THEORY OF TURBINE DESIGN 531 



through the wheel buckets which provides the turning moment on the 

 shaft. For this turning moment to be a maximum with a given value 

 of v and a given quantity of water, it follows that the value of w should 

 b3 a maximum, and therefore that a should be as nearly as possible 

 zero. 



On the other hand, the volume of water which a given wheel is capable 

 of handling per second depends on/, since it is in virtue of this component 

 of velocity that water is carried into the turbine buckets. As a is 

 diminished, therefore, the size of turbine for a given power, and the first 

 cost, increases, and the problem before the designer is to determine at 

 what point the diminution in efficiency due to an increase in a becomes 

 of more impDrtance than the corresponding diminution in first cost. A 

 similar state of affairs holds at exit. For maximum hydraulic efficiency 

 the energy rejected in the discharge should be reduced to a minimum. 

 This requires the absolute velocity of discharge from the wheel to be as 

 small as possible. The minimum permissible velocity of discharge is, 

 however, governed by the necessity for getting a given volume of water 

 per second through the limited sectional area of the buckets at this point, 

 and here also an increase in the velocity of flow at the expense of the 

 velocity of whirl will enable a larger volume of water to be dealt with and 

 a greater power to be obtained, but with a sacrifice of the hydraulic, 

 though possibly not of the economic, efficiency. 



Where an abundant supply of water is available at all times, the 

 efficiency of the turbine may become quite a secondary consideration as 

 compared with its prime cost, and a cheap but comparatively inefficient 

 turbine may be preferable on all counts. In such a case high efficiency 

 at part loads is a minor consideration and may be entirely subordinated 

 to considerations of cheapness and of ease of governing. Here, however, 

 it must be remembered that where a long supply pipe or channel is 

 necessary, a decrease in the efficiency of the turbine, particularly at full 

 load, necessitating as it does an increased water supply, may cause the 

 initial cost of construction of such channels or pipes to more than 

 counterbalance the decreased prime cost of the motor. 



Again, where the supply is variable and where in times of drought 

 barely sufficient water is available, it is highly important that high 

 efficiency at all gates be the first consideration. 



Thus the turbine designer must keep many conflicting possibilities in 

 view, each of which has its own effect on the most suitable design to be 

 adopted, and no hard and fast rules can be formulated for the design of 

 any type of machine. Certain broad principles may, however, be laid 



