THE LAWS OF FLUID RESISTANCE. 



93 



flow, does nob require, nay, does not admit of, the expendi- 

 ture of any power ; whether the fluid be caused to flow in 

 a curved path, as it must do in order to get round a 

 stationary body which stands in its way ; or to flow with 

 altered speed, as it must do in order to get through the 

 local contraction of channel which the presence of the 

 stationary body practically creates. Power, it may indeed 

 be said, is being expended, and force exerted to communi- 

 cate certain motions to the fluid ; but that same power is 

 also being given back, and the force counterbalanced, 

 where the fluid is yielding up the motion which has 

 been communicated to it, and is returning to its original 

 condition. 



In commencement, I will illustrate these two actions 

 by considering the behaviour of fluid flowing through 

 variously- shaped pipes ; arid I will begin with a very 

 simple instance, which I will treat in some detail, and 



FIG. 3. 



which will serve to show the nature of the argument I am 

 about to submit to you. 



Suppose a rigid pipe of uniform sectional area, of the 

 form shown in Fig. 3, something like the form of the 

 water-line of a vessel. 



The portions AB, BC, CD, DE are supposed to be 

 equal in length, and of the same curvature, the pipe ter- 

 minating at E in exactly the same straight line in which it 

 commenced at A, so that its figure is perfectly symmetric 

 on either side of C, the middle point of its length. 



Let us now assume that the pipe has a stream of friction- 

 less fluid running through it from A towards E, and that 

 the pipe is free to move bodily endways. 



It is not unnatural to assume at first sight that the 

 tendency of the fluid would be to push the pipe forward, in 

 virtue of the opposing surfaces offered by the bends in it 



