EXAMPLES 41 



Collapsing Pressures of Cylindrical Pipes. The sudden discharge of 

 water from a hydraulic pipe line, such as may follow a burst at its lowest 

 point, may, unless special provision be made, lead to the production of a 

 partial vacuum in the pipe and thus give rise to an effective external 

 collapsing pressure which is increased by the pressure of the earth filling 

 in the case of a buried pipe. Very few reliable experiments are available 

 as to the effect of such pressures on pipes of large diameter. K. T. Stewart l 

 as the result of experiments on steel lap-welded tubes of diameters ranging 

 from 3 to 10 inches concluded that if the length of the pipe is greater than 

 6 diameters the collapsing pressure p c is given by 



p c = WOO (l - l - 1600 ^-5) if PC is less than 



\ J-S Q / 



or ~ '023, 



- 



while p c = 86670 =r -- 1386, for higher values of p c or of -=- . 



MO t)o 



Here p c is in pounds per square inch ; t = thickness in inches ; D = 

 outside diameter in inches. If slightly distorted, later experiments 2 on 

 10-inch pipes with thicknesses of "15 to "20 inch indicate that the 

 collapsing pressure p c ' is approximately given by 



^-o*-W*- 



Where p e = collapsing pressure for corresponding circular pipe. 

 x = ratio of maximum to minimum outside diameter. 



EXAMPLES. 



1. In a hydraulic press the ram is 10 inches and the pump plunger 

 1 inch diameter, the leverage for working the pump 16 to 1. What is the 

 velocity ratio of the pump handle and ram ? Actually a force of 30 Ibs. 

 exerts a pressure of 44,000 Ibs. on the press table. What is the 

 efficiency ? 



Ans. : 1,600; 91-7 per cent. 



2. A dock gate is 12 feet broad and 14 feet deep, and the water rises 

 12 feet on one side and 3 feet on the other side above its lower edge. 

 Find the resultant pressure and centre of pressure for each side of the 

 gate and find the magnitude and position of the resultant of these. 



1 ' : Trans. Am. Soc. Mech. Eng.," 1906, p. 730. 



2 "Trans. Am. Soc. Mech. Eng.," 1907, p. 123. 



