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the velocity at the exit, that is, C 3. And, to calculate velocity at the exit C 3, we know beta 3, we also know U 3. And, how do we know U 3? Because rotational speed is given to us and the diameter at the hub or at the exit of the rotor is also known. So, from that we can calculate U 3. Since U 3 is known, beta 3 is known and we can calculate C 3 that is basically, U 3 cot alpha 3 should be equal to C3. So, once C 3 is also known, the static temperature as at the exit T 3 is equal to stagnation temperature T 0 3 minus C 3 square by 2 C p. And, so that, it is a rather easier way rather than this longest formula, I just shown. And then, substitute for that in the expression and we should able to calculate zeta r, which is the rotor loss coefficient. Nozzle loss coefficient is already known to us. It is 0.07. So, what you can see is that the loss coefficient for the nozzle. This case has been given as 0.07. And, for the rotor it is 0.62. And, so I think, I have also given some range of these values in the last class. I had mentioned typically, the rotor loss coefficient are on the higher side because of the fact that there are rotational effects come into picture losses, associated with the rotor are much more than the rotor losses associated with the stationary component like a nozzle; especially when the flow is accelerating. So, in this case the rotor loss coefficient is, in fact close to one order magnitude higher than the nozzle loss coefficient. So, this solves our second problem, which required us to calculate the total-to-static efficiency as well as the rotor loss coefficient. So, you can clearly see that this is slightly more involved question. In this, of course I have taken the easier route of directly substituting this in the formulae. What I would strongly urge you to do and probably leave that as an exercise for you to derive these equations from the first principles and not simply use the direct longest formulae. It is very easy to derive the equations from the first principles. In the total-to-static efficiency definition term, it is basically T 0 1 minus T 0 3 divided by T 0 1 minus T 3 s. Or, let us express that in terms of enthalpy, h 0 1 minus h 0 3 divided by h 0 1 minus h 3 s. The denominator gets expressed in two separate forms. One is to do with nozzle loss coefficient; second is the rotor loss coefficient. Numerator gets expressed in terms of mass flow rate C p and delta T and so on. So, from this, you can actually say denominator has a nozzle and rotor loss coefficient term. Numerator is already known to us.PDF Image | Turbomachinery Aerodyanmics
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