L891.] Tubes and Balloons distended by Fluid Pressure. 459 



Now, maintaining this force, let another stretching force act in the 

 lirection of y, which would, if acting alone, stretch By to icSy. 



Then 



p e will become - dx ; 



The force required to stretch &e to p $x is 



= q 





dy 



&u K 



id that required to stretch f- to j-Sy is 



vp vp 



= q 



v/p dx dz, 



rhere q is Young's modulus for the material. 



In the case of the cylinder, if x be taken parallel to the axis of the 

 cylinder and y round its circumference 



J<$a; = unstrained length of cylinder = Z ; 



j&y = circumference = 27rr ; 

 \Bz = ,, thickness ,, = t ; 



lence the whole elastic circumferential stress is 



K 1 



y = Q V p ZQ <)) 







id the fluid pressure, P, due to this stress is 



l / i 

 Vp 1 



P = 



27r */p */ 1 



27rg* K 1 



To Ktf K 



?his is a maximum when K = 3. 



