the Flow of Air through a Pijie. 399 



pressure is given with sufficient accuracy by the iormula 



\6'6 n .d 3 - 



8» = -00000125 Pm ' Vm ' lbs. per sq. in. 



1 ifi.fi» r/S-n 1 



where d and I are in feet and p m in lbs. per sq. inch. 



If Sp be measured in inches of water, the other units being 

 'unaltered, this becomes 



Sp = -0000346 A" 1 • v l • l ins> of water# 

 z 6-6" . d 3 ~ K 



If ^ and p TO be measured in kg. per sq. cmin., and if the 

 metre be taken as the unit of length, we get 



A=-00260; B = 1010. 



In the case of the lead pipes examined, the uncertainty 

 as to the condition of the interior surface of the pipe used 

 by Dr. Brix prevents any accurate deductions being drawn. 

 The effect of a variation in the physical condition of the 

 surface in a pipe of such small diameter is very marked in 

 the variation of n from 1*28 in the pipes used by the author 

 (the interior surfaces of which were exactly as left by the die) 

 to 1*49 in the pipe of Dr. Brix. Probably to be on the safe 

 side in practice, and to allow for irregularities in laying and 

 jointing, it would be advisable to take ?i = l*50 for all lead 

 pipes of small diameter. 



V. Effect of Temperature Variation. 



An increase in temperature tends to affect the resistance to 

 flow along a pipe with a given mean velocity and at a given 

 mean pressure, in two ways. 



(1) By reducing the density of the fluid it tends to reduce 



the resistance. 



(2) By increasing the viscosity it tends to increase the 



resistance. 

 Now if formula (4) is correct for all temperatures, in any 

 two experiments (1 and 2) carried out at the same mean 

 velocity and with the same mean pressures, but with different 

 temperatures, we shall have : — 



while if the mean pressures are equal and if Bp 1 =Sp 2 , ^ T e shall 

 have 



\r»»i/ L\^2' "\ t i/ J 



2 E2 



