We are talking about gas turbines and we just had a look at the basic theories of axial flow turbines and radial flow turbines. In today's class, we will take a look at how simple problems related to these two kinds of turbines can be solved using the theories that we have done. So, I will probably solve a couple of problems for you and then I will leave you with some problems for you to solve for yourselves using the gas turbine theory that we have done in the last two or three lectures. Now, these problems are set out for you, so that one, you can use the theory that we have done in the last lectures and secondly, you get a feel of the numbers. In engineering, it is extremely important that you not only understand the equations and the theories, that you also get a feel of the numbers. What are the possible correct numbers under various situations for various parameters, that feel is extremely important for good engineers. So, hopefully in today's class, I will be able to expose to you some of these engineering quantitative issues and you get a feel for the numbers. So, in today's class, we will do the tutorials, solved examples and tutorial problems on axial and radial flow turbines. Now, the radial and axial flow turbine that we have done, we know are slightly different kinds of turbines even though they do the same kind of job basically that they perform work. So, first we will take on the axial flow turbines and take a look at a problem which represents a typical axial flow turbine problem and then we will discuss some of the tutorial problems that you could possibly attack for yourselves and get a feel for the numbers. The first problem that we have is on axial flow turbine and this problem statement shows that if you have a cooled axial flow turbine. Now, we have discussed the cooling technology of axial flow turbines. So, if we and most of the modern axial flow turbines do tend to be cooled turbines unless it happens to be the last stage of a multi-stage turbine. So, let us take a look at a typical cooled axial flow turbine problem and the problems shows that it has properties such that its entry temperature is 1780 k and entry pressure is 1.4 megapascals and carries a mass flow of 40 kgs per second which means it is a medium sized engine. The mean radius data that means the mean is between the hub and the tip of a blade. So, the mean there is given as Mach number the entry absolute Mach number is given as 0.3. The exit from the stator is given as 1.15 which means the flow has indeed gone a little supersonic at the exit of the stator and the rotational speed at this mean radius is 400 meters per second. T03 that is the exit temperature from the turbine is given as 1550 k and some simplistic angular parameters are prescribed here that is alpha 1 is equal to alpha 3 is equal to 0 degree that means flow is coming in and going out axially that of course simplifies the problem, but it is also reasonably realistic. So, it is not just ideally simplified, but it does represent a realistic flow situation and then at the mean the radius is 0.4 meters and as I mentioned it represents probably a medium sized engine. The axial flow velocity ratio across the rotor Ca 2 by Ca 3 is equal to 1 that means the actual velocity across the rotor is conserved. This is again a simplifying assumption, but also a reasonably realistic assumption it is not very ideal it is a realistic assumption. The loss coefficients through the rotor and the stator the stator is of course, we have been calling it a nozzle. So, the loss coefficient across the nozzle is given as 0.04 and that across the rotor is given as 0.08. So, these two are prescriptions these numbers are realistic numbers and represent a reasonably real compressor turbine situation. Given other thermodynamic parameters the specific heat ratio gamma is given as 1.3 and the gas constant R is given as 287 J per kg k. Now, those are standard parameters and they have been prescribed for this problem also. Now, the problem asked for you to compute the flow properties along the mean line of the stage the degree of reaction the total temperature delta T 0 based on stage loading a based stage loading. Now, this is something which we have discussed before. So, we will try to compute this and then the isentropic efficiency which has been defined and the flow areas at various axial stations and at the hub and tip radii at the nozzle inlet at the nozzle exit and at the rotor exit. So, let us take a look at these problems the parameters that are given and see what kind of solutions we can get out of this problem that has been stated here. Now, we try to put the problem statement in terms of at the mean radius as it has been prescribed in terms of the velocity diagram that we have done before and the problem statement now cast on to the velocity diagram that we are familiar with shows that the entry temperature at station 1 has been prescribed 1780 k and pressure has been prescribed. Now, at the station 1 alpha 1 there is now prescribed as 0 degree and the entry mark number 0 3 corresponds to C 1 which is shown in the diagram. So, that C 1 corresponds to M 1 equal to 0.3 at that particular station. Now, at the exit from the stator nozzle the mark number prescribed is 1.15 which is corresponding to the velocity C 2 that is the absolute velocity and that absolute velocity is prescribed in the form of mark number as 1.15 depending on the local flow condition that is local temperature and the corresponding rotating speed u is given as 400 meters per second. So, in that velocity diagram you can see the value of u and that number quantitative number is given as 400 meters per second. The other thing that is prescribed is across the rotor the actual velocity ratio. Now, you can see C A 2 and C A 3 in the velocity diagram here and that ratio is prescribed as 1 in this problem statement. Also prescribed is that the exit absolute flow angle alpha 3 is 0. Now, this is something which is similar to the entry absolute flow angle. Now, corresponding to the prescription that has been given here we have the loss coefficients the loss coefficients prescribed for the nozzle or the stator nozzle blade is 0.04. The similar loss coefficient that is prescribed for the rotor is 0.08 normally you would see that the rotor losses are somewhat on the higher side because it is a rotating blade and in rotating blade the losses are normally of various origin and this is something we have discussed a little and you would probably appreciate the fact that the number related to the rotor is on the higher side actually it is almost double of that of the loss in the nozzle. The other thing that is given is that the exit total temperature is 1550 k which means it has undergone a total temperature drop of the order of 230 degree k across this turbine. That is the amount of work you can expect that this turbine would have probably accomplished in the process of functioning or in the process of transfer of energy from the gas to the rotor and then mechanical work. Now, this is something which is what the turbine exists for and the quantitative value prescribed here is 230 k that is a pretty large number and you would probably quickly notice that that number is substantially higher than what you can get in terms of temperature rise in any compressor stage. So, these are the prescribed values for the problem that has been put in front of us. So, let us go along and see whether we can complete the process of solution of this particular problem. Now, at station 1 if we look at the numbers that are given and try to find the static parameters. If we can get a value of T 1 and if we apply the isotropic flow conditions at station 1, we get T 1 is equal to 1756.3 k using the isentropic flow conditions and P 1 correspondingly using the same isentropic conversion from total to static condition. We get 1321 kilopascals converting from megapascals to kilopascals. Now, we are using isentropic flow condition because as we have done before in various thermodynamics that at any particular station conversion from static to total or total to static can be simply by using the ideal isentropic relations because at that particular station it is assumed that the flow is undergoing an isentropic conversion from total to static or static to total. That is an assumption that is of course, the theory and we can always invoke that theory at a particular station. There is no process from 1 to 2 it is only at a particular station 1. So, we can always invoke the isentropic flow condition at that particular station in an ideal manner. So, that is what we have done and we have got the static temperature and static pressure at station 1. Now, we can find the velocity C 1 as I mentioned M 1 that was given is corresponding to C 1 and that is dependent on the local temperature that we have just found and if we invoke the local temperature that has been just found we get a velocity which is 242.8 meters per second corresponding to 0.3 that has been prescribed there. Now, since alpha 1 is given as 0 C 1 effectively becomes equal to C a 1 and correspondingly C w 1 would be 0. So, if you keep your eye on the velocity triangle you would see that we are trying to solve all the parameters that are shown in the velocity triangle as far as possible and the trick of solving such problems is that if you can find all the parameters that are shown in this velocity triangle you would be able to calculate the performance of the turbine completely and fully. So, one of the things that you may like to do while solving a problem is to compute all the parameters that are shown in this velocity triangle. So, let us do that and we found that station 1 C w 1 would be equal to 0. Correspondingly then at station 1 we can say that the area a 1 would be equal to the mass flow M dot gas divided by the local density rho 1 into C a 1. Now, this of course, means that we are simply using the continuity condition at station 1 and simply using the continuity condition we can find out the area at station 1. You would notice that you would have to calculate the density rho 1 corresponding to T 1 and P 1 that we have just calculated. So, if you calculate rho 1 and plug in that value here you would get an area that is 0.0628 meter square at station 1 that is at entry to the turbine stator nozzle blade. Now, applying the same isentropic method of conversion from total to static we can find the temperature at station 2 because through the stator nozzle a lot of acceleration has taken place and the total temperature has remained constant, but static temperature has undergone a large amount of change and that shows up here that the static temperature now is 1485.4 k substantially lower than 1756.3 k that we have found at station 1. So, that is a drop due to the large change from potential to kinetic energy through the stator nozzle and correspondingly we find a C 2 using the same method again that is conversion from Mach number to velocity using the local temperature which we have found as 1485.5 and we get a velocity now corresponding to Mach 1.15 velocity of 856.1 meters per second. Now, this is a very high velocity jet and intended purpose of course, is that this would now be made to impinge on the rotor blade to make the rotor rotate. Now, as prescribed 4 percent of the kinetic head is lost in the nozzle blade the nozzle loss coefficient was prescribed as 04 and that is corresponding to 4 percent of the kinetic head as per the definition of the loss coefficient and as a result of which the we can sort of do a