CHAPTER X, 



Flow in an open channel Formulae Darcy and Bazin Prony Eytelwein Kutter 

 Manning Fidler Thrupp Williams Critical velocity Form of channel Channel of 

 constant mean velocity General equation of flow Non-uniform flow Standing waves 

 Backwater function Effect of dams Bridge piers Passage of boat through a narrow 

 canal Flow round river bends Distribution of velocity in an open channel Erosion 

 and Silting Gauging of flow in streams and channels Current meters Floats Pitot 

 tube Rating Tables Gauging of ice covered streams. 



ART. 85. FLOW IN AN OPEN CHANNEL. 



THE term " open channel " includes all rivers, artificial canals, 

 aqueducts, and conduits, and, in addition, sewers and pipes of whatever 

 section which run partially full, and which consequently do not present 

 a solid boundary to every side of the contained liquid. The force pro- 

 ducing flow cannot now be provided by any external head, but is solely 

 due to the slope or gradient of the channel. 



If a circular pipe be laid almost horizontally and if the surface level 

 of water flowing through the pipe be allowed to rise, the change from 

 the state in which the flow is governed by the laws appertaining to an 

 open channel, to that in which the ordinary laws of pipe flow hold, is 

 not abrupt, and it is to be inferred that a general formula is deducible 

 which by satisfactory adjustment of constants shall fit either type of flow. 



Still, the comparative simplicity of the conditions holding in the case 

 of a circular pipe, the complications which must of necessity be introduced 

 where water flows through a channel of uneven section, and the ease with 

 which accurate observations are made in the one case and the difficulty with 

 which even such a fundamental observation as the difference in level at 

 points widely distant is accurately determined in the other, render it 

 impossible that the laws governing the flow in open channels should be 

 so definite and of such universal application as those already considered. 



Assuming the resistance, R, to flow, to be proportional to the wetted 

 perimeter P of the channel, this may be expressed as 



E =/' S v n , 



where /' is a coefficient depending on the condition of the surface and 

 probably, from analogy to pipe flow, also on the velocity v, while n is a 

 number probably varying from 1'79 to 2*00, depending on the surface 

 and on the velocity v, and S = P X I, where I = length of channel. 



H.A. u 



