of the pump axially but when it flows through the impeller, it flows in the radial direction. Of course, there is no axial component of velocity which is why we say it's a radial flow machine, but there is a tangential component of velocity, no axial component hence it's called a radial flow machine and it is clear that in this case the impeller width is not very large, it cannot be very large because of the basic flow dynamic design and consequently the flow rates that it can handle is rather restricted but the head that it can develop is quite high because of the centrifugal action, the purely radial motion and the centrifugal action. So the centrifugal pump is thus ideally suited for high head but low discharge type of application and that is the reason why we find it to be unsuitable for low head and high flow rate applications such as this one. Now if we want to increase the flow rate through the centrifugal machine, the only way to do this is to widen the blade passage or open up the blade passage. So when you open up the blade passage, for example, let's say by a moderate amount, then we end up with the geometry of the impeller that looks like this. What is there? In this case, the flow through the impeller is not radial but it has both radial component as well as an axial component in addition to the tangential component that it already has. So the flow becomes highly three-dimensional and this is called a mixed flow machine because it is neither just radial, not just axial but has a combination of both radial and axial. So because we have opened up the impeller blade passage, the flow rate here is higher than what we see here. So this type of design is ideally suited for medium head and medium flow rate because there is still radial component that is present in this design. The head that it can develop can still be reasonably high, not as high as the purely radial flow machine such as the centrifugal pump. So this can still develop a reasonable amount of head. So it is ideally suited for medium head and medium discharge application. Now if you open it up further to increase the flow rate even more, then we end up with an axial flow pump like this. So this is a purely axial flow machine, there is no radial component at all. So the fluid has an axial component and a tangential component in this case and as you can see the blade passage is quite wide so this can develop or this can handle very high flow rate but the head that is developed across such a rotor is not very high. So this is ideally suited for low head and high flow rate applications, the sort that we are looking for in this particular case. So for the values that we specified it becomes clear that an axial pump is probably the best choice. Although this is not clear because these descriptions are still only qualitative. So what exactly do we mean by high, medium and low for head or for discharge is it 1 meter cube per second or 5 meter cube per second or 1 meter or 10 meter that is not clear but we can broadly classify them as high, medium and low. And the only way to actually make this quantitative is to have or develop parameter that actually can relate these two quantities in a manner that is applicable across all three types of design. So before we turn to that let us just quickly summarize some of the features of these types of machines although we will not go into any of the details. Just like what we did for centrifugal machine universal characteristics namely CP versus CQ and CH versus CQ can also be developed for mixed flow machines again for different simpler diameters RPM and different types of fluids and similar characteristics can be developed for axial flow machines also. So these types of characteristics are available for centrifugal mixed as well as axial flow pumps. So once we identify the pump that we want and the requirements the selection process becomes identical to what we did here. So we simply go to the dimensionless characteristic and calculate based on this non-dimensional quantity the quantity that we want. Like what we did in this example where we selected the diameter of the impeller and RPM and the head that could be developed was also evaluated. So in the case of C if we indeed say that an axial flow machine is what we want then we would go to the dimensionless characteristics of the axial flow pump and follow the same procedure that we did here. But in order to determine whether to select a mixed flow pump or axial pump or centrifugal pump we need a quantitative way to our quantitative manner in which we can decide. And the quantity the dimensionless quantity that relates all these types of designs is the dimensionless specific speed which is defined here like this. The quantities on the right hand side are all dimensional but NS itself is dimensionless it is called the dimensionless specific speed. So we obtain this by eliminating D between the definition for CH and CQ. Because in general in the case of a pump or when it comes to selecting a pump for any application normally the head and the discharge are usually known. And based on the electric motors that are available in the market we usually know the permitted range of speed for the electric motor also but the size of the impeller is generally not known. So from an application point of view this dimensionless specific speed is probably the best quantitative metric to connect all these three designs. So what is normally done is once we have the dimensionless characteristics for the centrifugal, the mixed and the axial flow pump the value of the dimensionless specific speed across each one of these ranges may be evaluated. We know the range of Q and we know the head range. So using the values for known values for head and Q the dimensionless specific speed for each one may be evaluated. And then if you arrange the values for centrifugal mixed and axial flow then we begin to see a pattern. So we can do the same thing for all the design centrifugal as well as mixed and axial flow pumps from the dimensionless characteristics then the values usually arrange themselves like this. Notice that the centrifugal machines typically have low values for specific speed because the head is high and the flow rate is low and the mixed flow machines typically have mid-range values because the head and the flow rate are mid-range values and the axial flow pumps are very high specific speed because the head is very low and the Q is very high. So they usually arrange themselves like this and they can also see how nicely the blade passage expands as we go from low flow centrifugal pump impeller to a high flow axial pump impeller. So you can see the passage opening up gradually and the specific speed increasing as we go from this design low head I'm sorry high head low flow rate to medium head medium flow rate to high flow rate low head type of a design and the specific speed comes out to be like this. So here you see the dimensionless characteristics of the three types of pumps. So you can see I mean these are not to scale but the dimensionless characteristics of all these pumps are available and you can see that the efficiency for the mixed and the axial flow pumps occurs closer to the maximum value of flow rate when compared to the centrifugal machine where the maximum efficiency or the best efficiency point is closer to the mid-range of values for the flow rate and the variation of power it increases monotonically for the centrifugal and the mixed flow machine but it is seen that the power actually decreases with flow rate for an axial flow machine. So these are interesting trends that must be kept in mind but the most important thing is the pump selection for a given q and h. We decide which one we want we can actually evaluate ns for each one of the design. So we select a centrifugal impeller we know the range of values for specific speed so we calculate the rpm and the impeller diameter assuming it is a centrifugal pump then we repeat it for mixed flow pump and do the same thing for an axial flow pump then based on the values that we get for the rpm and the diameter impeller we select the pump that we want based on how reasonable and physically realistic these values appear to be. So we make the best choice for the pump for the given quantities by selecting by evaluating ns for each one of this then going into the dimensionless characteristics and calculating the impeller diameter and the rpm and then choosing the best design. So the procedure remains the same the only thing we do now is evaluate this ns which connects all the three designs of pumps namely centrifugal, mixed and axial flow pump. So what we have outlined here is only a procedure for selecting pumps the actual process is somewhat more involved than what we have given here and it would be right and proper to have such a discussion in a full-fledged course on cargo machine and as I said in the introductory lecture here the objective is not to select pumps or turbines for a particular requirement but we outline the general procedure so that you have a basic understanding of the procedure and when you do a full-fledged course on cargo machines you will know all these details all these concepts and then you can work out the detail.