reverse engineering and back calculate and find that the ideal T 2 would have been T 2 prime would have been 1503.5 k and corresponding to that the ideal C 2 prime would have been 877 meters per second. Now, this is something we have discussed before in our lecture that through the nozzle because of the real flow situation the actual velocity C 2 is often a little less than what could have been the ideal velocity C 2 prime. Now, this change from real to ideal is quite often a situation that happens because you see at the end of the nozzle you are trying to achieve a sonic velocity sometimes as we see in this particular problem you are trying to achieve a slightly supersonic velocity. So, what happens is you end up getting a little less than what you prescribed or what you design for and hence the loss coefficient comes into the picture over here and this slight loss of a performance through the stator nozzle needs to be accurately factored in your calculation. So, that you know exactly how much you are losing in terms of the acceleration that the stator nozzle is expected to achieve. So, that is what we see here that the ideal velocity could have been a little more through the stator nozzle and as it happens we are getting a little less of the order of almost 20 meters per second, 21 meters per second. Now, this is something what every turbine designer needs to keep an eye on. Now, from the isentropic loss we can also find the value of static pressure P 2 at the end of stator nozzle and since P 0 2 is kind of only factors in the 4 percent loss it tells us that P 2 would be 625.5 kilo Pascal's. Now, at station 3 it is given that exit angle is 0, alpha 3 is 0 and at station 3 it is prescribed that alpha 2 would be corresponding to sin inverse psi into u divided by C 2. Now, this is from the definition of the work done which we have done before that is psi is equal to delta of enthalpy change across the stage divided by u square which is the rotating speed. So, it is used as a normalizing parameter and this is the definition of blade loading or the stage loading quite often used in case of turbines and also sometimes in case of compressors. Now, if you do that you get a parameter that is C a by u into tan alpha 2 from which we wrote down as above that you can get a parameter in terms of alpha 2. Now, C p of course from thermodynamics we know as gamma r divided by gamma minus 1 and if we plug in all those values the stage loading psi can be computed as 1.7878 and this is of course often as a non-dimensional parameter and this number is often an indication of the amount of loading that you can prescribe for a particular stage higher this number is higher the stages being asked to perform and. So, keeping an eye on this number tells you whether the stage has been sufficiently loaded or the stage loading has been maximized and in case of aircraft gas turbine engines as we have discussed before we would like to maximize this number without causing undue gas dynamic or structural problems. Now, from all these calculations what we get is alpha 2 is equal to 56.6 degrees this is the angle at which the flow is coming out from the stator nozzle correspondingly the C a 2 the actual component of this velocity would be 470 meters per second and C w 2 that is the world component or tangential component of the absolute velocity that would be 715 meters per second and of course your v w 2 that is the relative tangential component would be 315 meters per second. So, some of these are numbers which you would probably like to get used to because as you see these numbers are substantially different from what you found in station 1 where C w 1 was of course 0 and hence the change across the stator nozzle only even when no work has been done a substantial change in the velocity field has been achieved through a large acceleration and this is what was of course intended by the so called stator nozzle. If we move forward with these numbers and move on to the rotors what we find there is that at the entry to the rotor the relative flow angle beta 2 can be now found from the tangential velocity v w 2 and the actual velocity C a 2 and if we plug in those numbers we get beta 2 is equal to 33.8 degrees. Now, it can be also shown that corresponding to this that the m 2 relative at the entry to the rotor that is relative Mach number to the entry to the rotor would be 0.76 which is subsonic. Now, we just saw that the exit from the stator m 2 is actually supersonic that was prescribed as 1.15 and we see by conversion through velocity triangle the m 2 relative is now subsonic. Let us take a quick look at the velocity triangle you see corresponding to our calculations C 2 has been prescribed clearly as supersonic we got the velocity value and we got the v 2 velocity value when we converted v 2 to m 2 relative this is clearly subsonic by the local flow conditions and this is exactly what has been achieved through this velocity vector transformation that the exit velocity here can be clearly supersonic, but the entry here would be subsonic and as I have mentioned earlier this is done deliberately that if most of the modern turbines today still admit flow into the rotor which is subsonic. It is indeed possible to admit flow into the rotor which is supersonic that means you can indeed have supersonic rotors, but normally in aircraft gas turbine even today it is not a done thing supersonic rotors have been used in other applications notably in termination the applications in space crafts, but they are normally not used in aircraft gas turbines. So, in aircraft gas turbines we still keep the v 2 value subsonic this is deliberate and very done very consciously for the turbine design. So, that the losses through these turbines are somewhat under control as you can see the loss to the rotor is already little on the higher side and through the shocks it would have gone even higher and hence most of the aircraft gas turbines even today are essentially subsonic rotors. Let us get back to the calculations that we were doing through the rotor we can now find the area at the station 2 which is at the entry to the rotor and that is again found by using the continuity condition and the continuity condition tells us that value of a 2 can be written down in terms of the various flow parameters there and it comes out to be of the order of 0.58 meter square. Now, axial velocity at the exit of the stage can be found simply by using the velocity triangle that we were looking at and this comes out to be 470 meters per second. Now, we have seen that this actual velocity is constant across the rotor. So, the value of C a 2 would be exactly same. So, that is how this velocity has been computed. Now, at the exit again it is been prescribed that alpha 3 is 0. So, C w 3 would again be 0 and therefore, the value of V w 3 would be equal to the rotating speed of the rotor and that is 400 meters per second and corresponding relative velocity leaving the rotor would be 617 meters per second. Now, this is of course, relative velocity. So, as we can see that the relative velocity here is also essentially subsonic and we will see that it is a little on the higher side compared to V 2. Now, the exit flow angle beta 3 can be computed and this comes out to be 40.3. This is invoking the fact that alpha 3 is indeed 0 and static temperature at station 3 now can be computed again invoking the isentropic laws as we have done in station 1 and 2 and if we do that we find the temperature to be 1461 K. The total temperature of course, was prescribed. So, it is easy to use the isentropic laws and find the static temperature that is 1461 K and the sonic speed at that particular station is 738.3 meters per second and we can very well see that this velocity V 3 would be subsonic. So, the exit velocity from the rotor also is subsonic. So, both the entry and the exit velocity from the rotor are deliberately kept subsonic to avoid shock losses which again would reduce the efficiency of the turbine, increase the losses and reduce the efficiency and most of the designers present day designers are extremely sensitive to efficiency of the turbines and hence they try to keep the turbines subsonic even today. And the other thing is most of the work done is being accomplished higher level of work done is being accomplished by increasing the turbine entry temperature and this increase of turbine entry temperature is quite often the focus of attention of modern research and more and more cooling technologies applied and we have prescribed that this particular problem actually applies blade cooling and that is how that high entry temperature was admitted and hence we see that we have a cool turbine here which is a cool turbine the entry temperature is very high and that allows the designer to keep the rotors subsonic and hence the rotors are not under any compulsion to go supersonic to get more work done rotors can be kept subsonic. Another reason why modern designers would like to keep the rotors subsonic is because many of the modern rotors are also subjected to cooling technology. Some of these cooling technologies as we have seen are extremely intricate and if we have supersonic flow over them it will be an extremely complicated fluid mechanic situation and most of the turbine designers would like to avoid that kind of complication in their turbine design because it would impact on the efficiency or aerothermodynamic efficiency or what we call isentropic efficiency of the turbine quite adversely. So, as we see by the numbers that they are deliberately kept subsonic. Let us proceed with this problem and see whether we can complete it. The degree of reaction that we have prescribed before as we see now if it is computed using all the parameters comes out to be only 0.106 and as we have discussed in many of the modern turbines the degree of reaction values are of that order much lower compared to what you have done probably in your compressor chapter where the degree of reaction values are somewhat much higher than these numbers. So, you got to get the feel of these numbers that degree of reaction in turbine is substantially lower than that of compressors and these are the numbers you would need to get used to. The Mach number at the exit then the absolute Mach number is 0.6375 and the relative exit Mach number as we just saw is subsonic and it is 0.836. It is slightly higher than what it came in with into the rotor. So, the rotor is clearly a reaction turbine it has accelerated the flow a little and has produced a reaction and hence it is a reaction turbine. The relative total temperature and pressure at the exit can also be computed to complete the calculation and we get T03 relative as 1614 K and P02 relative as 897.3 kilopascals by applying the rotor loss. I need to mention here very clearly here that the rotor loss coefficient that was prescribed should be applied across the rotor in a relative frame. So, the 8 percent loss that was prescribed should be applied to P02 relative and if you do that you get P03 relative at as 872.7 kilopascals. Now, this is something you need to again very clearly understand that the loss prescription that is normally given should be applied in the absolute scale in the stator nozzle and should be applied in the relative frame in the rotor and when you are calculating the pressure losses respectively across these two rows of blades. So, losses in the rotor take place in the relative frame in the stator it takes place in the absolute frame. So, you need to take note of this and do your