108 PROFESSOR A. H. GIBSON ON THE RESISTANCE TO FLOW OF WATER 
from which K can be calculated. Knowing K, the value of y corresponding to any 
value of x can be readily obtained from equation (1), and the rectangular pipes were 
made to templates representing curves calculated in this way. 
In a circular pipe n= 1°22, while v’ecy~*, so that 
ah Pa, (22)"*— 
a (y~*) re = constant. 
' 
Ss 
Fic. 4. 
Proceeding as above, this gives 
Oat ym (a) : : : : ae () 
and on the same assumptions as before 
K =: { Te 2 aD 
/ being the length, and y, and y, the smaller and larger radii respectively. ‘The circular 
pipes were made to templates set out from this equation. 
Where the length of pipe is great, or the ratio of areas small, the curves thus formed 
may, at the smaller end of the pipe, diverge at an angle less than that (6° in a circular 
pipe and 11° in a rectangular pipe) giving minimum loss, and in such a case the pipe 
