200 HYDRAULICS AND ITS APPLICATIONS 



order to give the required flow without any external head. Evidently i 

 is independent of the units used, and the formula may now be written 



A.ffi- 

 where P is proportional to - and has the value 





= 



-03368 t + -000221 2 ' < 

 and A and B are constants. 



The values of these constants have been determined and 



if the units are feet and degrees centigrade | V, 



o 



metres and degrees centigrade ~ > 



The formula is found to hold, with fair accuracy, for all velocities above 

 or below the critical points by a suitable substitution for n. 



Reynolds gives the following mean values of n for velocities above the 

 critical, those for cast iron being deduced from Darcy's results 



n. 

 Lead pipe . ... T79. 



Varnished pipe . ... 1-82. 



Glass pipe . ... 1*79. 



New cast iron ...... 1-88. 



Old incrusted C. 1 ...... 2'00. 



Below the C. V., n = I for all surfaces, and the formula becomes 



h = B Plv 

 A ' d? 



n MI i 11, Pi P* 32 /u Z V , , , , 



Poiseuille s formula h = - -. - -^-, the head being expressed 



in centimetres of water and the units in the C. Gr. S. system, becomes, 



278 ?; P 



on transforming to the metre as the unit of length, h = j=-= - -^. ~w- 



4/"/ X J-U d 



v P I 

 = 5*83 X 10 ~ M . This is identical with the Reynolds formula on 



substitution for the constants A and B. 



If n = 2, the term containing P and involving the temperature 

 becomes unity, and therefore for old and incrusted pipes the resistance is 

 independent of the temperature, and the formula becomes 



A d 



= -000709 l -^ feet f Waten 

 d 



