FLOW OF WATER IN RIVERS AND CANALS. 



211 



For practical calculations on the flow of water in pipes, 

 see Ency. Brit., Vol. XII., p. 488. 



113. Flow of Water in Rivers and Canals. 



When water flows in a pipe, the section at any point is de- 

 termined by the form of the boundary. When it flows in 

 an open channel with free upper surface, the section de- 

 pends on the velocity due to the kinetic conditions. The 

 bottom of the channel and the two banks are called the bod 

 of the stream. A section of the stream at right angles to 

 the direction in which it is flowing is called a transverse 

 section, and of the line bounding this section, the part that 

 is beneath the Avater surface is called the wetted perimeter. 

 A vertical section in the direction of the stream is called the 

 longitudinal section or profile. 



Let ABCD represent a longitudinal 

 section of a limited portion of a stream, 

 AD, BC, two transverse sections, AB 

 the surface of the stream, DC the bot 

 torn of the channel, and AE a horizon- 

 tal line. Let I = the length of AB in 

 feet ; h = BE, the difference of level of the water surface 

 in feet at the two extremities of the distance I; 6 = the 



angle BAE, the slope of the stream ; sin = -j = the sine 



I 



of the slope, or the fall of the water surface in one foot ; 

 a = the area of the transverse section at BC in square feet ; 

 p = the length of the wetted perimeter of the transverse 



section at BC ; r = -, the hydraulic mean depth, or the 

 mean radius of the section ; Q = the discharge through 



the section at BC in cubic feet per second ; v = - = the 



a 



mean velocity of the stream in feet per second, which is 

 taken as the common velocity of all the particles. 



Fig. 60 



