 I welcome you all to this session of fluid machines. Today, we will start the discussion on reaction type hydraulic machines. The first introductory concept about the reaction types is like that as you know earlier that a reaction machine is a type of machines where both the change in velocity and pressure takes place while the fluid flows through the rotor. That means, the basic difference is that for an impulse machine the fluid the pressure of the fluid remains almost remains constant in the rotor of the machine. The fluid the energy of the fluid at the entrance of a fluid machine can be thought of to be comprised the kinetic energy and the pressure energy. That means, the fluid at the entrance to a machine comprises both kinetic energy and pressure energy. So, what happens in an impulse machine that the fixed part of the machine known as rotor which in case of a pelton is the nozzle that expands the fluid from this higher pressure to the ambient pressure. That means, the fluid coming out from the stator of the machine is in the form of a high velocity jet that means, it is fully in the form of kinetic energy. So, pressure energy is totally expanded the pressure energy is totally exploited in the form of kinetic energy. So, therefore, in the rotor it is only the change in the absolute velocity of the fluid or change in the kinetic energy of the fluid which is responsible for the work done by the rotor. But, while in case of a reaction machines the fixed part of the rotor of the machine does not exploit the entire pressure energy in converting it to kinetic energy. That means, a part of the pressure energy is being converted into kinetic energy. So, therefore, fluid approaching the rotor blades of the moving part of the turbine has both the pressure energy and the kinetic energy. So, therefore, fluid flowing through the rotor blades suffer a change in both its kinetic energy because of the change in its absolute velocity and also in pressure energy. So, how the pressure energy is changed then when fluid flows through the rotor passage then the flow area is changed and accordingly the relative velocity of the fluid with respect to the rotor changes or the pressure of the fluid changes. So, therefore, simultaneously velocity and pressure of the fluid changes in a reaction machine then the rotor of a reaction machine. So, that is the basic difference between a an impulse machine and a reaction machine of any kind. Now, the most popular type of reaction machines in the field of hydraulic machine is known as francis turbine which was first developed by an american engineer J. Francis this is the francis turbine. So, the first hydraulic turbine reaction type hydraulic turbine was developed by this is the name of J. Francis an american engineer who developed this known as francis turbine. It is a typically a radial flow turbine as you know that in case of a radial flow machine when it is a turbine that means it develops work then it has to be an inward radial flow. That means the inlet to the turbine should be at a higher radial location from the axis of rotation as compared to its outlet. This is because that the dynamic centrifugal head is released by the fluid. That means as the fluid passes through the rotor blades a decrease in its centrifugal head occurs which can be utilized in the form of work developed by the turbine. So, therefore, in case of turbine the radial flow machines will be inward flow type that means the inlet to the rotor will be at a higher radial location from the axis of rotation. So, here also it is a radial inward flow hydraulic machines. Now, the main components let us first see that this is the entrance this is the main entrance of the fluid which is having both the velocity and pressure high velocity and pressure. That means the energy at here which the fluid possesses is in the form of both kinetic energy and pressure energy. Then it flows through a typical space like that or typical projection like that where in the direction of flow the flow area decreases and this casing is known as this is a spiral type casing spiral type casing. This is a spiral type casing this is the first component of the machine spiral type casing which is known as crawl scro double lens crawl casing or volute can you see this volute casing volute volute casing. So, a spiral type casing known as crawl casing or volute casing why this spiral type because its area changes in such a way looks like a spiral as the liquid flows through it. Then there are certain veins or blades which are fixed and as the liquid flows through the spiral casing crawl casing or volute casing the liquid enters into the passages formed by this fixed blades. So, these blades are known as so these blades are known as these are the fixed blades fixed blades or veins blades or veins and this is the stator of the machine and this is the stator of the machine that means the fixed part. These are known as guide veins these are the terminology guide veins or wicket gates this is a peculiar terminology or typical terminology wicket gates in hydraulic machines wicket gates. I will come afterwards the function of each and every component before that let me tell you that what are the components these are fixed blades these are pivoted at those points. So, that these are they are usually fixed for a particular operating conditions, but they can