39 



and 



which determines the position of P. (Besant's Hydrostatics, 

 p. 154.) 



2. A straight tube AB, filled with liquid, is made to 

 rotate about a vertical axis through A ; find 

 how much flows out at B. 



Ans. All above P, where P is tangent to 



the parabola whose latus rectum is ~ and 



whose axis is coincident with the vertical o 



line through A, and AP = 3 cot cosec , 



where is the angle OAB. F| . , 8 



23. Strength of Pipes and* Boilers. An important 

 application of the theory of the pressure of fluids is the 

 determination of the thickness of pipes, boilers, etc. In 

 order that these vessels shall be strong enough to resist the 

 pressure of the liquid, their walls must be made of a certain 

 thickness, which depends upon the pressure of the liquid 

 and the internal diameter of the vessel. 



Let it be required to find the thickness of a pipe of 

 any material necessary to resist a given pressure. 



A cylindrical vessel may burst either transversely or lon- 

 gitudinally ; but the former is less likely to occur than the 

 latter, as appears from the following investigation. 



(1) When the rupture is transverse. 



Let ABCD (Fig. 19) be a section of pipe perpendicular 

 to its axis, the interior surface of which is subjected to a 



