156 SMALL WATER SUPPLIES. 



must be inserted in a stopper at the upper end to 

 allow the air to escape while filling, when full the 

 pressure is applied by a force-pump having a gauge 

 to denote the pressure. While under pressure the 

 pipe is subject to a radial pressure acting on the 

 whole circumference of the pipe equally all round 

 (except for the difference of head between the top 

 and bottom of the pipe which is of course negligible). 

 The component part of the force which tends to tear 

 the metal asunder acts in a direction tangential to 

 the circumference at all points and at right angles to 

 the radius ; consequently, although the pressure is 

 radial, the circumference receives nearly an equal 

 pressure all round. The force tending to burst the 

 pipe, / is proportional to the radius, and if p is the 

 pressure shown on the gauge, 



f=pr *% (45) 



r being the radius. 



Then if /=the thickness of metal, and 5 = strain 

 per sq. in. of metal acted upon, 



t = pr .... (46) 



Beyond the face, however, the metal is strained less 

 and less according as the radius increases, because 

 the portion of the metal acted upon by the force pr 

 is indefinitely thin, the metal at the back of the pipe 

 merely assisting the strength of that at the internal 

 face. The metal resists the bursting pressure with 

 a force inversely proportionate to the square of the 

 radius at that part, because the magnitude of the 

 bursting force is proportional to the internal radius, 

 and its proportional stress at any part of its thickness 

 is inversely as the distances at which it acts, the rate 

 of extension being also inversely as the same distance ; 