be moved they can be swivel about this pivotal point to regulate the flow through these guide veins in case of governing of turbines which will we will come afterwards. Then the last next component is a series of moving blades. So, these blade is moving this is moving this is the shaft where it is mounted the rotor. So, this is the rotor disc and on the periphery of the disc you see the number of veins are attached. So, these are known as moving or this is the moving veins moving veins which moves that means these veins are mounted on the periphery of a disc which is coupled to the shaft which is rotating. So, therefore, these veins rotate these have got an angular velocity. So, these are moving veins are known as runner. So, the moving veins that is the rotor the rotor part of the machine is known as runner. So, machine is composed of now we will come afterwards let us see moving veins and runners. Now, if you see the flow of liquid you see the liquid comes here at this point this is the entrance as the liquid flow through the guide through the sorry scroll case or volute case while liquid comes here the liquid goes on entering through the passage of the guide veins. Now, you see this area is decreased because to make an equal amount of fluid to flow through the passages of the guide veins as you see as the fluid flows through the passage of the guide veins. So, therefore, some fluid flow in the in this direction. So, when the fluid comes in the scroll case. So, the fluid mass is reduced. So, the area is accordingly reduced. So, that the entrance velocity of the fluid in the passage of this rotor veins becomes almost same that means to maintain the uniformity in the entrance velocity to all the passages this area that means this scroll case area is reduced this is because the amount of fluid as it flows in this scroll case in this direction is getting reduced the flow rate because of the flow in the vein passages guide vein passages. Now, the guide veins are pivoted in a such a way that this area passage area that means if you consider one such passage through made found by two guide veins is such that it gives a converging area to the flow of fluid. So, that what happens when the fluid flows through this pressure of the fluid is reduced and the velocity is increased. So, therefore, when the fluid flows through the guide vein what happens the pressure of the fluid is reduced and the velocity of the fluid is increased. So, one function of the guide vein is to increase the fluid velocity some of the pressure energy is being converted to kinetic energy another function of the guide vein is to direct the fluid to the runner blade at an appropriate angle that means the angle which is equal to the angle of the runner vein at inlet. So, that a smooth shock less entry to the runner take place. So, therefore, we can isolate here the the purpose of the guide veins which I will tell afterwards. Now, let us see that after guide vein what happens the fluid strikes the runner vein and it flows through this passages found by the runner veins the fluids are channelized like that. Then ultimately flowing out from the runner vein at a at a radial location which is nearer to the axis of rotation it flows to another tube known as draft tube draft tube. Now, we should conceive all this components to conceive all the components. Let us consider the way that this turbines are set in a horizontal plane that is the shaft is vertical that means the shaft is vertical usually all reaction turbines of this type except for turbines of very small capacities have vertical shock that means the entire thing is this turbine is in a horizontal plane. So, therefore, you see the entrance is like this fluid comes in to the scroll case then it enters to the guide vein the passages found by the guide veins then it enters to the runner or the rotor of the machine. And this entrance is a mixed entrance that means it is a combination of the radial and tangential that means the fluid here has got both radial velocity and the tangential velocity well here also fluid has got both radial velocity and tangential velocity. So, the radial and tangential velocity both makes a plane which is the horizontal plane then while coming out of the runner the fluid is turned axially. Axially means in the direction of the axis of the shaft and it flows through a draft tube. So, therefore, if you see the plane view of it then a simple plane view like this you will see which this is the scroll case well. So, this is the runner that means this is the scroll case scroll case this is the guide vein guide vein. So, this is the runner. So, fluid approaches like this. So, throughout this so I can show like this then it comes out to the runner this is the axial direction. So, this is the radial direction. So, this is the axial direction. So, here what happens a tube or a conduit is attached which has a diverging section why it is done? So, this is the draft tube why it is done? So, draft tube draft tube. So, now before coming to all the components again let me tell that why such a tube with diverging area is attached for the final discharge of the liquid from the turbine. So, liquid is not discharged from the rotor as such at the outlet of the rotor, but it is allowed to flow through a diverging tube or diverging closed duct known as draft tube. Why it is done? And you know