future problems accordingly. Using the isentropic relation we can now find the stator static values that is P3 as 566 kilopascals and the total pressure is 731 kilopascals. Correspondingly we can find the exit area at station 3 and this exit area is now a 3 equal to again using the continuity condition and using m dot which is constant across the stage the local density rho 3 and C a 3 the local actual velocity C a 3. If we apply all those we get at station 3 the area is equal to 0.63 meters per second you can see that the area across the stage is going slightly higher because the flow is actually losing its pressure and temperature and it is losing its density and hence the area requirement would be higher as you go through the stage. So, these are the numbers you need to understand and made I am trying to make it clear that when you get these numbers when you are solving a problem certain numbers would tell you whether your solution is proceeding along the right path and you get the feel of the number that you are probably when you get the numbers in hand. Let us finally, put them all together the performance parameters that we get from this in terms of temperature ratio the total temperature ratio is 1.148 the total pressure ratio or the pressure drop across the stage is 1.915 which is a modest total pressure ratio across turbine stage many of the modern turbines could possibly have much higher pressure ratio across its stage. The efficiency of this particular turbine can now be computed using the thermodynamic laws that we have done before and it simply is 92.9 percent which is a fairly good efficiency many of the modern turbines can have efficiency slightly higher than these, but 92.9 nearly 93 percent is definitely a good efficiency. At each of these stations the blade height can also be calculated simply using the geometry at that particular station that is H i equal to A i divided by twice pi or mean at that particular station and if we put them all in table in station 1, 2 and 3 we get the areas which we have computed before and these areas are now shown over here and then across the rotor as you can see there is been an increase in area and across the stage indeed there has been a slight increase in area. The height as you can see again has changed across the stations correspondingly the tip radius and the hub radius can be found using the geometry that is available with us. So, this table gives us an idea about the changes that typically occur across a stator and the rotor this may vary from one kind of turbine to another if you go from HP to LP this variations would be slightly different. If you go across to the last stage of a LP it will be again slightly different it depends on the turbine design and as I just mentioned that the pressure ratio 1.95 915 is a modest pressure ratio many of the modern turbines could indeed have pressure ratios are quite higher than this and if they are then all the values that you see here in terms of area height and the tip radius and so on would indeed change from station 1 to 2 to 3. So, it depends on turbine and every turbine would have unique such numbers except that if you get the feel of the numbers you would know whether the numbers are coming out in a correct trend and that trend is what you can get the feel of when you are solving a problem, but the numbers for every turbine would be quite different from each other. What I will do now is I will prescribe a few problems for you to solve for yourself using the methodology that we have just solved the problem. So, the first problem is actually that of a impulse turbine where reaction is 0 and if we do that we prescribe that it has a entry pressure of 414 kilopascals static pressure of 207 and exit pressure of P 0 from the stator nozzle of 400 kilopascals. So, it is lost about 14 kilopascals across the stator nozzle the exit static pressure from the whole stage is given as 200 kilopascals. Now, when operating with a rotating speed you mean at the mean of the rotor blade 291 meters per second the entry temperature given is modest 1100 k and alpha 2 that is exit from the stator nozzle is prescribed as 70 degrees that is from the exit of the stator nozzle. Again it is assumed or prescribed that C 1 that is entry velocity is equal to the C 3 which is exit velocity from the stage what is asked for is compute the total efficiency of this particular stage prescribed are the values of C p and gamma which are the normal values the C p is 1148 kg per kilo joules kg per k and gamma is 1.333. So, if you use those numbers you would probably get an answer close to 91 percent as efficiency of the stage I hope you can sit down and solve the problem using the method that we have adopted before. Let us go on to the next problem which corresponds actually now to not a impulse turbine. Let us look at the problem and we will see that the actual velocity as prescribed through the actual turbine is held constant by design that means C a 1 is equal to C a 2 is equal to C a 3 and this entry and exit velocities are also actual that means C a 1 is equal to C 1 C a 3 is equal to C 3 it is a simplified problem and the flow coefficient that is C a by u through the rotor is 0.6. Now, if you do that the gas leaves the nozzle with alpha 2 equal to 68.2 that is at the exit of the stator nozzle. Now, at all mean diameter that means across the stage if you if you just traverse through the mean diameter from the stator entry to the rotor exit you are required to find the stage loading coefficient psi the relative flow angles at rotor mean diameter beta 2 and beta 3 those are the relative flow angles the degree of reaction r x and the total to total and total to state static efficiencies that we have prescribed in our lecture earlier and you are required to find both the efficiencies and the answers given are that your stage loading coefficient is 1.5 the relative flow angles are 40 and 59 degrees the degree of reaction is 0.25 and the two efficiencies the total efficiency is 90.5 and the total to static efficiency is 81.6 as we have discussed during the lecture the total to static efficiency is normally lower than the total to total to total efficiency. So, these are the answers you would get by solving the second problem. Let us look at the third problem this is following the design data applied to an uncooled axial flow turbine you get P01 equal to 400 kilopascals T01 equal to 859 k and at mean radius alpha 2 equal to 63.8 degree degree of reaction is 0.5 and phi the flow coefficient as 0.6 P1 static temperature at the exit at the entry is 200 kilopascals and total to static efficiency is now prescribed in this problem is 85 percent. If the actual velocity is held constant as in the last problem through the whole stage you are required to compute the specific work done by the gas the blade speed and the stage exit static temperature. Now, these are the numbers that you would get you would get 131 kilo joules per kg and the blade speed would be 301 meters per second and the stage exit static temperature would be 707.5 k. If you look at the fourth problem it is an axial flow turbine now again with a cooled rotor now as I mentioned you could have cooled rotor. So, you have a problem here which says that the mass flow is 20 kgs per second the entry temperature total temperature is 1000 k and P01 is 4 bar C a is 260 meters per second and this is assumed to be constant through the entire stage again it is prescribed that C1 is equal to C3 you mean is 360 meters per second alpha 2 that is exit from the stator nozzle is 65 degree and alpha 3 at the exit to the stage is 10 degree and nozzle loss coefficient is prescribed as 0.05. You are required to compute the relative flow angles at the rotor mean diameter beta 2 and beta 3 at the mean the degree of reaction r x the stage loading coefficient psi the power output of this working turbine and the nozzle exit throat area neglecting the real flow effect that means you assume that it is an isentropic ideal flow and you can still find the nozzle exit throat area and if you adopt all these prescriptions the answers that you would be getting as the relative flow angles would be 37.2 degrees and 57.4 degrees respectively the degree of reaction would be 0.29 the stage loading coefficient would be a very good 3.35 power output correspondingly would be 43.40 watts and the nozzle exit throat area would be 0.04 meters per square. This is the throat area at the exit of the nozzle which is typically at the end of the converging channel that is prescribed or normally used in the stator nozzle. The fifth problem that is prescribed to you is the axial flow turbine with cooled nozzle and rotor blades that means both nozzle and rotor are prescribed to be cooled operates with the following flow parameters at the reference diameter which is the mean. The entry temperature is a respectable good modern temperature that is 1800 k the entry pressure is 1000 kilopascals C A 3 by C A 2 as we have done in our problem is equal to 1 that is axial velocity across the rotor is conserved mark number at the exit of the stator nozzle is 1.1 that is it is allowed to go slightly supersonic and u mean is 360 meters per second alpha 2 prescribed is 45 degree and alpha 3 at the exit of the rotor is prescribed as 5 degree. You are required to compute the following that is C 2 at the exit of the stator nozzle C A 2 the actual velocity between the stator and the rotor C w 2 the absolute tangential component of the velocity at station 2 between the stator and the rotor C 3 the absolute velocity at the exit of the rotor C A 3 the actual velocity and C w 3 the tangential velocity at the exit of the rotor. So, all these velocities that is you are required to complete the velocity triangle that we have seen before the total temperature drop across the stage and correspondingly of course, the total temperature ratio across the stage the pressure ratio across the stage and then P 0 3 for a polytropic efficiency of 89 percent. And if you adopt all the prescriptions that are given and the velocities that are and other parameter that are asked for you get those numbers the velocities are 830 meters per second 585 meters per second and 587 meters per second for C 3 and 585 meters per second for C A 3 and C w 3. You get a temperature drop of the order of 184 K corresponding temperature ratio is 1.148 and the corresponding pressure ratio or a pressure drop across the turbine is 1.792 which gives you exit pressure of 591 kilopascals. So, those are the answers you are likely to get if you adopt the prescription that are given in this problem. Let us now take a look at a problem of radial flow turbine. This radial flow turbine we which we have done in the last class using the simple theory that we have done in the last class we can try to solve this problem. What is prescribed here is that the mass flow is 2 kg per second which means it is a small turbine. The entry pressure is 400 kilopascals the entry temperature is 1100 K and the entry pressure undergoes a 1 percent loss that means the pressure at the exit of the stator nozzle is 0.99 times P 0 1. The nozzle exit angle alpha 2 is 70 degrees. The polytropic efficiency is prescribed as 0.85 for the turbine. The rotor maximum diameter that is at the tip of the radial turbine is 0.4 meters. The radial flow entry into the rotor is prescribed and that is assumed to be or allowed to be assumed to be equal to the exit of the rotor which is C A through and it is supposed to be axial. So, the axial velocity at the exit is to be taken