98 LECTURES TO SCIENCE TEACHERS. 



greater than that at A, in the proportion in which the sec- 

 tional area of the pipe at B is less than that at A ; and, 

 therefore, while passing from A to B the forward velocity of 

 the fluid is being increased. This increase of velocity implies 

 the existence of a force acting in the direction of the 

 motion, to overcome the inertia of the fluid ; that is to say, 

 each particle which is receiving an increase of forward 

 velocity must have a greater fluid pressure behind it than 

 in front of it ; for no other condition will cause that 

 increase of forward velocity. Hence a particle of fluid, 

 at each stage of its progress along the tapering contrac- 

 tion, is passing from a region of higher pressure to a 

 region of lower pressure, so that there must be a greater 

 pressure in the larger part of the pipe than in the smaller, 

 the diminution of pressure at each point corresponding with 

 the diminution of sectional area, corresponding, that is to 

 say, with the additional forward velocity assumed by the 

 fluid at each point of its advance along the contraction. 

 Consequently, differences of pressure at different points in 

 the pipe depend solely upon the velocities, or, in other 

 words, on the relative sectional areas of the pipe, at those 

 points. 



It is easy to apply the same line of reasoning to the con- 

 verse case of an enlargement. Here the velocity of the 

 particles is being reduced through precisely the same series 

 of changes, but in an opposite order. The 'fluid in the 

 larger part of the pipe moves more slowly than that in the 

 smaller, so that, as it advances along the enlargement, its 

 forward velocity is being checked ; and this check implies 

 the existence of a force acting in a direction opposite to 

 the motion of the fluid, so that each particle which is being 

 thus retarded must have a greater fluid-pressure in front 

 of it than behind it ; thus a particle of fluid at each stage 

 of its progress along a tapering enlargement of a pipe, is 

 passing from a region of lower pressure to a region of 

 higher pressure, the change of pressure corresponding to 

 the change of velocity required. Hence we see that a 

 given change of sectional area will require the same change 

 of pressure, whether the pipe be an enlargement or a con- 

 traction. 



Therefore, in a pipe in which there is a contraction and 

 a subsequent enlargement to the same diameter as before 



