554 HYDRAULICS AND ITS APPLICATIONS 



the absolute velocity v, while q k = the relative velocity v r of water and 

 vane. 



By obtaining v r in this way the pressure "p" at any radius r may be 

 easily obtained by an application of the formula 



W 



p p<z | 2 a M, 2 -f v r * 2 r,. 2 | Ibs. per square foot, 



where u and v r refer to a point at radius r. 



EXAMPLE. 



A turbine runner has an outer diameter of 5 feet 6 inches and an inner 

 diameter 4 feet 3 inches. It makes 300 revolutions per minute. The 

 space occupied by the blades being divided into five concentric strips, 

 each 1J inches wide, it is found graphically that the relative velocities at 

 the centres of these strips, commencing at the outside are, 



26 ; 24 ; 26 ; 40 ; 65 feet per second. 



The relative velocity at entrance is 27 feet per second and at exit is 76 feet 

 per second. The pressure head at inlet is 125*5 feet. 



Denoting these strips by a, b, c, d, e, we have : 



p " = lh ~ Iri < (86 ' 5)2 ~ (84 ' 5)2 + (26)2 ~ (27)2 > 

 = 2 - 280. 



P*=P* ~ q { (86'5) 2 - (80-5) 2 + (24) 2 - (27) 2 } 



p 2 820. 

 fi9'4 

 PC - P* - gq { (86'5) 2 - (76'5) 2 + (26) 2 - (27) 2 } 



= Pz - 1,510. 

 Pa = P* ~ g|q i (86'5) 2 - (72'6) 2 + (40)^ - (27 2 ) } 



= & - 3,010. 

 Pe=P*-jj^ 4 { (86-5) 2 - (68'8) 2 + (65) 2 - (27) 2 } 



:= p% 6,040. 

 At exit p., = jpa - |yj { (86'5) 2 - (66'8) 2 + (76) 2 - (27) 2 } 



= pz - 7,810. 



This affords a check as to the accuracy of the construction. Assuming 

 the pressure over the corresponding portion of the back face of the disc 



