94 LECTURES TO SCIENCE TEACHERS. 



that both the divergence between A and C from the 

 original line at A, and the return between C and E to that 

 line at E, would place parts of the interior surface of the 

 pipe in some manner in opposition to the stream or flow, 

 and that the flow thus obstructed would drive the pipe 

 forward ; if however* we endeavour to build up these sup- 

 posed causes in detail, we shall find the reasoning to be 

 illusory, and I will now trace the results which can be 

 established by correct reasoning. 



The surface being assumed to be smooth, the fluid, being 

 a frictionless fluid, can exercise no drag by friction on the 

 side of the pipe in the direction of its length, and in fact 

 can exercise no force on the side of the pipe, except at 

 right angles to it. Now the fluid flowing round the curve 

 from A to B will, no doubt, have to be deflected from its 

 course, and its inertia, by what is commonly known as 

 centrifugal action, will cause pressure against the outer 

 side of the curve, and this with a determinable force. The 

 magnitude and direction of this force at each portion of the 

 curve of the pipe between A and B are represented by the 

 small arrows marked/; and the aggregate of these forces 

 between A and B is represented by the larger arrow 

 marked G. In the same way the forces acting on the 

 parts BO, CD, and D E are indicated by the arrows H, I, 

 and J ; and as the conditions under which the fluid passes 

 along each of the successive parts of the pipe are pre- 

 cisely alike, it follows that the four forces are exactly equal, 

 and, as shown by the arrows in the diagram, they exactly 

 neutralise one another in virtue of their respective direc- 

 tions ; and therefore the whole pipe from A to E, con- 

 sidered as a rigid single structure, is subject to no disturbing 

 force by reason of the fluid running through it. 



Though this conclusion, that the pipe is not pushed end- 

 ways, may appear on reflection so obvious as to have scarcely 

 needed proof, I hope that it has not seemed needless, even 

 though tedious, to follow somewhat in detail the forces 

 that act, and which, under the assumed conditions, are the 

 only forces that act, on a symmetrical pipe such as I have 

 supposed. 



Having shown that in the instance of this special 

 symmetrically curved pipe, the flow of a frictionless fluid 

 through it does not tend to push it endways, I will now 



