Centrifugal Pumps

 

Example:  (Cont.)

 

                     

 

 

 

Step 3:  Conservation of angular momentum  (cont.)      T =  ρQ [ r2Vt2 ]

 

         Vt2   =   r2 ω  ˗  Vr2 / tan β2   = (1/2)(200)  ˗  19 / tan (30)  =  66.9 ft/sec

 

So    T  =  (1.94) (10) (1/2)(66.9)  =  650  ft lb      (result)

 

Power  =  T ω  =  (650)(200)  =  130,000 ft lb/sec  =  235 hp     (result)

 

Head  =  H  =  P / Q γ  =  130,000 / [(10)(62.4)]  =  208 ft         (result)

 

 

Step 4:  Conservation of energy: 

 

    ∆P  =   P2  ˗  P1  =  γ H  +  (1/2) ρ V12  ˗ (1/2) ρ V22     =   pressure increase by pump

 

Note:  V1  =  Vr1    and   V2  =  Vr2 er  +  Vt2 et    So  V22  =  (Vr2)2  +  (Vt2)2  

 

 

    ∆P  =   (62.4)(208)  + (1.2)(1.94)(28.6)2  ˗ (1.2)(1.94)(19)2  ˗  (1/2)(1.94)(66.9)2    

 

       ∆P  =   9 kN/ft2       (result)

 

 

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