Open Channel Flow        Introduction  (continued)

 

 

The principles of conservation of mass, linear momentum, and energy apply to

open channel flow.  Each principle is listed in the Table shown below.

 

 

 

Conservation of Mass

 

ρ1A1V1  =  ρ2A2V2

 

 

Conservation of Linear Momentum

 

ρ2A2V22  -  ρ1A1V12  =  Σ Fx

 

 

 

Conservation of Energy

 

P1  +  V12/2g  +  z1  =   P2  +  V22/2g  +  z2  +  hL

 

y1  +  V12/2g  +  z1  =   y2  +  V22/2g  +  z2  +  hL

 

 

 

 

where  indices  1  and  2  denote the upstream and downstream locations of the channel

            ρ1  and  ρ2  denote the densities at these locations and are generally the same          

           γ  denotes the specific weight of the liquid

           A1  and  A2 denote the areas of the channel at these locations and for a

           rectangular channel will equal the width of the channel times the depth of

          the channel at these locations

          V1 and V2 denote the speeds of the liquid at these locations

          Σ Fx  denotes the component of force along the channel

            P1 and P2 denote the pressures at 1 and at 2     P1 = γy1,  P2 = γy2

            y1 and y2 denote the depths of the liquid above the channel bed at 1 and at 2

            z1 and z2 denote the elevations of the channel bed at 1 and at 2

           hL denotes the head loss due to friction between 1 and 2

 

 

Click here to start with discussion of uniform flow.

 




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