COMPOUND PIPES AND PASSAGES 



89 



diverge uniformly at this best angle up to a point where its straight sides 

 would intersect the calculated curved sides. 



If, on the other hand, the length of pipe is small or the ratio of areas 

 large, the calculated curves may, towards the larger end of the pipe, 

 diverge at an angle greater than that giving a loss equal to that at a 

 sudden enlargement. 



In such a case a more efficient pipe is obtained by enlarging the pipe 

 to its final section by a sudden enlargement at the point at which the 

 angle of divergence becomes equal to this critical value. 



A still more efficient pipe is obtained if, from the point at which the 

 ingle of divergence becomes equal to the critical angle, the section is 

 enlarged gradually, the best angle of divergence being found to vary but 

 slightly in such circumstances and in any cases likely to be found in 

 practice, being approximately 20 for a rectangular pipe, and 10 for a 

 sircular pipe. 



Compound Pipes and Passages. 



The loss of head in a pipe whose section increases gradually from AI 

 ;o AS, and which then 

 suffers a sudden en- 

 largement of area to 

 (Fig. 43), is 

 approximately equal 

 to the sum of the 

 separate losses which 

 would be experienced 

 in the taper portion 

 of the pipe and at the 

 sudden enlargement, 

 if these were independent of each other. By reducing the angle of 



half -breadth is yil an = 0, and if I be the length of the pipe, and if y a be the half-breadth at 

 the larger end, # 2 .TI = ?, and 



FIG. 43. 



In a circular ipe n = 1-22, while a a ?/ - *, so that 



Proceeding as above, this gives 



yi - 1-25 _ y - 



and on the same assumptions as before 



= constant. 