as equal to the radial velocity relative radial velocity at the entry to the rotor. The up to tip radius ratio is 0.4 and T 0 3 at the exit is 935 K. The thermodynamic parameter is prescribed here gamma equal to 1.33 or equal to 287.287 kilo joules per kg K and C P as 1.158 kilo joules per kg K. The problem asked you to compute a rotor tip speed rotational speed and rpm of the rotor. The Mach number velocities the rotor width at the tip of the rotor and T 0 2 relative. The stagnation pressure Mach number hub and tip radii at rotor exit at the rotor exit plane the relative velocity v 3 T 0 3 relative relative flow angle beta 3 and the relative Mach number m 3 at mean radius of course, they are all connected to each other. The values of beta 3 the relative flow angle and m 3 relative at different radii at rotor exit. Now, these are the answers that are expected out of this problem statement. Let us look at the radial flow turbine diagram that we have done before what is prescribed is the tip diameter of the rotor is prescribed as 0.4 at the entry to the turbine what is prescribed is 0.0 P 0 1 equal to 400 kilo pascals T 0 1 equal to 1100 K and alpha 2 over here is prescribed as 70 degree v 2 R is that in this v 2 R here is to be equal to this C A 3. So, this radial component which is equal to v 2 here in this diagram as is normally often done in many gas turbines would be taken as equal to C A 3 that is this C A 3 that is coming out of the rotor the absolute component of the velocity and its axial direction. The T 0 3 prescribed is 935 K and the hub to tip radius ratio of the rotor at the exit station you see there is a hub here station and there is a tip of the rotor at the exit and this is prescribed as 0.4. So, these are the prescriptions with which we go forward the loss across the stator nozzle is 1 percent. So, with this we move forward to solve the whole problem the rotor tip speed can be simply found by using the isentropic laws and that tells us that if you use the enthalpy drop you get a rotor tip speed of 437 meters per second. Now, this rotational speed then can be found simply by dividing this u by r and that gives us to 285 radians per second corresponding to which you would get the rpm equal to 20870 rpm. So, as you can see here a typical radial turbine would be running at very high rpm compared to an axial flow turbine. The corresponding at the rotor tip the value of C 2 would be 465 meters per second using the velocity triangles that we have just seen the corresponding V 2 or would be 159 meters per second. The local speed of sound using the local temperature T 2 you have to do that and if you do that you get T 2 equal to 707 K and corresponding sonic speed as 620 meters per second. And then the nozzle exit Mach number M 2 comes out to be 0.75. So, as you see here it is not sonic it is still subsonic. The area at the rotor tip now is can be found using the continuity condition as we have always done before and this comes out to be 0.0164 you have to find the local density and before that the local pressure. So, if you do that you get this area at station 2 using this area at station 2 which is the entry to the rotor you can find the width of the rotor tip that is the actual width of the rotor tip using the geometry you can find the rotor tip width to be 0.013 meters. This is simple geometry and then you can find the relative total temperature using the flow condition that we have used before that is T 0 2 you take out the absolute flow kinetic energy and plug in the relative kinetic energy and if you do that the T 0 2 relative is 0.0171,017 k. The expansion ratio of the turbine at this operating point using the prescribed polytrophic efficiency can be found by using the relation that we have done before and it gives you a velocity value of 2.16 which of course gives us a P03 of 185 kilo Pascal's. Now given that V2R is equal to CA3 which would be then equal to 159 meters per second and this of course is same as V3 that we can therefore get M3 relative that is the relative Mach number at the exit of the rotor as 0.267 you would of course need to find T3 over there. So, which is taken to be constant from root to tip at the rotor exit. Now at station 3, A3 can be found as using the continuity condition as m dot divided by rho 3 into CA3 and this yields rotor exit area to be 0.02363 meters square. So, that is the area you would get at the exit of the radial turbine rotor. At the rotor exit area if you find the radius using the area that we have found we get the tip area using 0.4 as the ratio tip radius to be 0.0946 meters and hub radius to be 0.378 meters and hence the mean radius would be 0.606624 meters corresponding to which they are CW3 the tangential velocity which is equal to U3 would be 144.8 meters per second. The corresponding velocity triangle at the rotor exit would yield that C3 at the mean of the rotor exit between that is mean between the hub and the tip of the rotor exit is 215 meters per second and the T03 at that mean would be 944 K. The corresponding mean Mach number would can be now computed and you would get a value of 0.362 as the mean Mach number at the exit. The corresponding exit flow angle would be 42.3. The radial variation of these two parameters that is beta 3 and M3 relative can now be found and a Mach number and the exit flow angles go up with radius in a marginally non-linear manner. So, let us look at the solution in a graphical manner beta 3 is shown over here and M3 relative on the other y-axis and the change of radius across as we can see M3 varies along this line path and beta 3 varies in a slightly different manner both of them of course going up from hub to the tip of the exit of the turbine. So, this is what the solution of a radial flow turbine is I will leave you with a tutorial problem which you can solve on your own. The radial turbine problem prescribed here is that the operating point data are given to you P01 is 699 kilopascals, T01 equal to 1145 K. The prescribed nozzle exit pressure is 527.2 kilopascals and the nozzle exit temperature is 1029 K. The stage exit static pressure is given as 384.7 kilopascals and static temperature there is 914.5 K. The P03 value correspondingly is prescribed as 924.7 K. If it is given that the impeller exit area mean diameter to the impeller tip diameter is chosen as 0.49 that is the ratio between tip and mean the design rpm is prescribed as 24000 rpm assuming that the relative velocity at the rotor inlet is radial as we have done before and the absolute flow at the rotor exit is axial again as we have done before. You are asked to compute the total to static efficiency of the radial turbine, the impeller rotor tip diameter and the loss coefficients in the nozzle and the rotor using the definitions of the loss coefficient that we have done in the lecture. If you do those things you would get answers the total to static efficiency would be 90.5, the impeller rotor tip diameter would be 0.27 meters and the loss coefficients would be for the nozzle stator nozzle 0.05, 316 and for the rotor 0.2. As we see the rotor loss coefficient is substantially higher than that of nozzle loss coefficient. So, these are the numbers you would get and as you can see these numbers are quite different from that of axial flow turbine. So, we have done to solve two problems one on axial flow turbine, one on radial flow turbine and we have prescribed some problems for you to solve and as you can see you can get the feel of the numbers that the numbers corresponding to radial flow turbine are quite different from that of axial flow turbine. If you talk in terms of efficiency, if you talk in terms of rpm, you talk in terms of the mass flows the numbers of axial flow and radial flow turbine are quite different from each other and by solving the problems I hope you would get the feel of these numbers and that is very important for engineering people to get the feel of the numbers. We will leave the turbines with these problems and we will proceed in the next class, we will proceed on to the combustion chambers and that is what we will be doing in the next class. So, we have finished the turbine chapter and from the next class we will proceed on to the combustion chamber which actually spatially in a gas turbine you remember comes before the turbine. So, we will now look at how the hot gas is created that is applied to the turbine and that is what we will be doing in the next class.


And then Andrew and Senator strongly condemned all forms of violence against women and girls, emphasizing the need for more robust measures to safeguard their interests. This position was articulated during Thursday's plenary, where the senators actively participated in the 16 days of activism against gender-based violence on women and the girl child. Details on this report. Adorning orange sashes as a symbol of solidarity for the advocacy. The lawmakers, including the president of the Senate, Gotswilakpabiu, were united in their commitment to address this critical issue. The advocacy motion was sponsored by 17 senators, spearheaded by Senator Ereti Kingibe, representing the FCT. Since the launch of the National Gender-Based Data Room and dashboard, over 28,000 cases of gender-based violence have been reported nationwide. In all these reported cases, over 9,000 have been opened against offenders, while over 8,000 are still pending in various courts. As over 1,800 cases have been withdrawn, either by the courts, community intervention, family and victims that have become afraid or intimidated to withdraw the case. The number of convictions are only 455. And sadly, the number of fatalities from GBV are over 1,250. Voicing their support to the motion, Senators Adams Oshomole, Natasha Okoti and Abdul Ninge, among others, acknowledged the virtues and sacrifices made by women globally, with a specific emphasis on those in Nigeria. I think we'll job between justice to the foundation of our own, of our system, by not only passing motions like the UN is doing without teach to bite, we should pass laws with appropriate tools and encourage the police to afford those laws and prosecute. I'd lend my voice in calling for a stop in all form of violence against girls, children, schools, workplaces, and also ask that all the agencies that are responsible in mitigating this floor step up in their responsibilities so that women will have a safe place to live and thrive. I so submit. Thank you. It takes two to tango. The women folk also must, at every given time, know their position in society. If you may, as they listen to also rise to the occasion, they are human beings like every other of us. And therefore, they must not allow themselves to play circumpedic. They are not circumpedic. They are the important foundation of every human society. In concluding the debate before the motion was passed, the Senate president declared that all the senators are in agreement that violence against women and girl child must be unequivocally condemned. Please, as we protect the rights of women, we should also protect the rights of men. There are men who are suffering under their wives. There are many men who are groaning and nobody is listening to them because United Nations has not yet taken up the issue of violence against men. On that note, I thank all of us for your contributions and all that God Almighty will give all of us the wisdom to protect the women and protect the girl child. A minute silence was thereafter observed to honor the memory of all women and individuals who lost their lives due to violence.


