392 Mr. A. H. Gibson on the Resistance to 



unit mass) for p in equation (2), this becomes: 



$p = k.d n -z.fi 2 - n . [^\ l ~\v n .U. . .] [(3) 



Writing this in the form 



p l ~ n . Sp = k . d"- 3 . fjL 2 ~ n . {cr) l - n . v n . SI, 



and putting m ^ m for r, where v^and p OT represent the mean 

 velocity and pressure in the pipe, we get, on integrating, 



On putting 



_£l+£a. *_ P1~P2 



Pm— g ' ^ 2 ' 



this gives for the whole pipe 



Sp = k . el-* . v?~» . [f ™]" _1 - K, ■ h ■ (4) 



as the equation for the resistance to the steady isothermal 

 flow of a compressible fluid. 



With stream-line motion, i. e. at all velocities below the 

 critical, n = l, and equation (4) becomes 



S P=^T' L 



This indicates that under these conditions the pressure 

 drop is independent of the mean pressure in the pipe, and, 

 except for the effect of the varying viscosity, also of the 

 temperature, both of which conclusions received verification 

 by the viscosity experiments of Dr. Grrindley and the author. 



In the majority of the experimental results available to 

 the author , the temperature r was not given and could be 

 only estimated approximately from a consideration of the 

 climatic conditions presumably obtaining at the time of the 

 experiments. In only one series of experiments (by the 

 author on a lead pipe of small bore) was the variation of 

 temperature known, and of sufficient magnitude to enable 

 the above formula to be fully checked. As, however, if the 

 formula is correct, the variation in resistance is small for a 

 temperature variation not exceeding 20° F. (not above 3 per 

 cent, in any case), it was thought well in the first case to 

 combine the factors involving temperature (either directly or 

 in its effect on viscosity), to take the factors thus obtained 

 as being sensibly constant during the experiments to be first 

 considered, and afterwards to verify the law of variation 

 with temperature by a separate series of experiments on the 

 author's lead pipe of 1/8 inch bore. 



