LOSS AT CONTRACTION OF AREA 98 



ART. 35. Loss DUE TO SUDDEN CONTRACTION OF AREA OF A 



STREAM. 



When water flowing along a channel or through a pipe meets with a 

 sudden contraction of the area of the pipe, as shown in Fig. 45, we also 

 get a loss of energy which is due, not directly to the contraction of the 

 stream, but to the subsequent re- 

 enlargement which always takes place. 



The stream, after passing the con- 

 traction, suffers a further diminution 

 in area, and for a short distance 

 fails to fill the pipe, afterwards re- 

 expanding as shown. 1 Up to the con- 

 tracted section the loss is solely that due to simple viscous resistance. 



If A represents the larger stream area 



a smaller 



a c vena contracta 



V, v and v c representing the velocities at these sections, the loss of energy 

 due to this enlargement is approximately 



(f?g ~ V ^ ft. Ibs. per Ib. 

 Writing C c for , the above may be expressed in the form 



Here F is called the coefficient of hydraulic resistance, and can only be 

 determined experimentally. 



A series of experiments carried out by the author on the apparatus 

 shown in Fig. 45, having a value of m = 10'96, and having pipe diameters 

 of 2*15 inches and "65 inch, gave a mean value of "600 for C c , over a 

 range of values of v from 1'35 to 8*69 feet per second. The value 

 diminished from *610 with the lowest to '587 with the highest of these 

 velocities. Experiments on a 6-inch pipe, contracting respectively to 

 a 3-inch and to a 4-inch pipe, give in the former case a value of F = 7*37 

 (C e = -595), and in the latter case F = TO (C c = '692). 



t; 2 

 If C e has the value '586, the loss = "50 ^. This is approximately 



the value of C e , where the area A is so large as not to affect the stream 



1 This action may occur even though the pipe is full of water, the space shown empty in 

 Fig. 46 being now occupied by dead water which takes no part in the flow through the pipe. 



