84 



HYDRAULICS AND ITS APPLICATIONS 



and for pipe diameters ranging from *50 inch to 6 inches, can be expressed, 

 within narrow limits, by the relationship 



loss of head = 



102- 



wi- - 2'Od f ( Vl r 2 ) 2 

 ~2~ 



. 

 feet. 



The following table shows the results obtained by the use of the formula, 

 against those experimentally obtained : 



ART. 34. Loss IN PIPES AND PASSAGES WITH A GRADUALLY INCREASING 



CROSS-SECTION. 



The loss of head accompanying a gradual enlargement of section would 

 naturally be expected to be less than that experienced at a sudden 

 enlargement of section between the same initial and final areas. To 

 determine the extent to which this conclusion is justified a somewhat 

 extended series of experiments on such pipes was recently carried out by 

 the author. 1 



Circular Pipes with Uniformly Diverging Boundaries. Calling 6 the angle 

 of conicity of a pipe, the following table, as also Fig. 41, shows the mean 

 of the results obtained. 



Loss of Energy expressed as a Percentage of 



t<a) 



, the Theoretical Loss at a 



Sudden Change of Velocity from t>i to r 2 . 



1 "Proc. Roy. Soc. A.," vol. 83, 1910. " Trans. Roy. Soc, Edinburgh," vol. 48, 1911, p. 97. 



