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by 2 M 0 2 square. This again follows from the isentropic relations. We have already seen that, it is the relation between stagnation temperatures to static temperature, stagnation pressure to static pressure and so on. We can also relate the corresponding Mach numbers in this way. So, since we have calculated M 0 2, we substitute that here and then, we get the static (( )) Mach number based on static conditions that the absolute Mach number as 0.775. So, this is again, this can be calculated in multiple ways. The other way, which I suggest you can try to calculate would be to take the ratio of T, absolute velocity; that is, C 2 divided by square root of gamma or T 2. Stagnation temperature is known at the inlet and to find static temperature, we need T naught minus C squared by 2 C p. So, is basically we need to calculate C square at the inlet. And, to calculate C square we will of course, need the blade speed because you need to calculate because blade angle is known. And so, if you know the blade speed at tip, that is U 2, you can solve C 2, and then, therefore, calculate Mach number. In this case, of course we are doing at other way round. We are calculating the Mach number first and then, we are now going to calculate the blade speed at the tip. But, it can also be done the other way round. So, let us now calculate the blade speed at the exit of the nozzle or, that is the entry rotor, entry tip of the rotor. Delta W by C p T 0 1 as we know is equal to gamma minus 1 into coos beta 2 into U 2 square by a 0 1 square. So, here a 0 1 is speed of sound based on stagnation temperature, square root of gamma r T 0 1. This can be calculated as 633.8 meters per second. Assuming, T 0 1 is equal to T 0 2. Since in this case, we know the power output as stagnation temperature and beta 2, we can simply substitute for these values and then, calculate the blade speed at the tip U 2. And, that comes out as 538.1 meters per second. So, the other approach to calculate Mach number would be to actually calculate the blade speed first and then, since blade speed is known and alpha 2 is known, you can calculate C 2. And, from C 2 you can calculate the static temperature T 2. T 0 2 minus C 2 square by 2 C P. And therefore, Mach number would be C 2 by square root of gamma or T 2. So, this is the other way of calculating the Mach number. We have calculated that in the slightly different way.PDF Image | Turbomachinery Aerodyanmics
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