that for any fluid machines at the discharge of the machine for example, if the liquid is discharged from the runner outlet it has a velocity and that velocity corresponds to a kinetic energy and that is totally loss of energy. If you think of your for example, if you think of your work done you know that head that is is equal to head developed by the machine is equal to what 1 by 2 g if you recollect v 1 square minus v 2 square plus v r 2 square minus v r 1 square plus u 1 square minus u 2 square. So, therefore, you see even for an impulse machine we have seen in Pelton wheel for an impulse machine this is 0 this is 0 for an axial flow impulse machine. So, therefore, head is developed by virtue of the change in kinetic energy whereas, our initial head is 1 by 2 g v 1 square by 2 that means even in an ideal case without friction we cannot have an 100 percent efficiency of the wheel this is because some amount of kinetic energy is rejected. So, this is the head developed and this is the energy input the ratio of which we define as the hydraulic efficiency. So, therefore, the energy which is wasted at the outlet of the machine is the kinetic energy that means this kinetic head we cannot utilize if we could have made this velocity 0 at the discharge. So, the entire energy that is the kinetic energy in case of an impulse machine could have been utilized. So, which now I like to say that for any physical situation liquid has to be discharged with some velocity discharge means it has to be discharged with some velocity which corresponds to some kinetic energy which is a loss. So, therefore, this is a loss. So, this has to be made as small as possible. So, what happens when the liquid is coming out of the runner outlet it has got a high amount of velocity that means the velocity at the discharge of the runner outlet. So, if we can reduce this velocity at the final discharge then what we can do we can reduce the loss in the form of the kinetic energy of the liquid. So, therefore, if it is allowed to pass through a divergent duct as you know for an subsonic flow a area increase makes that it increases the pressure and reduces the velocity. So, velocity is reduced as the consequence of continuity for an incompressible subsonic flow. So, therefore, if we allow a divergent duct to be followed at the runner inlet. So, liquid after the runner inlet with a high velocity relatively higher velocity flows to the divergent duct and ultimately it is discharged at the final discharge level with a lower velocity. So, therefore, this is precisely the function of the draft tube to extract a part of the kinetic energy discharge from the runner outlet. So, that we can effectively gain in the head developed or the work developed by the turbine. So, therefore, we come up to very most important components of a Francis turbine is that important components are first is the volute casing volute casing volute casing next is guide vents or wicket gates guide vents or wicket these are the terminologies wicket gates wicket gates next is moving vents moving vents moving vents or runner and next is the draft tube. Now, we have to understand the function of each and every very simple this is the entrance point liquid enters to volute casing. So, volute casing initially guides the liquid to guide vents the function of guide vents is to increase the velocity partially partly partly part conversion of pressure to velocity and another function is to direct to direct to direct the liquid to direct the liquid in a proper manner in a proper manner in a proper manner to the runner in a proper manner to the runner what does it mean that means it decides the correct angles when the liquid flows through it the vane outlet angle are set in such a way that when the fluid comes out through this its velocity its angle should match with the angle of the vane at the runner blade at the inlet. So, that a smooth shock less flow occurs to the runner at its entry another function is there which will come afterwards that it imparts imparts an initial an initial angular momentum an initial angular or tangential you can call the same thing tangential momentum of the liquid momentum of the liquid momentum of the liquid. So, therefore, you see that there are three distinct functions of the guide vents it partly converts the pressure energy to kinetic energy by allowing the liquid to flow through a converging passages formed by two successive guide vents this is number one number two it directs the liquid in a proper manner to the runner that means. So, that the runner the entry to the runner becomes smooth and shock less that means the liquid velocity relative to the runner becomes equal to the angle to the runner at the inlet and it imparts that initial angular or tangential momentum of the liquid this we will come afterwards then moving vents moving vents is the vane where the head is extracted that means the energy of the fluid is extracted in the form of useful work that already we know there the same principle as happens in imparts machine except the case here as it is a reaction machines the most important part is there when the fluid flows through this moving vents you can see how you can distinguish a reaction machines if you are given a runner then you will see that it forms the passage in such a it is converging in this direction that means in the direction of