Professor Gordon on Hie Discharge of Water through Pipes. 269 



velocity of discharge, p= a constant factor ^ and Z= the length of the pipe. 

 0*82 is the co-efficient of contraction of water at entering the pipe, 

 and g = 32*2 feet The experiments above named were employed to 

 deduce p by the method of least squares. It is found that p is very 

 nearly inversely proportional to the diameter of the pipe, and therefore 

 k=pr, is introduced. The formula may then be written: — 



A = 0-23c2 H- ib-c »-75 

 r 



In Provis's experiments, r = 0*75 — -01 = '74 p = 0*0474 . • . * = -0035 

 Hagen, . . r = 0-117 — -01= '107 /) = 0*0447 .*. it = -00478 



Dubuat, 3 . . r = 0-089 — -01 = '079 p = -0619 .'.k=i -00488 



Couplet, 3 . . r = 6-45 — '01 = 6*44 p = -00103 . • . ife = -00622 



•01 inch is taken from the radius to allow for the film of water adhering 

 to the pipe. These are a selection from the fifteen sets of experiments 

 used, and which prove that h is not constant, but varies with the cir- 

 cumstances of the pipe as to the actual velocity through it and the amount 

 of curvature or bending. Provis's experiments give the same co-efficient 

 to the third or fourth decimal places with those of Dubuat and Bossut 

 in analogous circumstances, of a small velocity of discharge and straight 

 pipe. Hagen's agree excellently with one another. In these the velo- 

 city was great and the diameter very small ; so that internal interfering 

 motions in the water in the pipe were recognisable. Dubuat's experi- 

 ments in analogous circumstances correspond well with those of 

 Hagen. The co-efficient deduced from Couplet's experiments rises as 

 the degree of sinuosity designated in the original tables. The pipe 

 from which the result above given was found is designated as mwcA 

 hentj but the velocity through it was small. Upon these grounds I 

 proposed that for practice we might employ the co-efficient -00315 in 

 very regular pipes ; for gentle curves this rises to -005 ; and for very 

 sharp curves might even amount to -01, because in practice there not 

 only occur the curves or hends^ but contractions from deposits and from 

 collecting air in these bendings. 



The formula for straight pipes would then stand thus : — 



A = -023 02 -f 0-003 -c ^75 

 r 



and as in ordinary practice the first member (on the right hand) is 

 generally small whilst the sinuosities are numerous, though gentle or 

 accidental interferences occur, it appeared that this might be reduced 

 to— 



A = -005-0 »75 

 r 



as a simple formula of approximation. 



Mr. Wilson at last meeting proposed that the above formula should 

 be tested by application to the following question : What should be the 

 diameter of a pipo of eight feet in length, laid horizontally, in order 



