THE LAWS OF FLUID RESISTANCE. 105 



total endways force impressed on the pipe by the fluid 

 flowing through it must be nil. 



We see then that a frictionless fluid flowing through a 

 pipe of any form, whether tortuous or of varying diameter, 

 will not tend to push it endways, as long as the two ends 

 of the pipe are in the same straight line, and have the 

 same sectional area ; in a word, as long as the speed and 

 direction of flow of the fluid are the same in leaving the 

 pipe as in entering it ; and in this compound proposition 

 concerning the flow of fluid through pipes, I have laid the 

 necessary foundation for the treatment of the case of the 

 flow of an ocean of frictionless fluid past a submerged 

 body. 



I have dealt with the instance of a single stream of 

 uniform sectional area (and therefore of uniform velocity 

 of flow) inclosed in a pipe of any outline whatever, and I 

 have dealt with the instance of a single stream of varying 

 sectional area and velocity of flow ; and in both these cases 

 I have shown that, provided the streams or pipe-contents 

 finally return to their original direction and velocity of 

 flow, they administer no total endways force to the pipe or 

 channel which causes their deviations. 



I am now going to deal with a combination of such 

 streams, each to some extent curved and to some extent 

 varying in sectional area, which, when taken together, 

 constitute an ocean of fluid, flowing steadily past a 

 stationary submerged body, see Fig. 15 ; and here also, 

 since the combination of curved streams surrounding the 

 body, which together constitute the ocean flowing past it, 

 return finally to their original direction and velocity, they 

 cannot administer to the body any endways force. 



Every particle of the fluid composing this ocean, as it 

 passes the body, must undoubtedly follow some path or 

 other, though we may not be able to find out what path ; 

 and every particle so passing is preceded and followed by a 

 continuous stream of particles all following the same path, 

 whatever that may be. We may then, in imagination, 

 divide the ocean into streams of any size and of any cross 

 section we please, provided they fit into one another so as 

 to occupy the whole space, and provided the boundaries 

 which separate the streams exactly follow the natural 

 courses of the particles. 