fluid flow the passage through two runner vents is converging that means whether that means when the fluid flows through this passage between the two runner blades this pressure is change that means both the kinetic energy of the fluid and the pressure energy of the fluid changes that means in terms of velocity both the absolute velocity and the relative velocity changes what happens to the relative velocity relative velocity at the outlet increases from that at the inlet this is because of the convergent duct from which we get a release or a pressure energy is released in the form of the work developed by the turbine try to understand this part another very important fact that distinguishes an impulse machine from a reaction machine that since in an impulse machine pressure in the turbine rotor remains constant that means we can have free jets as the liquid in the rotor of an impulse machine and the liquid in the form of jet can engage one rotor at a time one rotor blade sorry one rotor blade at a time but in case of a reaction machine since the pressure changes while the fluid flows what happens the pressure changes when the fluid flows through the turbine rotor of the turbine therefore the fluid should feel the entire passage of the rotor that means entire passage formed by the rotor blades so it should not engage any particular blade at a time it should totally feel the runner and runner should not be exposed to atmosphere for example we have seen that pelt all runner runner is exposed to atmosphere and the liquid which comes out from the nozzle is a free jet because they are the entire pressure through the rotor of the machine is atmospheric so therefore the runner of a reaction turbine should be completely enclosed and the liquid at for example the water it should feel the entire passage of the rotor so that the pressure is always above atmosphere and it goes on changing while the liquid flows through the rotor blades or the runner of the turbine so therefore it happens so here so after that it goes to the draft tube the function of the draft tube is to reduce the kinetic energy at the runner outlet to a lesser value so that the final discharge from the turbine takes place with a very low velocity of the liquid corresponding to a low kinetic energy which is definitely the loss which cannot be converted in the form of useful work developed by the turbine now before going to the analysis for work developed very important thing is that we must have an idea about the different types of head and how the head varies across a reaction turbine and from here we can get a clear idea of providing a draft tube a clear idea of the working principle of the draft tube now let us consider a very simplified diagram which will give you a clear concept of the change of head across the turbine let us consider this is a reservoir at higher height that means the liquid is stored here which is at a great height from the ground level which is the main source of energy and this is the long pipeline known as penstock as you know this is known as penstock penstock is the pipeline leading to the turbine from the high head reservoir so this is the penstock this is the long pipeline which is tunneled to the rock in the mountain then it comes to the turbine this is the turbine you see this is the turbine is a flange coupling that this shows the typical turbine and this is the draft tube so this water level where it discharges finally this is known as tail rest this is the terminology so this is the final discharge level of the water for the turbine so turbine is set at a distance above this liquid level the tail rest level where the turbine is connected by a divergent duct known as the draft tube now this is the arrangement now we see the heads so if we consider this tail rest level that is this the water level where the discharge is taking place as the datum then you see at this point the liquid has got only the potential energy so head of the liquid corresponds to this height head means energy per unit weight if we consider the atmospheric pressure to create a zero head that means here of course liquid has a pressure rate which corresponds to atmospheric pressure so whenever we will consider the pressure energy of the fluid we will consider it above the atmosphere so therefore the liquid energy here it corresponds to this height that energy per unit weight that means this is h0 is the gross head to the turbine so h0 is the gross head to the turbine now as it flows through this pipeline the liquid comes here so this is the section 1 the entrance to the turbine so this head is lower than this h0 by an amount which is the frictional loss in the penstock the pipeline leading to the turbine from the reservoir so if we apply the Bernoulli's equation between this point and this point we see that the total energy per unit weight at this point which comprises both pressure energy and velocity energy is less than the total energy here which is h0 by the amount h a that is the frictional head loss so here the fluid has got an energy which is h0 minus h a and is denoted as h1 so therefore we see h1 is the net head at entrance to the turbine well so this head comprises both kinetic energy and velocity pressure energy this is because the liquid flows through this penstock develops a velocity so the fluid here is having high pressure and high