 Good morning, we welcome you to this session, where we will discuss the energy transfer in continuation of our earlier discussion and the concept of impulse and reaction machines and the definitions of efficiencies of hydraulic or fluid machines. So, let us start from the discussion on energy transfer again, which we have already recognized in the earlier class that the head which is being transferred by the fluid to the machine can be written in three distinct components, which we have already seen. One is the change in the dynamic head that is due to the change in the absolute velocity of the fluid. Another component is the change due to the motion of the rotor from one radial location to other radial location. This is usually called as centrifugal head due to the change in the centrifugal head for which the static head or the pressure head of the fluid is changed and another is due to the change of the relative velocity of the fluid with respect to the rotor from its outlet to inlet, which is the change also in the static head or the pressure head of the fluid. Now, here with this concept we can identify different types of fluid machines. One type of fluid machines is axial flow machines, where the main direction of the fluid flow is in the along the axis of the rotation of the rotor. Just you see here, just if this be the rotor, let us write here this be the rotor and if this is the axis of rotation, if we consider two vanes mounted on the rotor disk, then the fluid inlet velocity if it is like this and the fluid discharges this direction, then we see that the inlet and outlet conditions of the fluid are such that the main flow direction is along the axial direction of the fluid. The most important thing is that the inlet and outlet of the fluid does not vary in their radial location from the axis of rotation. That means you see that throughout this radius there is a change in the radius from this point to this point, but throughout there is an inflow and here also throughout there is an outflow. That means we can take a representative point or representative plane of inflow at some radial location, for example which may be the mean of this height. Similarly, at the exit we can take a representative point or representative section, which is at some mean height from the root to the tip of the plate. Therefore, the inflow and outflow of the fluid does not vary in their radial location from the axis of rotation. So, what happens in this case with respect to this equation we can simply tell that for axial flow machines u 1 is equal to u 2. That means change of static head due to the change in the rotor velocity, because of a change in the radial location for inlet to outlet does not take place. That means there is no centrifugal head transfer between the fluid and the rotor in axial flow machines. Now, this component if we come whether there will be a change in the static head due to the change in the relative velocity of fluid from with respect to the rotor between outlet and inlet that depends upon the passage here you see that depends upon the area of the passage as the fluid flows through this passage. For example, this two vanes whether the area is converging or diverging in the direction of flow or not. So, that depends upon the setting of the blades if the blades are set and their curvatures are such that if the passage that is the passage that means the area normal to the flow is converging one then what will happen the relative velocity in the outlet will be more compared to that at the inlet for which the pressure at the outlet will be less compared to that at the inlet. That means the fluid will release this pressure that means fluid will release this pressure energy which will be contributed as a positive term to the energy or head transfer to the rotor. That means here we can conclude that in a turbine the blades are carved in such a way and it is placed in such a way that the flow passage in the direction of the flow is a convergent one in that case what we get is that v r 2 is less than v r 1 ok v r 2 sorry v r 2 is more than v r 1 v r 2 is less than v r 1 if v r 2 is more than v r 1 this quantity is positive because positive quantity positive sign of each and every quantity represents the energy transfer to the rotor. Well now we come to another class of machines according to their direction of flow radial flow machines now radial flow machines are machines where the main direction of the flow is in the radial direction and here what happens the radial location of the fluid that inlet and outlet changes there may be two possibilities one is the radial inward flow another is the radial outward flow. In radial inward flow the fluid flows inward radially inward that means the inlet of the fluid is at a higher radial location from the axis of rotation of the rotor let I write this as rotor and it is discharged at a radial location which is lower than that at the inlet that means the main direction of flow is in radially inwards just the opposite one is the radial outward flow where the main direction of flow is radially outwards that means the inlet position is at a radial location which is lower than that at the outlet location from the rotor axis. So, therefore, for radially inward flow we can write that u 1 is greater than u 2 what is u 1 u 1 is the rotor velocity at this location that is that inlet and u 2 is the rotor velocity at this location. So, if you see here you see that in this case we get a positive value of this quantity which means the centrifugal heat is being released by the fluid which means the pressure is being released by the fluid pressure here is lower pressure here is higher because the centrifugal head which we discussed earlier is higher here and it is lower here. So, while the fluid flows radially inward it releases its pressure energy or the centrifugal head and that is being transferred to the rotor. So, in case of turbine for these reasons the radial flow in case of radial flow turbines the