Who's excited to learn about growth hacking marketing and design today? Much more awake than I am that's fantastic So who knows who knows who this product is? Evernote does anyone use ever now? Everyone love ever note so I've been using ever note for quite a few years Probably close to a decade, and they're one of my favorite products And also they are one of the best examples of growth hacking that I've seen So just a little bit of history about ever note So they started around 2008 and they started with a closed beta and they did no marketing for the first few years while they were around The product founders wanted to focus on building the best product that they possibly could And so they did a lot of really cool techniques that generated a lot of buzz so Early 2008 they started with about a hundred invites And they wanted to kind of do like some user testing with these hundred invites And it kind of spiraled out of control to about a hundred and twenty five thousand users in 2008 Ah, hi, and then they started working with this premium model. So What they did was actually really brilliant. So you could download and use ever note for free Up to two devices. So if you're like me, you've probably got more than two devices at any given time I'll probably have my phone my laptop and tablet And so I want to make sure that all my work is synced across these devices But where they got me was that the three device mark. So I started paying them because I had to use the three devices and one of the really cool things they've done to Initialize some growth was that they had a lot of key partnerships one being with 3M and sticky notes So what they did was basically with every pack of sticky notes that you bought you get a year with premium Which is really cool growth tactic And so back in 2008 this was kind of unheard of but if anyone is familiar with ambassador programs They kind of started this way back when and so what they did was actually really brilliant And so they would have these power users And if you've ever been in an office environment where there's like a bunch of people having a meeting around a board table And there's always that one person just on their laptop typing away, right? And so they did was they've made these stickers for those those users to put on their laptop So it said I'm not being rude on taking notes with ever note and it kind of spread like wild wildfire there Which is pretty cool and then address the real-life concern because people like why is this person on their computer? Not paying attention and so that was a great little marketing technique So a little bit about me before we move forward at UX designer working on jetpack and automatic With a broad focus on overall customer experience Marketing and product making sure there's cohesion between the two for a better experience and research and growth And if you want to follow along while I give this talk, it's just slides comm slash Jeff Galinsky slash growth slash life Sorry for the long URL, but you can pull it up on your phone your laptop right now I'm just all along you can't see the slides that well So we've got a lot to cover today and just to give you a little feel for what we're gonna be talking about I'll be talking about growth hacking as a methodology the history behind it What is it? Traditional marketing versus growth and then a bit about the process behind that And then I'm gonna dig into how growth design transcends marketing and into products There's this thing called the a3r3 growth plan I don't know if you can comment to that and how you can apply that process over your work And then finally I'll be talking about how to harness and some tips to help you with your marketing products and Service design and especially a focus on quantitative and qualitative reason. So what is all this stuff? So I'm gonna be talking about hacking marketing design and I'm gonna be throwing these terms around a lot and just so you know Basically growth hackers and growth marketers place an emphasis on the business itself using like these little hacks and marketing techniques to Drive growth in the business Growth designers take that like another step deeper and what they do is they kind of focus on User-centric design to make sure we can grow the business but also offer great customer experience So let's set the stage. So this all started around the mid 90s. You went during the dot-com boom You know starts for exploding Microsoft became huge Apple was huge and There was a shift in the way people Used and absorb information the internet became like a household thing things started moving a lot quicker and then Traditional marketing wasn't working the way it used to it's very expensive. It was very wasteful And so this new sort of mindset came out. How can we get in front of customers? How can we slide things across their desk rather than trying to market to them on a grand scale? and So one of the examples that I love to use And talking about growth hacking growth marketing growth design is actually Airbnb So if you're not familiar with Airbnb's history, they actually started as a company That focused on getting people to rent out their living rooms only as a bed and breakfast So someone would literally sleep on like their couch like a couch server or maybe in their bedroom And then they would actually offer the full bed and breakfast experience Just in their living room and so what Airbnb found is that that's kind of a niche thing And not many people are into that weird experience of just eating breakfast in someone's tiny room So they discovered that there was a bigger market to be had there And so they expanded to allow people to rent out their entire apartment or rent out their entire house And now they're a $10 billion company because they saw a different product market fit there And they pivoted and changed their business model quite a bit And so another thing that they've done which is really awesome, which I love is how many people here? Travel places and they open up yell and you go and you're looking to find like a new place to eat Revenue I and then I do this all the time But I don't just grade like possible experience on like the ratings I look at the photos pretty heavily, especially if I'm looking at somewhere eat And so if a customer posts these absolute terrible photos that are like half blurry half eaten burrito I'm likely did not go to that restaurant just because that customer posted that weird-looking photo of that half eaten burrito So what Airbnb did was actually send professional photographers around the world To these different people who are trying to rent out their homes and their apartments And they have pro photographers take photos of their places to put on their website to keep the value of their marketing up which is pretty cool and Growth hacking especially is about moving quickly shipping and iterating shipping and iterating just getting things out the door As a traditional designer I've always been the type of person who likes to be a perfectionist And I'll work on the redesign of my website for like six years before I ship it and then I've redesigned like eight times And it was really difficult for me to get out of that mindset of just get an MVP out the door Just get a minimal viable product just get it out there And so to dig in a little bit more in growth marketing versus traditional marketing When we look at traditional marketing over the past decades throughout the 20th century In the history of traditional marketing It's it basically places a focus on driving awareness and acquisition of a product Spending a ton of money to get people to know a product so if you look at like take for instance like radio advertisements and if we're thinking about like a An automobile dealership and they'll spend like whatever $10,000 for a month long commercial marketing campaign and radio and they send it out there and the radio station will play these ads to however many people listen to the radio between nine and five Monday to Friday and They just try to market to as many people as possible and they just throw a ton of money at it But it's not really directed at any specific type of person just what I was listening to the radio Our friends at Squarespace wicks and Shopify do this They spend like $50 million a year trying to advertise to as many people as they can so we think about like Super Bowl ads in Squarespace that's all they do they throw a ton of money and have commercials at Super Bowl But it's for a bunch of people watching football and not necessarily a bunch of people who need small business websites If you're thinking in terms of growth hacking what we would do is we would target more specific people that way people who might be looking for a website So the main takeaway here is that marketing is making people want the product Whereas growth marketing is making a product that people want And so seeing how people interact with your products seeing how people react to the marketing of your product and then changing the product based on that and Here's a little real life example of a little growth hack that I discovered so On the side I'm a hobbyist photographer and I made a promise to myself that when I was younger any hobby that I have I would Make myself kind of recoup my costs of the hobby through the hobby itself So what I do is try and sell my photo prints and I took this photo in Canada a couple years ago And what I did was I posted it on my Instagram and I've got a Facebook page You know everything that every small business owner would do And you know you get a couple likes and a couple people comment like wow, that's beautiful But no one bought the print and so what I did was a little experiment experiment on Instagram where I am So I posted it and set the location. This is in British Columbia, Canada And then what I did was I clicked on the Instagram map And then I looked at all the people who had recently been to this location and then posted similar photos of this And I'm like wow, this is a great place and in a very creepy sort of way I followed all those people and commented on all their photos Because they had an emotional connection to this place They then drove traffic to my website and I sold 15 prints from those people that I wanted to follow it So I specifically targeted people who had been there and enjoy their time there and had an emotional connection And the great thing about that was my customer acquisition cost was zero because I spent zero dollars I didn't do any sponsored content on Instagram or sponsored content on Facebook So that's kind of like a little growth hack right there You can kind of specifically target these different people and You grow your business that way Alright, so let's dig into the process my my favorite. I'm a very analytical person So as I mentioned before growth hacking growth marketing growth design is all about shipping and iterating And so a great product process to start doing that is to start with a little bit of research Dig into Google Analytics look at some talk to some people get a baseline for like how people are using your products How they're using your service how they're using your marketing website and then come up with an idea I just think of you know, like okay. I looked at Google Analytics I see that this try it free button on the homepage or the sign up button on the homepage in this location isn't working very well Why what's going on here? Let me let me think about a new place to put that on the homepage and just