1914] on Fluid Motions 73 



The facts then are plain enough, but what is the explanation ? It 

 is really quite simple. In steady motion the quantity of fluid per 

 second passing any section of the tube is eyery where the same. If 

 the fluid be incompressible, and air in these experiments behaves 

 pretty much as if it were, this means that the product of the velocity 

 and area of cross-section is constant, so that at a narrow place the 

 velocity of flow is necessarily increased. And when we enquire how 

 the additional velocity in passing from a wider to a narrower place is 

 to be acquired, we are compelled to recognize that it can only be in 

 consequence of a fall of pressure. The suction at narrows is the 

 only result consistent with the great principle of conservation of 

 energy ; but it remains rather an inversion of ordinary ideas that 

 we should have to deduce the forces from this motion, rather than 

 the motion from the forces. 



The application of the principle is not always quite straight- 

 forward. Consider a tube of slightly conical form, open at both ends, 

 and suppose that we direct upon the narrower end a jet of air from a 

 tube having the same (narrower) section (Fig 5). We might expect 



Fig. 5. 



this jet to enter the conical tube witliout much complication. But if 

 we examine more closely a difficulty arises. The stream in the 

 conical tube would have different velocities at the two ends, and 

 therefore different pressures. The pressures at the ends could not 

 both be atmospheric. Since at any rate the pressure at the wider 

 delivery end must be very nearly atmospheric, that at the narrower 

 end must be decidedly below that standard. The course of the events 

 at the inlet is not so simple as supposed, and the apparent contradic- 

 tion is evaded by an inflow of air from outside, in addition to the 

 jet, which assumes at entry a narrower section. 



If the space surrounding the free jet is enclosed (Fig. 6), suction 

 is there developed, and ultimately when the motion has become 

 steady the jet enters the conical tube without contraction. A model 

 shows the effect, and the principle is employed in a well-known 

 laboratory instrument arranged for working off the water-mains. 



I have hitherto dealt with air rather than water, not only because 

 air makes no mess, but also because it is easier to ignore gravitation. 

 But there is another and more difficult question. You will have 

 noticed that in our expanding tubes the section changes only gradu- 

 ally. What happens when the expansion is more sudden — in the 



