Type 3:   Hydraulic Jumps

 

Key Concepts:  When the upstream flow is supercritical, Fr > 1, (Froude number is greater than 1)

 the flow is unstable.  Local nonuniform flow causes a steep upward slope of the surface profile with violent turbulence transitioning to subcritical, downstream uniform flow.  See the figure below.

 

 

                                  

 

Apply the principles of conservation of mass, linear momentum, and energy to

analyze hydraulic jumps along with the specific energy diagram.

 

Conservation  of Mass:          ρ1A1V1  =  ρ2A2V2 ,  y1V1  =  y2V2  =  q

 

Conservation of Linear Momentum:      ρ2A2V22  -  ρ1A1V12  =  Σ Fx  =  F1 – F2 

 

or                          ρQV2  -  ρQV1   = ρQ(V2  -  V1)   =  F1 – F2 

where  F1 = P1A1   =  γ y12 w/2  and   F2  = P2A2  =  γ y22 w/2 , (hydrostatic pressure distribution)

 

                                  y1V12  +g y12/2  =  y2V22 + gy22/2       

               

Cons of Energy:  P1/γ  +  V12/2g + z1  =   P2/γ  +  V22/2g  + z2 +  hL           z1  =  z2  = 0

Now  P1  =  γ y1 ,  P2  =  γ y2   So the energy equation becomes

 

                      y1  +  V12/2g   =   y2  +  V22/2g   +  hL                or  E1  =  E2  + hL  

 

or                   y1  +   q2 /2gy12   =   y2  +   q2 /2gy22  +  hL               

 

 

Click here to return to home page on Open Channel Flow.

Return to Notes on Fluid Mechanics


Copyright © 2019 Richard C. Coddington
All rights reserved.