get it out there Just ship it and then as you ship it it's gonna start measuring I'm gonna start collecting data on that even ask people This doesn't make sense to keep this button here, you know and And then you you can look at that data and then you can go back and revise and change and ship and measure and etc Keeps going on at home So who here is familiar with the authors Seth Godin or Tim Ferriss pretty much everyone, right? So it's a great story about how this process worked for them We all know that they both have a ton of books You can go into any Barnes and Noble and just buy one of 18 books that they've published Every one of their books or at least most of their books all started as a blog post on the website They posted a couple ideas a couple paragraphs. They got some feedback. They got some buzz They built upon that idea then they released ebooks and then they got more feedback You know, they changed the added things and then it eventually just led to what published So both authors started with a blog post worked up to like an ebook and then eventually published a book because of that So small ideas turned into big ideas because I kept iterating and shipping iterating and shipping It's a lot different now because you don't see the same success of an author who goes and hides in the cabinet of Woods for a year and just comes back with a 400 page novel unless there's even thing of course So Once you start working with that process a little bit more I like to stack multiple processes on top each other to keep a more efficient workflow So I'll start with a little bit of research On one idea. I'll build it and I'll ship it and then while it's out there collecting data people are using it I'll start with another one and I'll let that one collect and measure data And then I'll start with another one and then as you get more and more comfortable You can kind of maximize your efficiency here and work on various processes And if it's just you I would recommend maybe just doing three things at once Otherwise it's kind of hectic and if you have a small team, you can just stack on all the stuff So let's talk about how growth design marketing hacking transcends marketing and product or service So this is called the a3r3 funnel. So there are a couple of variations of this in the wild Some people call it pirate metrics because the acronym is three a's and three ours So are which is a terrible terrible stereotype So it's either that or the a3r3 which I refer and then you might see different versions of this where awareness and acquisition Are kind of one item and then referral and revenue are kind of reversed. It doesn't really matter. It's all the same process So digging in a little bit into that. So let's talk about awareness. What is it? It's education it's informing people of what you have to offer it's becoming known and Why it's important because you can't have customers that they don't know what your product or services pretty standard stuff One success story that I really love is actually hotmail who remembers hotmail Rest in peace So before Microsoft bought hotmail they did this really brilliant thing in the mid 90s, which was unheard of at the time But if someone sent an email through hotmail, which was a free service They applied a simple plug in their footer. This email was sent by hotmail get your free account now Which now sounds ridiculous because it's been done to death But they were the first people to do it and so because of that small email plug on their free product They went from one user to being bought for I don't know how many million dollars by Microsoft because their growth exploded People saw that and they were using their terrible squirrel mail accounts, and they were like, let's try this new service and they loved it And another success story which is huge on Instagram is ambassador programs, which I mentioned before with Evernote and So many companies will find Advocates of their product or service and then they'll give them free swag and stuff just to kind of promote their brand Which actually works quite well, especially in the photography community You'll see a lot of professional photographers as like Nikon ambassadors or Fuji film ambassadors And so you see these people posting amazing photos That's like hashtag shot with Fuji film and it causes other people to buy the product because they want to have great photos, too so That's a great example of awareness moving on down the line. It's acquisition So it's this is the point where people know your product and then they become emotionally invested They haven't yet signed up for your product, but you're kind of roping them in a little bit And if you're not intriguing people with a solution to a problem or just intriguing them in any sort of way They're gonna be like why would why would I care about your product? So a lot of people who have done this really well, of course Facebook with the exclusivity factor If anyone knows how Facebook started they started in the Harvard College campus And then you know college Harvard kids were talking to their Yale friends and Yale was like what's this Facebook? Why can't we have this and then Facebook was like we'll give you Facebook and then Yale got Facebook And then the Princeton kids are like why do these kids have it? Are we not good enough Facebook rolled out to them and they slowly built up their audience and then by the time they had all The college campuses general public was like we want Facebook and then finally Facebook rolled out to everyone And then that's how they slowly built staircase kind of broke And then the mailbox app would just no longer with us again rest in peace actually did this really well was that they built this exclusivity factor where They had like a numbered list on their site and it was like sign up for mailbox app your number 459,000 in line and so what it would do is it would trigger this thing in your brain We're like I'm gonna get on this list right now because I don't want to be the 500,000 person in line and have to wait for this product So they had this this number ticker going all the time whether it was fake or not no one knows but People people signed up quick because who cares just an email address and then we're now we're gonna dig into Activation a little bit. This is the exact moment where someone enters their info and click sign up And so this is the part where everyone starts to get the growth so this is One of the things we've actually done in the jetpack side of things to do this who here is familiar with the process of Installing a plug in and WP admin. I hope everyone So one of the things we've noticed is that When someone is in WP admin the plug-in section they search for a plug-in you have to install it Then you have to activate it and what happens after you activate the plug-in usually nothing. You're just left there in the Plug-in screen. What do you do next? No one knows unless you're really savvy with WordPress So one of the things that I designed was that at the moment that someone clicks activate We'll just show a full-screen dialogue putting them into a linear flow like okay, you've activated jetpack We know you want to use it. Here's what to do next. Well, I'm a jetpack connect to wordpress.com Here's what we offer and so over the past few years We've seen our connection skyrocket and the uses of jetpack skyrocket because of this one small tweak that we experimented with We saw that a lot of people would activate jetpack and just not do anything because they didn't know where to go after that So now that we put them into like a linear flow. It kind of keeps them on board a little bit longer Which leads me to my next topic which is retention keeping happy happy customers longer One of the things to keep in mind here is churn So it really doesn't matter if you have a hundred thousand sign-ups on a Friday if you know 50,000 of those people leave on Saturday morning because that you just wasting everyone's time at that time at that point So what you need to do is work on having happier customers And some people who who do this really well obviously again This is why they're so successful the big three Facebook Twitter and Instagram With the invention of mentions and hashtags and it's something not many people think about But it keeps people roped in so right now I'm sure some of you have a notification on your phone from Facebook someone's tag you and something They start a funny meme and they'll like you know come check this out And they mention you and then at that moment you pick up your phone You see the notification you tap it and then you get brought back into Facebook You get brought back into Twitter and that's how Facebook and Twitter and Instagram keep you coming back So they can keep showing you advertisements and things like that and keep you engaged longer They're very smart you watch out for them And so Next down the funnel is referral programs So I know these have been done to death over the past decade or so, but you can get really clever with the way that you do these One company who did this really well is Dropbox if anyone remembers when Dropbox first came on the scene What they would do is say hey sign up for Dropbox And if you refer your friend will give you a hundred free megabytes of space up to 10 gigabytes And so I remember I went crazy and referred everyone I know for free drop-off accounts and to this day I still have 10 gigs of free space from Dropbox and I know a lot of my friends actually ended up paying for Dropbox because they didn't get as much space as I did So they got their customers. They grew their business. I still have a free account. We're doing good and if everyone remembers Groupon, I don't know if they're still around much but Groupon was great at like these group events and giving coupons for different You know services and local businesses and so Groupon was great about saying hey You can get this offer for free You can get like this go play paintball at this paintball course to free if you refer five friends And then I'm like hey friends check this out sign up for this so I can go play paintball for free And so that's how Groupon kind of drew their customer base And then finally there's revenue and I don't really need to talk about why you want to make money But one of my favorite quotes that's been said a lot is we don't make movies to make money We make money to make more movies And I don't know if that's Amazon scheme probably not but one of the one of the great success stories about Amazon Has anyone heard of smile.amazon.com? That's fantastic So if you are an Amazon shopper Amazon does this really cool thing that they don't really advertise too much But if you shop from smile.amazon.com you can select a charity and like 1% of all the money that you spent on smile.amazon.com goes to that charity So they kind of drive their business selling the same products that they normally sell but with this Subdomain attached to it. It's like a charity program So 1% of all the money that you spend goes through different charity That you select and it kind of is a nice way to drive business yet also give back and I think that was very clever of Them to do that So next up you all remember both of these things So what I like to do is keep moving all of my different pieces moving forward It's not like a game of chess where you're more strategic It's more your game of checkers where you just kind of move up the board So what I do is I'll find I'll be like okay What do I want to do to