flow is radially inward. Similarly, in case of radial outward flow we can write that u 1 is less than u 2 because here 1 is here at this section and the outlet section is at a higher radial location. So, therefore, what happens this term is negative that means the fluid gains the centrifugal head or fluid gains in static head that is the pressure head. So, this happens in case of pumps or compressors. So, therefore, in pumps of compressors to utilize the centrifugal head in the useful energy we make the designs such that the fluid flows radially outward. This pumps and compressors are radially outward flow machines for turbines the radially inward flow machines provided they are radial flow machines. Nevertheless there are axial flow machines pumps and compressors also after this I now come to the definition of impulse and reaction machines. Now, if we look to this equation again we see that there is a distinct difference between the first term and other two terms which we have discussed the first term is known at the change in the dynamic head. That means due to the change due to its absolute velocity and these two terms represent the change in the static heads. That means change in the pressure head one is due to the change in the radial position and another is due to the change in the pressure. Now, the proportions of the change in the head due to this dynamic one and the static one is a very important parameter in the design of fluid machines and this relative proportion between the changes in dynamic and static head is characterized by a very important parameter known as degree of reaction. Let us denoted by a symbol r degree of reaction r. So, degree of reaction is defined as change in static head change in static head change in static head in the rotor in the rotor divided by change in total head which means what fraction of the total head is being changed by the static head. So, if we recall the expression we can write the change in static head is one by two g times u one square minus u two square this changes I write with the positive sign as that delivered by the fluid with the usual convention and then v r two square minus v r one square and divided by the h. That means what fraction of h r represents is responsible for the change in the static head well with these definitions we can define or we can divide the fluid machines into very two important categories one is known as impulse machines impulse machines another is reaction machines. Now, impulse machines are those machines where the degree of reaction r is 0 which means there is no change in the static head. That means the change in the total head that means the total head transferred between the fluid and the rotor whether it is transferred by the fluid or the rotor to the rotor or by the rotor to the fluid is only by the change in the dynamic there is no change in the static head. So, very first consequences first consequence of this impulse machine where r is 0 is that if you look back again in this equations if there is no change in the static head. So, if we consider first the two terms would be independently 0 then u 1 has to be u 2 that means the impulse machine has to be has to be an axial one has to be an axial one again there should not be any change in the relative velocity of the fluid which means that an impulse machine the flow passage should be uniform in cross section to the direction of the flow. So, that the flow velocity that means the relative velocity of the fluid with respect to the machine should not change for which the pressure of the fluid will remain constant and this constant in pressure of the fluid in the rotor makes a simplification for the design of an impulse machine is that impulse the rotor of the impulse machine may be made open it may not need any casing. For example, it may be open to atmospheric pressure. So, that there may be a change in the absolute velocity, but throughout the flow the pressure will be constant at atmospheric pressure and one of the impulse hydraulic machines rotor is made like that. So, therefore, this is a simple design for impulse machine. So, we can write therefore, for impulse machine the pressure will be constant for impulse machine we write for impulse machine for impulse machine the outcome is axial flow that means u 1 is equal to u 2 pressure in course of flow through rotor rotor is constant which means v r 2 is equal to v r 1. So, therefore, r is 0 in this case since the dynamic change in the static head is 0, but you can argue one thing theoretically I must tell in many books you will not find this statement that you can tell sir why independently it will be 0 some of this made me may be made 0 for which an axial flow machine is not a immediate outcome of an impulse machine impulse machine may be a reaction type where the two effects may be opposing to each other that means it may be a radial inward flow. So, that the head is released by the fluid and at the same time passage may be made such diverging passage. So, head may be gained by the fluid. So, static head released by the fluid due to the change in the centrifugal head may be balanced by the static head gained by the fluid due to the change in the pressure two opposing effect, but that design is very difficult. So, usually it is not done in practice though theoretically one may conceive that that the two components may give an opposing effect to cancel each other, but according to that the design of a radial flow impulse machine is difficult. So, you may note here a very important thing that is why the impulse machine is always an axial flow machine. So, next we come to the reaction machine. So, it is very simple that as impulse machine is defined where the degree of reaction is zero that means the static head change in the rotor is zero reaction machines are those machines where along with the change in the dynamic head static head of the fluid also changes. That means there is a provision for the change in the static either by virtue of