SUDDEN ENLARGEMENT OF SECTION. 199 



Substituting this value of d in (2), we have 

 log d = | [I.987Q309 + log (2500 + 4.5 x 4.7533)] 



= .6777337; 

 /. d = 4.761 inches, 



which approximation is sufficiently accurate for all practi- 

 cal purposes. 



108. Sudden Enlargement of Section. Whenever 

 there is a change in the cross-section of a pipe or any other 

 conduit, there is a change of velocity, the velocity being 

 inversely proportional to the cross-section of the stream 

 (Art. 75). If the cross-section of a 

 pipe is suddenly changed, there is a 

 sudden change in the velocity of the 

 current of water, and therefore there is 

 a loss of kinetic energy. Thus, sup- 

 pose the pipe AECP is suddenly en- 

 larged in section at BD ; then, as the 

 water in the smaller pipe has a greater 

 velocity than the water in the larger one, there will be an 

 abrupt change of velocity at BD, and this change of veloc- 

 ity will be accompanied by a loss of kinetic energy, in the 

 same way as when two inelastic bodies impinge upon each 

 other. 



Let v and v' be the velocities of the water in the smaller 

 and larger pipes, respectively, a and a' the areas of the sec- 

 tions of these pipes, and W and W the weights of water 

 discharged from them per second. 



Now as the water moves out of the smaller pipe into the 

 larger one, it impinges against the more slowly moving cur- 

 rent in that pipe, and after the impact the two bodies of 

 water, W and W, move on together with the common ve- 

 locity v'. And since in this case W is very small compared 

 with W, we have, from (3) of Art, 98, 



