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centimeters. So, it is 0. 2376. This divided by 60. So, here U 2 comes out, may be if you substitute these values, we get U 2 as 474.50 meters per second. Now, this is where the velocity triangles come into picture that, if we need to calculate V 2, if you have the velocity triangles in front of us it is very straight forward, it is ratio between V 2 and U 2 is related by tan alpha 2 or cotangent alpha 2 or cot alpha 2. So, let us look at the velocity triangle V 2 and U 2. So, tan alpha 2 is U 2 by V 2 and therefore, V 2 is U 2 into cot alpha 2. Alpha 2 is given as 7 2 degrees and therefore, V 2 the relative velocity at rotor inlet is 154.17 meters per second. Similarly, C 2 is U 2 sin alpha 2. C 2 is this, and this. So, sin alpha 2 is U 2 by C 2 and therefore, C 2 is U 2 sin alpha 2. And, since alpha 2 is 70 degrees, we get C 2 as 498.90 meters per second. Now, C 3 square, that is, the absolute velocity at the exit, C 3 square is V 3 square minus U 3 square. V 3 is given as twice of V 2, and, that is, 2 into 154.1 7 square. And, U 3 is related to U 2 because the diameter at U 3, station U 3 is half that of U 2. Therefore, U 3 is 0.5 times U 2. So, 2 into V 2 and 0.5 times U 2. So, what we get is that the square of this. We basically get C 3 square. C 3 square is 38, 786 meters squared per second squared. Similarly, let us find out the three individual components, U 2 square minus U 3 square. This is U 2 square into 1 minus 1 by 4; this is 1 by 2 square. And, so it is 1 by 4. This should be 1, 68, 863 meter squared per second squared. The second term is V 3 square minus V 2 square, that is, 3 into V 2 square because V 3 is twice of V 2. So, this is 71, 305 meter squared per second squared. The third term is C 2 square minus C 3 square. We already know C 2 and we know C 3 square. So, that difference is 2, 10, 115 meter squared per second squared. So, these are the three individual components, which contribute towards the specific work done. So, the next specific work done would be 1 by 2 times the sum of these three components. So, we add up all the three, divide that by two we get the specific work done. Now, this is one way, while probably the direct way of calculating specific work done. we can also approximate specific work done without having to undergo any of this, but of course, this is an approximate estimate of the specific work done, that is, simply equalPDF Image | Turbomachinery Aerodyanmics
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