546 HYDRAULICS AND ITS APPLICATIONS 



Example of Design. As an application of the results of the foregoing 

 analysis, consider the design of an inward radial flow turbine of the 

 Francis swivelling gate type, to give 10,000 H.P. at 300 revolutions pei 

 minute under a total head of 260 feet. The wheel vanes to have radia\ 

 tips, the velocity of flow to be kept constant, and the wheel to be 

 supplied through a steel penstock whose length is 450 feet. 



Assuming a probable full-load efficiency of 84 per cent., the capacity 



10,000 X 550 

 of the penstock must be sufficient to allow of a supply of ^ ^ - - 



= 404 cubic feet per second. 



Allowing a mean velocity under maximum load of 12 feet per second in 

 the penstock, the area of this becomes 33f square feet, corresponding to 

 a diameter of approximately 6 feet 6 inches. 



In such a turbine it is usual to arrange the design so as to give a 

 maximum efficiency at about f full-load. At this load the velocity of 

 pipe flow is approximately 8 feet per second, and if the coefficient of 

 friction be taken as "005, the loss of head due to friction and to the 

 velocity of flow (assuming the kinetic energy due to the latter to be 

 entirely lost) may be written as equal to 



v2 /f L ^^\t 64 f'005 X 450X4 , J. 



-5 I + 1 ) feet = ^- - -f- 1 \ feet = 2'37 feet. 



2 g \m I 64 4 4 I 6'5 J 



The effective head H r is thus 257'6 feet, so that V 2 g H' = 129 feet 

 per second. 



Taking a = 13, tan a = '231, tan 2 a = -053, while from (1) we have 



129 

 7*2 = / . AKQ 90- 1 feet per second. 



\f ' 



The outer radius of the runner is then given by the relation 

 2 TT r 2 N 60 X 90-1 



* 



.*. Outer diameter of runner = 5 '74 feet = 5' 9". 

 Assuming an efficiency of 86 per cent, at f load, we have : 

 Q = 296 cubic feet per second, so that from the expression 

 Q = 2 -n 1 2 & 2 tan a w 2 , we get : 



h = Q _ _ 296 _ 



2 TT r a w a tan a 2 TT X 2*87 X 90'1 X '231 



= "79 feet = 9'5 inches (approximately). 



2*87 



= 1*30, we have r 3 = ^-^. = 2'21 feet 

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diameter of the runner is 4' 5", while b 3 = '79 X 1*30 = 12^ inches. 



2*87 



Taking n = 1*30, we have r 3 = ^-^. = 2'21 feet, so that the innei 



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