HYDRAULICS AND ITS APPLICATIONS 



T1 



and, from (3) /= -- * + ,.2- ( 6 ) 



Assuming, as is generally permissible in practice, that when r = r ,i.e., 

 at the outer circumference, p = o, and putting p =pi when r = r it i.e.., at 

 the inner circumference, we get on substituting, 



A=pi 



ri* 



( r? - rf 



Substituting these values in (6) we have 



n 



7-n 2 1 (7) 



Evidently this will have its maximum value when r = i\, i.e., at the 

 inner circumference, and at this point. 



This may be written 



(8) 



(9) 



The value adopted for the working stress / varies with the pipe diameter, 

 and with cast-iron pipes increases gradually from about 2,000 Ibs. per 

 square inch in a 2-inch pipe to 3,000 Ibs. per square inch in an 8-inch 

 pipe, and 3,500 Ibs. per square inch in a pipe or cylinder of 24 inches 

 diameter. 



The following table indicates the thickness of cast-iron pipes and 

 cylinders for heavy pressures, as calculated on the above assumption. 