the change in the radial location of the fluid in course of its flow from inlet to outlet along with the change in the pressure because of a change in the relative velocity due to a varying area passage of the flow while it flow which takes place through the vane passages or blade passages. So, therefore according to this definition we can write reaction machines react this r is greater than zero or rather we can write more explicitly zero less than r less than one because the maximum value of r will be always less than one. So, therefore this is the definition or difference between impulse and reaction machines. Now, this concept of impulse and reaction machines before coming to the description of actual machines can be well understood by this very interesting, but simple examples of two popular fluid systems. You see one here is a simple paddle as you know the simple paddle these are certain straight blades which are being rotated by a flow of water jet which is coming from a fixed nozzle. You see the nozzle is fixed where high pressure water enters into the nozzle and it flows through a convergent duct which converts the high pressure low velocity fluid to a low pressure and high velocity fluid and it comes out with a high velocity fluid jet. So, water is used. So, water jet which makes this wheel to move this gives a very good example of an impulse machine. So, this nozzle and this wheel can be thought of as a fluid machine here I like to tell you one thing a fluid machine as a whole consist two parts one is the fixed part known as stator another is the moving part known as rotor. So, as far as the definition of the degree of reaction is that it is the proportion of the energy transfer that takes place rotor because the energy transfer takes place only in the rotor energy transfer means the transfer of stored energy to mechanical energy or mechanical energy to stored energy. So, therefore, here we see if this two constitutes a fluid machines. So, in the rotor the fluid pressure is throughout constant that means it is atmospheric pressure. So, the transfer of fluid energy or head to this rotor of the moving part of the fluid machines which is the paddle wheel is because only of the change in its absolute velocity and this is known as the impulse action by which the water jet is capable of rotating the paddle wheel. This is an example of impulse machine here you notice one thing that the pressure initially in the machine the input is the pressure energy of the water, but this pressure is being totally exploited in terms of the kinetic head or the velocity of the water in the fixed part of the fluid machines. That means nozzle when it strikes the rotor rotor is open. So, its pressure remains same and there is no change in this static head. Now, next you see another very interesting example well the interesting example of a reaction machine. If you consider a lawn sprinkler what is the lawn sprinkler probably you know that it has got two nozzles mounted on two arms of a rotating device. That means if you make free and if the water at high pressure enters into this system like this and it flows through these two arms is the two pipes and comes out from the two nozzles in the form of high velocity jet. Then due to the change in the angular momentum that means if you can find out the momentum of the fluid here it is take the moment about this axis and of course of this makes gives a turning moment for which it rotates. So, if you make it free it will rotate that means the energy is being transferred from the fluid to this lawn sprinkler. So, this way lawn sprinkler can be thought of a fluid machine where you utilize the high pressure energy of the fluid at the extreme inlet to develop the work output from the lawn sprinkler which is capable of rotating if you keep it free. Now in this case you see that this nozzles where the fluid pressure is changed from high pressure to low pressure it also moves. That means in this case nozzle was the stationary part, but here nozzle is the part of the rotor. So, therefore, you see while the fluid flows through the rotor both the absolute velocity of the fluid changes there is an increase in the absolute velocity and at the same time the relative velocity is changed. How we can realize it because there is a change in the pressure because pressure here is high pressure here is high pressure here is high only in the nozzle part which is also moving pressure is changed. That means in the rotor both the absolute velocity and the pressure of the fluid is changed. That means we get both the change in the dynamic and the static at in the rotor where in this case there is only a change in the dynamic. So, lawn sprinkler is a very good example of a fluid machine a reaction fluid machine the very good example of a reaction fluid machine while a paddle fluid is a very good, but simple example of a impulse fluid machine. Now next I come to the definition of efficiencies of fluid machines efficiencies efficiencies of fluid machines eta efficiency as you know the efficiency of any system is defined as in the output to input. So, similarly for a fluid machine the efficiency is defined in a generalized sense at the useful energy delivered useful energy useful energy delivered that is the output energy divided by the energy supplied. So, this is the basic definition of efficiency of a fluid machine that is the useful energy delivered divided by energy supplied. Now there are two types of efficiencies that are defined in fluid machines one is hydraulic efficiency afterwards we will refer to these two types of efficiencies. So, you must know the definition at this juncture that one is hydraulic efficiency eta h symbolize that another is overall efficiency overall efficiency eta o. Now hydraulic efficiency concerns about the energy transfer between the fluid and the rotor and overall efficiency concerns about the energy transfer between the fluid and the shaft coupling. The difference between these two is the energy that