THE LAWS OF FLUID RESISTANCE. 97 



fluid will not tend to disturb the pipe, and therefore all 

 that will be necessary to hold it in its position will be an 

 equal and opposite tension supplied by the anchorages at 

 the ends, to prevent the ends being forced towards one 

 another. And if, instead of anchoring the ends, we put a 

 strut between them to keep them apart, the pipe thus fitted 

 will require no external force to keep it in position. In 

 other words, whatever be the outline of a pipe, provided 

 its beginning and end are in the same straight line, a 

 frictionless fluid flowing through it will have no tendency 

 to push it bodily endways. 



So far I have dealt only with pipes having uniform 

 sectional area throughout their length, an assumption which 

 has been necessary to the treatment pursued, as the velocity 

 has in each case been assumed to be uniform throughout the 

 length of the pipe. I will now proceed to consider the 

 behaviour of fluid flowing through pipes of varying sec- 

 tional area, and consequently flowing with varying velocity. 



FJG. G. 



It is, I think, a very common impression, that a fluid in 

 a pipe, meeting a contraction of diameter (see left hand of 

 Fig. 6), exercises an excess of pressure against the entire 

 converging surface which it meets, and that conversely, as 

 it enters an enlargement (see right hand of Fig. 6), a relief 

 of pressure is experienced by the entire diverging surface 

 of the pipe. Further, it is commonly thought that there is 

 in the narrow neck of a contracted passage (see Fig. 6) an 

 excess of pressure due to the squeezftig together of the 

 fluid at that point. 



These impressions are in every respect erroneous ; the 

 pressure at the smallest part of the pipe is, in fact, less 

 than that at any other point, and vice versd. 



If a fluid be flowing along a pipe A B which has a con- 

 traction in it, the forward velocity of the fluid at B must te 



H 



