122 WATER CONDUCTORS AND ACCESSORIES 



t = thickness of pipe in feet; 



m = weight of material in pipe line in pounds per cubic foot 

 = 490. 



q = average flow of water through pipe during twenty-four 

 hours, expressed in cubic feet per second. 



6 = sale value of 1 foot-pound per second for one year, meas- 

 ured in water before delivery to turbine. 



i = annual interest, profit and depreciation charge on 1 pound 

 of material in pipe line in place, expressed as a ratio. 

 This value should be multiplied by whatever factor is 

 necessary to make allowance for excess of actual 

 weight of pipe line over theoretical weight due to lap, 

 rivets, etc. 

 c = friction coefficient. (See page 106.) 



The factor X for a 50 per cent load factor will generally vary 

 from 1.3 to 1.5. It may be figured from the formula: 



x-y 



Average of the cubes of load curve ordinates 

 Cube of the average of load curve ordinates ' 



This means that the load curve may be divided into as many 

 sections as desired for accuracy, and the mean ordinate of each 

 section used in the formula. 



Having determined the economic diameter for a given thick- 

 ness, that for any other thickness, all other conditions remaining 

 the same, varies inversely as the sixth root of the thickness. 1 



Speed regulation must also be considered in determining the 

 size of a pipe line, and this point is probably of more importance 

 than the economical consideration. Load changes on the tur- 

 bine cause the governor to open or close the turbine gates rapidly, 

 thus causing pressure changes in the penstock. These pressure 

 changes are due to the acceleration or deceleration of the water 

 column in the pipe line, and the magnitude of the same depends 

 upon both the length of the penstock and the change of velocity 

 in same. 



The pressure changes always act in opposition to the action 

 of the governor; thus, when a load suddenly goes off the gener- 



^ee also "Economical Penstock Size" by M. Warren A.S.C.E., 

 Dec. 2, 1914. 