drive more awareness on this product that we have like I work for jetpack So what am I going to do to drive more jetpack awareness? I'll do a little bit of research I'll come up with an idea. I'll ship it I'll let it measure and then while it's gaining data people are using or looking at the website and We're looking at Google Analytics. I'll go to retention How do I what can I find in the product to make it a little bit better to people a customer happier longer? Then I'll do the same thing with that. I'll come up with an idea. We'll ship it We'll do like an AV test sign it out there for a couple weeks or a month and while that's just sitting there percolating I'll work on something. I'll do like revenue like how do we make more money with this product again? Same thing and then you just keep revisiting and revisiting one of the big keys here is that You never want to come up with an idea ship it launch it and forget about it You always want to make sure that you're coming back to the idea whether it be two weeks whether it be a month Whether it be six months you need the follow-up. Otherwise, you're not going to keep up with that constant growth And now we're going to talk about how to help your marketing and your product and some tips and tricks there So research I know research gets a bad rap, especially if you had to write tons of thesis papers in college or high school But it needs to be done whether it's quantitative or qualitative try and get a mix of both You're going to need to utilize them You're going to need to know how people are using your product or service And if you need to change your business goals if they're not using the way you thought maybe the way that you design your business Isn't the way you need to have your business and So starting with qualitative research everyone knows this one It's having things like Google Analytics and heat map setup. That's the wrong slide It's having things like heat map setup Google Analytics, Jetpack, stats. I use quantitative things like analytics For a lot of investigative work. So let me show you some examples of that. Hodger is one of my favorite tools for heat mapping So what we can do is we can anonymously kind of monitor how people are using our website So on jetpack.com we have this setup and we can kind of look at what devices they're on if they're using You know if they're on large screens and laptops if they're on tablets if they're on their phones We can see how they're what they're clicking on we can see where they're scrolling and moving around the screen And so it gives us a little bit of insight because if we like the Warmer marks or the people are clicking most and if you highlight over those you can see exactly how many clicks you've had And the given sample size that you've assigned so most of the time I'll say alright Let's set up a heat map for jetpack.com. We'll set it to for the next 2000 unique views we'll see how people use the site what they're clicking on where they're going what they're doing And if we see that maybe we've got this call to action button set up in the bottom right on the side somewhere And they're not clicking on it Maybe it's time to think about changing that location or changing the verbiage that sort of thing and then we can Set up things like flows and funnels where we can see like okay We've got 7,000 people who visit the home page only a lot less than that only like 2,900 of those people end up going to the pricing page from there only 1,000 people actually end up becoming customers and then there's a steady decline there all the way down to actual Registration of our product and it's really nice to be able to just really quickly look at this and say alright So out of the 7,000 people who visit the home page 3,000 visit the pricing page. That's a pretty steep drop off. What's happening here? Why are we not intriguing people? Are we not giving them enough information? Are you know as our pricing structure wrong that sort of thing? So you can quickly just dive in and this is the initial part of that process I was talking about the research part, so I'll say alright, maybe the home page needs more. Let's look at that I've come up with an idea. I'm gonna ship it. We'll test that we'll set up a new funnel in a month To see how that's doing and then next up is the qualitative research I've gotten really into this over the past year at automatic In speaking with people I find that if you have one 20-minute conversation with someone who's a customer It's better than any Google Analytics dashboard you can investigate because I can learn a lot about how people are using my product What are they doing? What do they love? What don't they do? What don't they love that sort of thing? But when you're doing these things if you have like like survey setup or formal interviews where you have video calls with customers It's important to have a pretty big sample size because it's always that outlier You could talk to one person who's very specific niche Like if we're talking to you all you're probably pretty technical with WordPress You might not be the intended demographic that we're looking to get information from we might want less technical people Maybe we want to interview Developers specifically or pro marketers that sort of thing and so it's important to have big sample sizes So you can kind of formulate trends and the information and kind of sympathize all that and So just a couple tips to get started Start with the research as I mentioned Do the quantitative stuff dig in form some baseline hypotheses and then start to build and ship and just figure out What works and what doesn't So I'm very technical with my my processes you can formulate your own But just make sure the important thing is that follow-up coming back to your ideas seeing how they've worked out How they haven't worked that sort of things One of the things that I love to do is kind of creating flow charts of the different flows of our product So kind of mapping everything out seeing where people are going what they're doing where they're spending their time and then kind of Formulating different hypotheses to figure out. Okay at one point. Can I work on this part at what point? Can I work on this part at what point can I work on that part and just moving forward slowly there? Make sure that you're continuously experimenting It really doesn't cost much money to whip up an AB test if you if you have like a marketing website There are plenty of plugins that do that come up with an idea See you never know something you might have thought of might not have thought of six months ago might be Awesome at generating traffic and generating users now and So a couple tactics that I've been out there for a while that have kind of been overplayed There's this I Don't know if anyone has seen this in recent years envision app got really good at doing this But you'll you'll get like these seemingly personal emails from people you don't know and it's like hey Jeff I love what you're doing it automatic great work on with the new website jetpack.com Do you have a minute to talk about Marvel app? Here's an example that happened to me in September by my friend jinter who I've never met apparently who knows me very well They wanted me to use Marvel app and on September 4th He sent me two emails and on September 12th He sent me two emails and then on September 18th. He sent me another one and in one of them. He said hey Jeff I know how inboxes can get busy. I wanted to make sure this didn't get lost on the shuffle and I was like you serious dude Like stop this. I'm not gonna respond to this. I know this is marketing I didn't be getting this work really well, and I'm sure it got a lot of leads And was really successful But in the tech industry this no longer works because I know this is being auto-generated and just my name is being Applied to it and that sort of thing And Another one which I'm sure you all know very well These pop-ups the minute that you load a page or a site if you're on Google looking for something and these things will pop up like hey Subscribe now and get six free ebooks or whatever and in the beginning that worked great But now that'll make me immediately close your site And so that was a small growth tactic that was really successful for a while That's been overplayed to death and so That's just another example of things you might not want to do So that's it for me right now if you have any questions I'll be around so I can answer right now and my slides are at slides comm slash Jeff Linsky slash growth so Over the past few months. I've been using whimsical.co. Have you heard of it whimsical? It's it's a very simple very intuitive tool. It's very dynamic And it's their free offering is fantastic. Definitely check it out That's a good question So one of the important things about as I mentioned before it's kind of You need to be contextual and you need to get in front of people at the right time when they're trying to do a very specific thing So as I mentioned with the jetpack close like we didn't just show up like a full pop-up page and said hey Get started with jetpack now welcome It was only the second after that they activated so the second that they did a very specific thing So one of the things I think we do on the jetpack blog is that we'll write like an article and at the very bottom of the article We won't throw up a pop-up and trying to annoy anyone But we'll have like learn more about this check out our plans that sort of thing right at the very end after they've read The content and they're engaged. They've been acquired, you know that sort of thing So Yeah, that's a great question So I didn't mention the talk but one thing to be careful of is this term called vanity metrics So, I don't know if anyone's familiar with that term But so things like general raw page views don't really matter that much like you get like a hundred thousand visit unique visits Tomorrow and that doesn't matter if you're not converting anyone if you've got a hundred thousand unique page views and just five sign-ups There's probably something wrong there. What's going on and that's that's something to keep in mind because a lot of people get Really intrigued with things like follower counts and like these numbers that really intrigued people like total page views and stuff like that But the things you want to be mindful of are more along lines of actual sign-ups and who's converting on things and stuff like that Sure Okay, I don't think so. I can probably download this and send it Mm-hmm Oh sure you're talking about like the the software itself or like Yeah Is it just Yeah, I think that it's it's especially being in the tech industry I think that we just have a tendency to see these trend worker and more and then like we can see them getting overplayed in our industry a lot like that tactic probably works if you're advertising to a lot of non-technical folks, but you know me being me I see that I'm like I know what they're doing and then seeing my inbox being flooded by 20 of those style emails every week You know it's just one of those tactics that might work at first But the more that it's been done the less effective it becomes I mean, I'm sure it's very successful in some industries for sure Yes Yeah, sure well, there's one person in particular that I love his name is Ryan holiday and he wrote a book called growth hacker marketing Which I highly recommend Which is I've got a couple resources here One of the first ones here, and it's a quick read