velocity corresponding to a head h1 now you see when it comes out of the frances runner or the turbine runner at 2 so work is developed so work is coming out so then it has got a very low head again it is flowing through the draft tube where there is no change in the head first of all we discard the friction in the draft tube then we can tell that there is no change in the energy but the kinetic energy is reduced so therefore finally we discharge the water at the tail rest level so if we show this as the velocity energy at the discharge velocity energy sorry kinetic energy kinetic energy at the discharge v3 square by 2g 3 is the section at the outlet of the draft tube then this h this much is the net head producing work that means if we neglect the friction in the turbine so we can tell this is the head at h1 and this is the head which is being rejected that means energy per unit because the final discharge is an atmospheric pressure so this is the head h1 above atmospheric pressure so what is the head at discharge above atmospheric pressure this is only v3 square by 2g kinetic h okay so difference is h which is the net head producing work or sometimes it is referred at head across head across the turbine that means in absence of friction this is the amount which is responsible for the work that means this is equivalent to the work developed by the runner alright so here you see that this is the pressure energy I have shown you this is the kinetic energy so it is mostly in the form of pressure energy and a little is kinetic energy so these are the different forms of head so therefore we see that the head across the machine or turbine or net head producing the work is the difference of head at the inlet to the turbine and outlet to the turbine what is the outlet to the turbine outlet to the turbine is the point three now neglecting friction we can write that now first of all head across the machine or across the turbine head across the turbine head across the turbine is what head across the turbine is is inlet head h1 minus either h3 or h1 minus h2 considering h2 is equal to h3 neglecting friction in the draft otherwise neglecting friction in the draft then you can ask me a question sir if it is so then why do you provide draft you because h1 minus h3 is h1 minus h2 why do you provide the draft you draft you is provided this is the because the with the use of this draft you this h2 is lowered as compared to the case where there was no draft I would like to show that you understand that h1 minus h3 is equal to h1 minus h2 consider the case where there is no friction in the draft you so energy at 2 and energy at 3 remains same what happened to the draft you because there is no energy interaction with the surrounding a part of the pressure energy at point two a part of the kinetic energy at point two sorry is being converted to pressure energy at point three that means here pressure energy is less kinetic energy is more here the kinetic energy is less pressure energy is more so if you now apply you can see this two and the Bernoulli's equation at two and three then we can write if you apply the Bernoulli's equation between point two and three I can write p2 by rho g well plus v2 square by 2 g is equal to what I can write p3 by rho g is zero because we are considering the pressure above the atmospheric pressure sorry sorry plus z plus z z is this height vertical height zero plus v3 square by 2 g so you see that p2 well p2 by rho g p2 by rho g is equal to minus z plus what is there v2 square minus v3 square by 2 g now in this situation for a divergent duct as the draft you you know v3 is less than v2 so therefore this quantity is positive this quantity is definitely the height positive so therefore we see always we have a suction pressure that is pressure is below the atmosphere it is also a common sense intelligent student can very well gas gas speed that if there is a divergent duct and the final discharge of the duct is at atmospheric pressure so somewhere upstream the pressure will be always less than the atmosphere but divergent duct always goes on increasing the pressure and when the final discharge pressure is at atmosphere level at atmospheric pressure so any point upstream in the duct will be having a pressure lower than the atmospheric pressure and the minimum pressure or the maximum suction pressure will occur at the minimum area that is at the inlet to this draft that means at the outlet of the turbine so therefore you see by giving this draft you we can create a negative pressure here that means precisely this h2 is getting reduced that means if you do not give a draft you discharge the water there at the exhaust without a draft you this h2 will be increased because there the pressure will be the atmospheric pressure so you have understood this thing so therefore the h2 increasing means the head across the turbine will be reduced so therefore the purpose of draft tube is to create a negative pressure at the outlet of the turbine to increase the head across the turbine or net head producing work by making it possible by making the turbine to be set at a height from the tail raise so this is another very important point so you should not you do not have to place your turbine at the tail raise so that you can place your turbine at a greater height at a height above the tail raise and at the same time we do