WATER CONDUCTORS 121 



sure. Because of its initial high relative cost and consequent 

 interest charge, a careful consideration of the pipe line must be 

 made; otherwise, an injudicious monetary expenditure may result. 



It is obvious that for a given water quantity, the size of the 

 pipe is determined by the velocity at which the water is allowed 

 to run. This is the difficult point to settle, and varies anywhere 

 from 6 to 12 feet per second, the average probably being around 9 

 feet. A high velocity entails a considerable friction loss, while a 

 low velocity necessitates a larger pipe and thus increases the cost 

 of construction. For a low-head development a rather low veloc- 

 ity should be used, because the loss of head will then form a much 

 larger percentage of the total head than where a high head is 

 available. In high-head pipe lines of some length it is, of course, 

 also more economical to use smaller diameter and larger velocity 

 at the bottom, where the pressure is higher and thicker pipe is 

 required. 1 



Consideration must also be given to the load factor at which 

 the turbine is running, i.e., the average amount of water which the 

 pipe line is to carry. Some plants require that the turbines are 

 run continuously at full gate opening, while in other instances 

 they may operate normally at half gate, only opening up occa- 

 sionally to full gate to take care of momentary peak loads. In 

 such a case the friction loss should naturally be based on the water 

 conveyed when the wheels are operating at half gate opening. 



Theoretically, therefore, the economical diameter of a pipe 

 line for a water-power development should be such that any 

 increase in the diameter of the pipe would cost more than the 

 value of the power which could be obtained from the decrease in 

 loss of head due to friction from such increase in diameter. Or, 

 stated in other words; the size of pipe should be such that the 

 value of the power annually lost in friction plus the annual interest, 

 profit and depreciation charges on the pipe line should be a min- 

 imum. For a steel pipe this leads to the following formula: 1 



/ J20xrxX 2 Xg 3 Xe 

 a = 







Where 



d = economic diameter in feet for thickness t\ 



Y- weight of water in pounds per cubic foot = 62.4; 



1 By courtesy of J. G. White & Co. 



