 The key takeaways from the previous lecture or as follows, it is possible to affect a certain transfer of work to the rotor of a turbo machine by means of the change in specific enthalpy of the fluid in the rotor passage or by means of a change in specific kinetic energy of the fluid in the rotor passage or both. The fractional contribution of the change in specific enthalpy to the total specific work transfer is defined as the degree of reaction as indicated here. In addition, in the case of an axial machine, any change in specific enthalpy of the fluid across the rotor passage always results in the change in the relative velocity of the fluid in the blade passage. Furthermore, in the case of an axial or radial machine, any change in relative velocity in the rotor passage determines the change in pressure along the streamline which passes through the rotor blade passage. So, now, it is clear from this discussion that when work transfer takes place to a rotor, the absolute velocity of the fluid, the relative velocity of the fluid as well as the blade velocity in the case of a radial machine can change between the inlet and the outlet of the rotor. We have also seen that it is customary to indicate these velocities by means of a velocity triangle since the absolute velocity of the fluid B at any location is the vector sum of the blade velocity plus the relative velocity. So, it is imperative that we gain clear understanding of velocity triangles and also be in a position to interpret velocity triangles and try to get as much information from velocity triangles as possible. So, this is what we will discuss next. So, here we are given two velocity triangles, one at the inlet to the rotor, one at the exit to the rotor. Let us see how much information we can infer from these two velocity triangles. Now, we notice right away that U2 is not equal to U1. So, the blade speed actually increases from inlet to the exit of the rotor which implies that the machine is a radial flow machine. Furthermore, since U2 is greater than U1, it follows that R2 is greater than R1. So, the machine is actually a radial outflow machine. Next, since R2 is greater than R1, dr is positive and judging by the magnitude of the relative velocity from inlet to outlet, we can see that C2 is less than C1 which means that dc is negative and so this term contributes positively to the overall right hand side and so dr is positive, dc is negative. So, both these things together give rise to a dp being positive in this case, which means that P2 is greater than P1. So, this corresponds to the rotor of a compressor or a pump. We notice further that at inlet, the relative velocity C1 is perpendicular to U1 and it is clear from this that beta 1, the blade angle at inlet is equal to 0. In this particular case, since the machine is a radial machine, this implies that the blade at entry is actually a radial blade. That is, it is aligned in the radial direction. Since beta 1 is the angle that the tangent to the blade profile makes with respect to the reference direction. So, in this case, because the reference direction is the radial direction, we call this a radial blade. Now, in case the reference is the axial direction, beta 1 equal to 0 would suggest that the blade is axial, it is an axial blade. In case it is an axial machine. Now, in contrast, if alpha 1 is equal to 0 at inlet, for instance, that situation would be referred to as radial entry in the case of a radial machine and it would be referred to as axial entry in the case of an axial machine. So, beta equal to 0 would imply that the blade is radial or axial as appropriate and alpha equal to 0 would imply radial or axial entry or exit as the case may be and depending on whether it is a radial machine or axial machine. Furthermore, since the relative velocity C curves away from the direction of the blade speed, notice that the blade speed is in this direction and that the relative velocity curves away from the direction or angular velocity direction, we can infer that the blade is a backward curved blade for this particular case. So, here we are again given the velocity triangles at the inlet and exit of a rotor. It is also said that u1 is equal to u2, so that it is also indicated here. So, that means that it is an axial machine since u2 is equal to u1 and since the C1 is not equal to C2, there is a change in the relative velocity in the blade passage. So, that means it is the reaction machine. As we have already discussed, there is a reaction machine. Furthermore, since C2, the magnitude of C2 is less than the magnitude of C1, the relative velocity actually decreases in the blade passage, which means the blade passage acts like a diffuser or it is a diverging passage. And so, what we are looking at here is actually a compressor or an axial compressor or an axial pump. Again, application of this information to this equation makes it clear that this term is zero because it is an axial machine and DC is negative. So, that means this term becomes the overall term contributes positively to the pressure change. So, that means the pressure increases in this case. Let us move on to the next example. So, here we are given once again velocity triangle at the inlet to the rotor and it exit to the rotor. And it is given that u1 is equal to u2, which means that this is an axial machine. It is also clear from the velocity triangle that C2 is not equal to C1, which means that it is a reaction machine. And if we now look at this equation, dr is zero because it is an axial machine and C2 is greater than C1, that means DC is positive. So, that means this term contributes in a negative fashion to the DP term. So, DP is less than zero. This is equal to zero and this entire term is negative. So, DP is less than zero, which means that the pressure decreases in this passage. C2 is greater than C1 implies that the blade passage is a converging passage. So, the flow accelerates which means the pressure decreases. Therefore, this is the rotor blade of a turbine. And furthermore, we see that the relative velocity at inlet is perpendicular to the blade direction, which means that beta1 is equal to zero in this case. Since this is an axial machine, we refer to the blade at the inlet or the blade profile at the inlet actually is in the axial direction. So, it is an axial blade at entry. So, this is an axial reaction machine with axial blade at or axial blade profile at entry. So, looking at this velocity triangle, it is indicated that U1 is equal to U2. And furthermore, it is also indicated that C1 is equal to C2. So, let us see what information we can glean from this velocity triangles. So, U2 equal to U1 implies that it is an axial machine, C2 equal to C1 implies the following. Since it is an axial machine, dr is zero. And since it is given that C2 equal to C1, dc is equal to zero. So, that means dp is equal to zero for this rotor, which means that the pressure remains constant and there is only a change in direction of the fluid. So, that means it is an impulse machine. Is it an impulse type of work absorbing machine or an impulse type of work producing machine? May be determined by looking at the tangential component of the absolute velocity. Notice that v theta 1 is in this direction here and v theta 2 is zero because v2 is perpendicular to U2. So, v theta 1 is positive, v theta 2 is zero. So, that means that from Euler turbine equation, the work is W dot is positive. So, this is an impulse axial impulse turbine. So, this discussion makes clear how much information can actually be presented or associated with velocity triangles between the inlet and outlet of a rotor. And students should actually go through this very carefully and make sure that they are able to interpret the velocity triangles given any particular situation and draw these types of inferences even before doing any calculation. What we will do in the next couple of lectures is to work out examples where we try to draw velocity triangles based on the given information in the in the example and try to do some calculations.