is being absorbed by the mechanical system like bearings couplings that means it is the energy which is lost in the transmission in the mechanical transmission. Well we can understand this better if we see that if we can think in this way that let us consider turbine in case of turbines in case of turbines. Let us see that let this is the turbine let this is the turbine you know in case of turbine what is the input energy is the stored energy of the fluid as we recognized earlier that is the stored energy of the fluid yes. Now this stored energy of the fluid here we consider the turbine rotor rather you write it sorry is the rotor r rotor simply rotor we are doing it for turbines. So, it is the rotor rotor of the turbine rotor of the turbine stator plus rotor you can write s plus r that means stator plus rotor the total machine. So, it comes to the stator and rotor then what happens just from the rotor we get useful or we get the mechanical energy out that means the rotor delivers the mechanical energy to whom it is delivered to the shaft to a mechanical to a mechanical transmission system. Yes that includes everything mechanical transmission it goes to the shaft it goes to the shaft and the shaft gives are the work w s that is the shaft work known as shaft work or this is the work delivered at the shaft coupling that means the work delivered coupling you can very well understand it that rotor due to its motion when the fluid flows through the rotor the energy is transferred to the rotor and immediately rotor delivers some work. So, hydraulic efficiency concerns with that transfer then that work is being transmitted through mechanical transmission system to the shaft where we get finally, from the shaft as the shaft work what delivered at the coupling at shaft. So, therefore hydraulic efficiency according to its definition is w by e s that means it is dealing with this conversion from the stored mechanical stored energy of the fluid to the mechanical energy or output given by the rotor whereas, the overall efficiency the input is same e s, but the output is the final shaft work that means which takes care of the losses in the mechanical transmission system the loss is due to bearing glands shaft couplings all this thing. So, if you see that that from the two what is eta o by eta h eta o by eta h will be w s by w that means this is the ratio between these two which can be defined as eta m that is mechanical efficiency mechanical is very simple to mechanical engineers that overall efficiency for a work producing device is the hydraulic efficiency into mechanical efficiency which takes care of the hydraulic losses as it flows through the turbine for which there is a discrepancy between these two quantities and the mechanical loss which takes care of the discrepancy between these two things because of the mechanical friction similar is the case for pumps and compressor if you see that pumps and compressors pumps and compressors the concept is same here what happens the mechanical energy e m is being first put as the input energy through at shaft coupling at shaft coupling that means the extreme output terminal for the turbines is the extreme input terminal for the pumps and compressor that means here also we can consider the mechanical transmission mechanical transmission well after which this mechanical energy goes to the stator plus rotor of the compressor that means as a whole the fluid machine the compressors are pumped and final output point and if at the final output point we get the stored energy of the fluid that means this is the useful energy delivered useful okay e sorry i am sorry correct correct it is e s i am sorry e s useful energy correct useful energy delivered that means in case of pumps or compressors as we know the useful energy delivered is the stored energy of the fluid so in this case we see that this mechanical energy is being changed when it comes to stator and rotor due to the mechanical losses due to friction in this mechanical transmission system let this energy is e so therefore in this case what is hydraulic efficiency hydraulic efficiency concerns with the energy transfer between the fluid and the rotor so therefore the hydraulic efficiency will be e s that is the stored fluid energy that is the useful energy delivered in this circumstances divided by the energy which is being received by the rotor similarly the overall efficiency which deals with the energy transfer between the fluid and the shaft coupling that means the output is the same in both the cases the useful energy delivered stored energy in the fluid but now input will be the extreme at the extreme terminal point where the input comes initially that is a shaft coupling e m that is the mechanical so in a similar fashion we can write that eta o by eta h is e by e m it remains the same that means it is this energy which is being received by the rotor divided by the energy which is being fed at the shaft coupling which is nothing but the mechanical efficiency and takes care of the losses in the mechanical system mechanical transmission system so we have now recognized the different efficiencies in a fluid machine is the hydraulic efficiency which concerns the energy transfer between the fluid and the shaft coupling that difference between which is taken care of by the mechanical friction or the friction in the mechanical system well so we will I will stop here next class I will discuss the principle of similarity now I request you so if you can you please read and the principle of similarity as well as the principle of similarity so if you can you please read and the principle of similarity as already you have read earlier make a recapitulation of that so I will start from a basic recapitulation recapitulation of principle of similarity and then I will discuss the application of principle of similarity in fluid machines which is very important in designing any equipment for our engineering applications the principle of similarity ok well thank you