Finite Control Volume – Translating CV

 

A jet of water with absolute velocity of  V =  8 i ft/sec and diameter 4 inches strikes the plate, AB,

driving the plate to the right on a straight line.   Calculate the force, F, acting on the plate so

that the plate translates to the right at a constant speed of 4 ft/sec.  See the figure below.

                 

                       

 

Strategy:  Construct the control surface and control volume.  Then apply conservation of linear

momentum with a translating control volume as given below.

 

                                    

                                                 

                                ∫ W ρ (W . n ) dS  =  Σ F    =  ˗ ρ W2 A  i  =  ˗ F i

                              cs                                 

             

  W  =  V i  ˗  Vcv i  =   8 i  ˗  4 i  =  4 i  ft/sec,      W2 = 16 (ft/sec)2,     n  =  ˗ i  ,  

    ρ  =  1.94 slugs/ft3

                                    A  =  (π / 4)( 4/12)2  =  0.0873 ft2

 

              ( ˗ 1.94 ) (16) (0.0873)  =  ˗  F,      F  =  2.7 lb    (result)

 

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