116 WATER CONDUCTORS AND ACCESSORIES 



head in the penstock at the point of measurement and subtract- 

 ing the residual velocity head at the end of the draft tube. The 

 velocity head in the penstock shall be taken as the square of the 

 mean velocity at the point of measurement, divided by 2g; the 

 mean velocity being equal to the quantity of water flowing in 

 cubic feet per second, divided by the cross-sectional area of the 

 penstock at the point of measurement in square feet. The residual 

 velocity head at the end of the draft tube shall be taken as the 

 square of the mean velocity at the end of the draft tube, divided 

 by 2g, the mean velocity being equal to the quantity flowing 

 in cubic feet per second, divided by the final cross-sectional 

 discharge area of the closed or submerged portion of the draft 

 tube in square feet." 



The loss of head is due to the loss in the entrance of the pen- 

 stock, to the friction of the interior surface, to curvature, and to 

 various other obstructions such as headgates, racks, and valves. 

 In the case of impulse turbines, there is a further loss caused by 

 the necessity of placing the wheel clear of tailwater so that after 

 leaving the wheel the water drops freely through the vertical 

 height between the wheel and the tailwater surface, and fails to 

 utilize the head corresponding to this free fall. It is customary 

 in computing the efficiency of impulse turbines to charge against 

 the wheel only the net head with reference to the elevation of 

 the center of the nozzle taken as datum. 



Loss of Head in Entrance. This loss of head is probably 

 due to internal friction of the particles of water against each 

 other when they converge towards the contracted entrance. The 

 loss depends on the shape of the intake, but for ordinary purposes 

 it may be obtained from the formula 



*-< , 



Loss of Head in Friction. For determining the loss of fric- 

 tion in pipe lines there are two formulas in very general use: 

 Chezy formula: 



v = cVrs (for values of c see page 106). 



Williams and Hazen formula: 



. = 1.32 cr 063 s 054 , 



