Rapidly Varying Flow   The Hydraulic Jump   (continued)

 

                               

                                  

To develop a relation between the upstream depth, y1, and the downstream depth, y2,

following the hydraulic jump combine the expressions for conservation of mass and

conservation of linear momentum to eliminate  V2  and use the definition of the

Froude number at the upstream station,  Fr1  =  V1/√gy1   .

 

 

Mass:                                               y1V1  =  y2V2   ,    V2  =  y1V1 / y2                   (1)

 

Linear Momentum:    y1V12 /g   +  y12 /2  =    y2V22 /g  + y22 /2                              (2)

 

Combine (1) and (2):   ( y2 /y1 )2+ ( y2 /y1 ) -  2 Fr1   =  0     Use the quadratic formula

to obtain the solution for  y2 /y1 the downstream depth divided by the upstream depth.

 

 

                  ( y2 /y1 )   =   [ -1  +  √( 1 + 8 Fr12) ] / 2  

 

 

Likewise    ( y1 /y2 )   =   [ -1  +  √( 1 + 8 Fr22) ] / 2  

 

 

The head loss across the hydraulic jump is also of interest.  To obtain an expression for this

loss, hL, apply conservation of energy.

                                                                                Click here to continue this discussion.

 

Return to Notes on Fluid Mechanics


Copyright © 2019 Richard C. Coddington
All rights reserved.