|g$ HYDRAULIC INVESTIGATIONS. 



c^il e \/ ft 



/is found, for the second case, equal to -tt-~ f - — - — . 



d* (y + w) d 



For example, suppose the height a 2 feet, 6 r {, c z: 1, 



and consequently e — 1, then d becomes i, « r 4, and y 



:= R ; and in the first case z rz *1, and in the second z tt 



•14. 



Varieties of If v, the velocity of the obstacle, were great in com pa- 



th e velocity a 



and open rison with m \/ -, the velocity of a wave, and the space c 



ifp co. 



below the obstacle were small, the anterior part of the ele- 

 vation would advance with a velocity considerably greater 

 than the natural velocity of the wave : but if the space be- 

 low the obstacle b«re a considerable proportion to the whole 

 height, the elevation z would be very small, since a mode- 

 rate pressure would cause the fluid to flow back, with a suf- 

 ficient velocity, to exhaust the greatest part of the accumu- 

 lation, which would otherwise take place. Hence the ele- 

 vation must always be less than that which is determined by 

 the equation m \/ z c zz e v, and z is at most equal to 



? a 



'— b ; but since the velocity of the anterior mar- 



V m cy 



*in of the wave can never materially exceed m \/ '-, espe- 



x 



cially when z is small, and </ — being in this case nearly </ 



—■ »/ b J which, multiplied by z, shows the utmost quan- 

 tity of the fluid that can be supposed to be carried before 

 the obstacle. Supposing b ~\ c, this quantity becomes m 



\/ - . rj . - ; and if- be, for example, T V, it will be ex* 



pressed by TT W?r a v, while the whole quantity of the fluid 



left behind. 

 A contraction A similar mode of reasoning may be applied to other 

 moving aiong cases f t h e propagation of impulses, in particular to that of 

 an elastic pipe. ~r i , I • ■ r ,• 



a contraction moving along an elastic pipe. In this case, an 



increase of the diameter does not increase the velocity of 

 the transmission of an impulse ; and when the velocity of 



the 