maybe a hundred pages or so maybe less And so he's a really great person He kind of got me started on this whole growth hacking thing and he's a great person to follow He stays up to date with a lot of the trends out there and stuff like that so And then there's a few like UX blogs that I stay up to deal with other than that I just see him in the wild right and then I investigate. Yeah Oh So I guess it's not maybe the email isn't the best channel to reach me specifically so for instance in that example that I sent out That was someone working for this Marvel app Which is some UX program and if I'm sitting there on a Monday morning checking my inbox trying to catch up on emails That's not the best time to try and sell me on a product, you know And so maybe as a company their growth tactics would be better to use somewhere else like it as a designer I'm out there like some like googling some some new flow mapping tool or something And maybe they could kind of pinpoint their marketing in a different place in a very contextual manner like when I'm actually out They're looking for something like that as I mentioned before like the way squicks and Squarespace does their marketing right they market to like Millions of people at once and hopes to get a few of them right During like the Super Bowl and maybe that's not the best tactic because it's very expensive and if maybe that they were marketing more specifically like if someone was to go to YouTube and You know look up like WordPress tutorials, which people do all the time and you'll see a Squarespace ad there That's more targeted marketing. I guess that Hey, just Right my expectations were set with the subject line only to be fooled when I read the email This person Right I couldn't unsubscribe to it because it was it's like it's actually sent by someone It's not Also


La Liga guaranteed whoa showdown SBC. Oh, yeah, this was leaked. Where's the SBC though? The one that we're looking for a La Liga Tots upgrade. It is two segments 84 86 with a team of the season required 84 86 with a team of the season. Okay turning in two of the cards.  I haven't even packed Fakir yet But we're trying to say trying to manifest the Griezmann the Pejri the Levandowski the Benzema the Vinny the Kunde La Liga Tots player pack on the account starting off. Come on first one. Come on any sports Yes, it's a blue. It's not a moments Germany ter Stegen, you know what? I kind of needed that needed for the links needed for the arojo links. That's That's mid. That's mid usable, but mid. I can't say dubby to that, bro. Good luck, bro Good luck. Tots La Liga pack second one. I wanted some bangers today real bad for you guys real bad No, are we two for two? Ah? Ter Stegen guaranteed packs. Here we go Here we go. All right. Good luck, man. Good luck. Good luck. Good luck. Please EA sports Kihei sports Wait, Pedri. Oh, okay, Marina Marina Marina. That's that's uh Technically the most expensive one that we've packed so far today Technically that is the most expensive one because other than that it was ter Stegen. Is that a dupe for you though? There's probably a lot of dupes with these in there No, it's not all right. Not bad. The French flag is what we want or or Brazil if you see France It's a dub use its agreement Benz or Coonday Brazil is a dub too. All right. Here we go Argent, ah Molina all right. These are not starting off that great not starting off that great What's the price of this SBC 100 K 115 K to do it? So realistically you need to pack ball day or above to make your money back all day or above to get your money back Man, is this even worth doing considering what we all know we're going to get I think it is though like you do the 81 times 11 every day just in case right you do this just in case you get Somebody other than ter Stegen or marino which so far that's basically all that we've gotten I imagine that ter Stegen and marino are both dropping right now because they're getting packed from this I would have to imagine Who's this? Somebody different. No. Oh, yeah, somebody different somebody worse. Oh my goodness David Garcia like what is this man? Not even a taste of something good. Come on. Give me a taste EA Spanish Pedri oh Oh, they gave us a taste chat. Boom Let's go Pedri Hey, what did we say like one in ten chances one in seven right? That was like the seventh one we've opened bang Fudge this one's for you a Moment be right mid Fikir that's the first time we got Fikir today. Oh, I'm sorry. Losi and those senior. I am sorry on it's a duplicate as well Dizzy sorry, bro. Okay. Here we go It's Molina next week chat We're gonna be thinking about Argentina and it's gonna be all about messy messy messy, but right now it's Molina, bro All right, here we go. Oh, it's a moments be right mid be right mid No, it's not even Spanish. It is not even Spanish, bro other than that They're probably gonna start rebounding like Pedri here probably pretty soon. Yeah. All right. Here we go again speaking of Pedri Can we speak that into existence one more time? No, it's her staggin Ripsky, bro. It's just a quick flip if anything Nah another Molina, bro. Yikes. All right, here we go Molina, you know what? Molina and her staggin are by far the most common that we've seen they are by far the most common right chat. Okay. Who are you gonna get Spanish? Ball day. That's the first ball day other than mine from upgrade packs, bro That's a dupe. I'm trying to watch the loudly guitars cars. Let's see if they're gonna go up today or not Spanish center mid. It's not Pedri. It's Marino wasn't counting up fast enough man Well, well, well at least it's not a dupe. All right loudly guitars player. Good luck, man Somebody different here, please somebody cool Spanish Pedri Gabi Vega. Okay rip. Are you supposed to get nominees this time? Oh, we got one over here Spanish center back It's a rip. Oh Man Cardi G. I'm sorry about that. David Garcia, bro Moments the care are just L's Unfortunately L's because the pack weight most often Spanish center mid Marino, wow, this is really a Marino simulator. Isn't it my Brazil sometimes? Oh Victor Who's this one gonna be? Javi Galan, of course for staggin is the only player I pack from loudly guitars and now they give me him again from the pack the cure Dang, bro. All right. Here's another one We haven't seen a flag other than the Spanish and a couple Argentina and then the Germany flag, bro moments Pick your paint, bro. You got edder militao, but I have him read Do theory can we get edder militao? Can we see a Brazilian flag? No Spanish left-back ball day again? Holy dub just packed your rent a can't believe it said right mid nice. All right Come on. We just have some your rent a you have two of them. I think we got some your rent a Mike theory happening right now Let's see it. Oh, no way. It's a moments. Oh No way. Oh, no freaking way. Why does that happen so often chat Mike theory? Mike theory. Wait, is that a duplicate? It's not freaking dub, man Bro, that happens like every single stream somebody in the chat's talking about your rent a they just pack him He's in the rotation chat. He's in the rotation. Nah, here we go. Show me right mid again. No way. Oh It's Javi galan oof. Oh, that's a duplicate too. It doesn't get any worse than that EA hook him up Don't hook him down hook him up EA sports team of the season No, I've seen way too many Molinas today way too many EA is giving out all these Molinas so that you can link Him to your flashback Carasco that really nobody wants to use either man. That's pain dude. Thank you for the share play though moments Your rent a your rent a oh no way chat. He's in the rotation. That's two of the last three almost I think that's two of the last three unless I can't count bang No What? You probably have him like red to oh, no, you don't you have him right there Man, I feel like so many people are getting duplicates for the ones that they have read to W turned L so fast. Okay, here we go Spanish left-back ball day. Hey, you can link to your level not a dupe. W. All right, Todd's pack for Barca ma Spanish Pedri nope Vega you can kind of tell right like midway through the animation if the numbers are counting up really fast You know, it's Pedri. I mean we did see that once today, so we kind of knew but dang man All right, here we go loudly guitars. Good luck, bro. How are these loudly guitars cards moving to I want to look at prices in a second blue Spanish center mid come on No, I'm a Reno, bro. Yeah, I'm gonna get my second guaranteed pack from finishing the cup today right mid Nope, it's for cure and thank you guys for all the follows today.  Oh? Hey Luca for that we're gonna play Hey Don't tell me it's a dupe. It's not a dupe. Let's freakin have it man Finally somebody a W other than Pedri wait, do you have him read? No, we opened your red. Oh, you do have him read frick You do have him read that's right. Potter is up from where it's been during Tots But if you bought a pre Tots, it's probably still down overall. It's high rated Spanish center-back. Oh my gosh the nemesis Man, but uh if they're baiting us with Renato that is that's naughty of them, bro Hey, is the Modric luck in let's go bro. That's a big freakin dub big freaking W I just hope it's not a dupe at these days. I don't know man. We packed Modric five minutes ago And it was a dupe blue Spanish Ta oh 81 11 you're telling me. There's a chance Right mid show me the right mid. No, thank you. That's a duplicate to golly, bro. Here we go Wait Vella. Whoa. Whoa. Whoa. Whoa. Whoa. Was that your MLS guaranteed?  Hey, yo Yeah, Eddie loves that one. All right now time for the La Liga. Can your luck carry over? No used all your luck on Carlos Vella, man. Yikes. Oh pH Bressi icon. No, I think I still have him. I gotta put him into some sort of SBC though Petrie, please. No, it's Marino, bro. It is Marino bum bum bum. Okay second time's the charm, right? No way. It actually is Modric Luca Modric Bang eG's man five hundred thousand coins G freakin G's Hot to lead pack. Wow.  That's cracked actually cracked Fedeida and Sebastian Dree you see as well any other bangers ter Stegen You know what if those are tradable duplicates, then you're really in the money But I don't know if those are tradable for you or not fair play man Toffee Titans you're going for the top German Wait, is that a big bro Little bro. Lawn little bro. Lawn man. I'm sorry, dude. All right. Never mind Wait, wait, who was was that? Oh, Javi Galan. Yeah, you kind of knew didn't you pain? All right. Good luck, bro. I Come back. It's a primer George best only if only man. All right, here we go French off a cured nah rd. Thank you for trying though, bro My reds first couple weeks not good then all of a sudden boom kunday Modric You know, so it's like that's you're kind of doing it hoping to get a big one from like this, bro That's the first Loa That's the first Loa, but that's kind of what you're grinding for right? Yeah, you know Maybe every week you're not gonna get the best player from a team, but that's that's big You just wait for your time to come and you hit one You know, but like exactly like you said all it takes is one like Clove said all it takes is one Lawn League of Tots player pack Vamos Vamos Spanish left-back ball day. Yep more of the same more of the same Good try moral the story is we know these packs are never that amazing But you still do them for the gamble and the what if for the guy that got Benzema today for the guy that got Uh the Modric for the guy that got the Pedri with their lucky day, man