LOSS OF HEAD IN TAPEE PIPES 87 



Rectangular Pipes with Uniformly Diverging Boundaries. Three sets of 

 rectangular pipes were examined, these having one pair of sides 

 parallel and 1*329 inch apart in every case. The areas of the small and 

 of the large ends of these pipes were, in the case of the pipes having 

 area-ratios of 4 : 1 and 9:1, identical with those of the circular taper 

 pipes having the same ratios of enlargement. 



The results of the means of the experiments on these pipes are plotted 

 in Fig. 42. From these it appears that the percentage loss is very 

 approximately the same for all ratios of enlargement between 2*25 : 1 

 and 9 : 1 for values of between 10 and 40, and that it varies but 

 little with the dimensions of the pipe. The minimum loss is obtained 

 when 6 is approximately 11, the percentage loss under these circum- 

 stances being about 17*5 per cent. As 6 is increased the loss increases 

 rapidly, and attains a value of 100 per cent, when 6 is between 31 and 

 40, the value of this critical angle being less with the smaller ratios of 

 enlargement and with the pipes having the smaller mean sectional areas. 

 For values of 6 between 10 and 35, the only values of any use in 

 practice, the loss can be expressed with a fair degree of accuracy by the 

 relationships 



loss = *0072 1 ' 40 fo ~ ^ feet, where is in degrees. 

 = 5*30 [tan-?.] ^ Vl n Vz feet. 



Experiments on rectangular pipes having an enlargement ratio of 9 : 1, 

 and having respectively 40, 50, and 90, showed corresponding losses 

 of 115, 122*3, and 119 per cent. This indicates a maximum loss when 

 is approximately 70, or when it has sensibly the same value as gives 

 maximum loss in the corresponding circular pipe. 



Pipes of Square Section with Uniformly Diverging Boundaries. Five 

 pipes, having a smaller section 1*329 inch square and a larger section 

 2*658 inches square and with respectively 5, 7*5, 12*5, 20, and 30, 

 were examined, the results being plotted in Fig. 42. The percentage loss 

 is a minimum for a value in the neighbourhood of 6, practically the 

 same as for a circular pipe, and has a value of about 14*5 per cent. 



Trumpet-Shaped Pipes. From a priori reasoning it would appear that 

 when the initial and final areas and the length of a pipe are fixed, the 

 loss of head may be reduced by making the pipe fcrumpet shaped, the 

 angle of divergence of its sides being least where the velocity is greatest 

 and vice versa. To test this point several pipes were examined, these 



being designed so as to make either the retardation K%\ constant, the 