not drop you do not have any drop in the available head or head producing work or net head across the turbine by attaching a draft tube that means a diverging duct to the turbine so therefore it is clear that a draft tube reduces the kinetic energy at the outlet or in other way it increases the net head producing work or head across the turbine and at the same time allows the turbine to be set at a greater height at a greater elevation or at an elevation from the tail raise water so I think today that is all about the energy transfer head transfer across the reaction turbine and the basic introduction to reaction turbine if you have got any question please ask any question please you can ask the question in the session please yes this diagram yes good yes yes yes that the inlet to the turbine so at the inlet to the turbine the total head comprises both pressure head and the velocity head so v 1 square by 2 I have seen shown the relative proportion usually a small kinetic head but a large pressure head why because this pen stock this line is of large cross sectional diameter large cross sectional area diameter of the pipe is very high so therefore the velocity head here is not very high but due to the flow of the liquid it has got both the velocity head that it has got velocity head and the pressure head so sum of this 2 is equal to the h 1 that means h 1 is so what is h 1 h 1 is from this point to this point oh sorry plus plus because it is the reference data that means the energy at any point in a flowing fluid mechanical energy is the sum of kinetic energy plus pressure energy plus the data energy that means the potential energy that means velocity head kinetic head pressure head and the potential head so we have chosen this line that means this tail rest level as the data so therefore the total energy comprises of velocity energy which is v 1 square by 2 g plus the pressure energy p 1 by rho g plus this z so therefore this is the total head at the inlet to the machine while the total head at the inlet to the machine and this is the total head at the outlet where pressure is reduced to 0 that means atmospheric pressure head potential head is 0 because we have taken this tail rest level as the datum and the velocity is v 3 square by 2 g so this is given by this so this much amount is the net head across the turbine which is equal to the work done provided the friction loss is neglected so actual work done will be less than that because of the friction loss it is a very important question sometime I ask that a hydraulic machines there is a for hydraulic turbine there is always an hydraulic efficiency even if you have an inviscid fluid as the working fluid inviscid liquid as the working liquid which is not the case in case of pump which is not so in case of pump I will come across afterwards because in a hydraulic turbine you will have to reject some energy at the end of the machine as the kinetic energy so even if you remove friction there is a difference simple example that for a impulse machine or axial flow type as your pelton wheel it is a tangential flow type so the work done even for an inviscid liquid without friction is equal to 1 by 2 g v 1 square minus v 2 square that means the change in the kinetic energy that means initial kinetic energy when the final kinetic energy so final kinetic energy can never become 0 we can we have to discharge the liquid with some flow velocity whereas the inlet energy to the fluid turbine is v 1 square by 2 g or it is more little more than that if you consider at the entrance of the nozzle because of the friction loss in the nozzle but if you neglect the friction in the nozzle totally in the fluid so v 1 square by 2 g is the net head coming to the turbine in the form of pressure energy which was converted in the velocity energy kinetic energy at the outlet of the nozzle and that is being converted to work by an amount 1 by 2 g v 1 square minus v 2 square so therefore even for an inviscid fluid there is an hydraulic efficiency because we have to reject some amount of energy but this is again reduced because of the friction between the liquid and the solid parts of the machines and also because of the friction between the liquid layer that is the liquid viscosity clear any other question yes the height of the drop tube that means at which height runner should be placed what should be the cross sectional area of the how much divergence we will have to give what should be the cross sectional area we will be discussing after these are very interesting problems and the basic physical phenomena which determines these things are known as cavitation this is limited by or constrained by the physical phenomena known as cavitation which will discuss in the next class which will give the limitations for this height above which a turbine has to be placed or which should be the height of the drop tube and what should be the cross sectional area of the drop tube why we cannot reduce the discharge velocity from the drop tube to a very low value that means how much low pressure we can allow at the inlet to the drop tube the very simple that this pressure should not fall below the vapor pressure of the liquid at the working temperature liquid vaporize liquid you will vaporize it is very simple ok I will discuss it in the next class that phenomena is known as cavitation thank you please