[ no ] 



XL Moseley's Theory of Steady Flow. By Major Allan 

 Cunningham, R.E., Honorary Fellow of King's College, 

 London*. 



ANEW Theory of the Steady Flow of a Liquid was pro- 

 posed by the late Canon H. Moseley, in an important 

 essay published in this "Magazine in 1871-72f. The paper was 

 valuable as an attempt to form a rational theory of the steady 

 motion of a real fluid, and to deduce results of great scientific 

 and practical interest from it. Formulae were arrived at for 

 the Velocity at any point in a Pipe flowing full, and for the 

 Discharge both of a Pipe flowing full and of an Open Channel, 

 and for some other quantities of less importance. 



In the investigation it was assumed that: — 



I. Pipes. — In long uniform pipes at uniform slope, flowing 

 full,— 



1. The motion is a steady motion in lines parallel to the axis of 



the pipe. 



2. The surfaces of equal velocity are similar, and similarly 



situate, to the enclosing margin. 



3. The measure of tangential resistance to the fluid at the en- 



closing margin is (A, + ;« 1 ^ 2 ). 



4. The measure of tangential resistance to fluid particles flow- 



ing past each other is (X+/x . {Ivf). 



5. The whole of the kinetic energy lost by any particle of the 



fluid under subheads 3 and 4 is probably converted into 

 heat energy, or, at any rate, lost as kinetic energy. 



II. Open Channels. — In long uniform open channels at uni- 

 form slope, — 



6. The discharge is one half of the discharge of a pipe flowing 



full whose lower half is the open channel in question, and 

 upper half is similar to the lower (reversed) . 



The evidence as to the reality of the assumptions Nos. 1, 2, 

 5 is not stated: they are apparently only working hypotheses. 

 No. 3 is accepted from Poncelet's experiments on the friction 

 of a fluid on a solid. No. 4 is merely an assumption that the 

 expression for fluid-friction is of the same functional form as 

 that between a fluid and a solid. No. 6 is accepted from 

 Darcy's experiments on pipes and open channels. 



It must be remarked, in passing, that there is really no evi- 

 dence as to the existence of steady motion in parallel lines 

 even in pipes flowing full, and that in the case of open chan- 



* Communicated by the Author. 



t Vol. xlii. 1871, pp. 184 and 349; vol. xliv. 1872, p. 30. 





