DISCONTINUOUS MOTIONS. 



101 



K\ erythiug being at rest ID begin wit.li, let n. slowly increasing 

 velocity be oommunioated to tho plug P % so that (for simplicity) 

 the motion at any instant may bo regarded as approximately 



steady. At first, provided a sufficient forco bo applied to Q t a 

 continuous motion of tho kind indicated in the diagram on p. 83 

 will he produced in the fluid, there being in faet only one type of 

 motion consistent with the conditions of the question. As the 

 acceleration of the piston /* proceeds, the pressure on Q may 

 become enormous, even with very moderate velocities of P, and if 

 Q be allowed to yield, an annular cavity will be formed at each end 

 of tho tubo. 



The further course of the motion in such a case has not 



yet been worked out 1'rom :i ! heoivl leal stand point. In avtuai 

 liipiids the problem is modified by \iseosity.\vlueli prevents any 

 slipping of the fluid immediately in contact with the tube, and 

 must, further exercise a considerable influence on such rapid 

 differential motions of the fluid as are here in question. 



As a matter of fact, the observed motions of fluids are often 

 found to deviate very widely from the types shewn in our dia- 

 grams. In such a case as we have just described, the fluid issuing 

 from the mouth of the tube does not immediately spread out in 

 all directions, but forms, at all events for some distance, a more or 

 less compact stream, bounded on all sides by fluid nearly at rest. 



