S.mmetrical diagram. The symmetrical-type diagram is constructed so that the entrance and exit diagrams have the same shape: V3二 W4 and V4二 W3. This equality means that the reaction is
R二 0.5 (9-9)
If the work factor requals 1.0， then the exit swirl is zero. As the workfactor increases， the exit swirl increases. Since the reaction of 0.5 leads to ahigh total efficiency， this design is useful if the exit swirl is not counted as a loss as in the initial and intermediate stages.
Impulse Turbine
The impulse turbine is the simplest type of turbine. It consists of a groupof nozzles followed by a row of blades. The gas is expanded in the nozzle， converting the high thermal energy into kinetic energy. This conversion can be represented by the following relationship:
J寫寫寫寫寫寫寫寫寫寫寫
V3二2川h0 (9-10)
The high-velocity gas impinges on the blade where a large portion of the kinetic energy of the moving gas stream is converted into turbine shaft work.
Figure 9-6 shows a diagram of a single-stage impulse turbine. The static pressure decreases in the nozzle with a corresponding increase in the abso-lute velocity. The absolute velocity is then reduced in therotor， but the static pressure and the relative velocity remain constant. To get the maximumenergy transfer， the blades must rotate at about one-half the velocity of the gas jet velocity. Two or more rows of moving blades are sometimes used in conjunction with one nozzle to obtain wheels with low blade tip speeds and stresses. In-between the moving rows of blades are guide vanes that redirect the gas from one row of moving blades to another as shown in Figure 9-7. This type of turbine is sometimes called a Curtis turbine.
Another impulse turbine is the pressure compound or .atteau turbine. In this turbine the work is broken down into various stages. Each stage consists of a nozzle and blade row where the kinetic energy of the jet is absorbed into the turbine rotor as useful work. The air that leaves the moving blades entersthe next set of nozzles where the enthalpy decreases further， and the velocity is increased and then absorbed in an associated row of moving blades.

Moving 
Blades 
Nozzle 
 

PT
o, o Vabs
PT
s, s
Figure 9-.. Schematic of an impulse turbine showing the variation of the thermo-dynamic and fluid mechanic properties
Nozzle Vo  Moving Blades Absolute  Turning Fixed Blades P Total Pressureo  Moving Blades 

Velocity 
P Statics  Pressure
Figure 9-7. Pressure and velocity distributions in a .urtis-type impulse turbine

Figure 9-8 shows the .atteau turbine. The total pressure and temperatureremain unchanged in thenozzles， except for minor frictional losses.
By definition， the impulse turbine has a degree of reaction equal to zero. This degree of reaction means that the entire enthalpy drop is taken in thenozzle， and the exit velocity from the nozzle is very high. Since there is nochange in enthalpy in therotor， the relative velocity entering the rotor equals the relative velocity exiting from the rotor blade. For the maximum utiliza-tion factor， the absolute exit velocity must be axial as shown in Figure 9-9. The air angle α for maximum utilization is
cos α3二 2u (9-11)
V3
The air angle αis usuallysmall， between 12 0 and 250. The limit on thisangle is placed by the throughflow velocity， V1 sin α. If the limit is too small，the angle will require a longer blade length. The flow factor， which is a ratio

Figure 9-8. Pressure and velocity distributions in a Ratteau-type impulse turbine

Figure 9-9. Effect of velocity and air angle on utilization factor
of the blade speed to the inletvelocity， is a useful parameter to compare with the utilization factor (Figure 9-9).
The optimum value of u/V3 is a criterion indicating the maximum energy transfer to the shaft work. It also represents the departure from the optimum design value of cos α， causing a loss of energy transfer. The losses will increase at off-design conditions because of the incorrect attack angle of the gas with respect to the rotor blade. The maximum efficiency of the stage will still occur at or near the value of u/V3二cos α3/2
　
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