Analysis of Centrifugal Pumps

 

Velocities at entrance (1) and exit (2) of vane on impeller:    V  =  U  +  W     where

                V  =  the absolute fluid velocity measured in the inertial frame of reference

                U  =  the velocity of the vane rotating about  the z-axis

               W  =  the velocity of the fluid relative to the vane

                          

 

where   er = unit vector in radial direction,          et = unit vector in tangential direction

              n1= unit vector along vane at the entrance (attached to vane)

              n2 = unit vector along vane at the exit (attached to vane)

               ω = absolute angular speed of impeller

            r1 = radius at entrance section of vane,  r2 = radius at exit section of vane

          β1  = angle of vane at entrance,      β2 = angle of vane at exit

 

At entrance 1:                                                                 At exit 2:

U1  =   ˗  r1 ω  et                                                          U2  =    ˗ r2 ω  et   

 

W1  =    w1   n1                                                          W2  =   w2  n2

 

V1  =  ˗ r1 ω  et  +   w1   n1                                         V2  =   ˗ r2 ω  et   +  w2   n2

 

V1  =   r1 ω  et  +   w1 ( er sin β1 ˗  et  cos β1)            V2  =    r2 ω  et   +  w2  ( er cos β1 +  et  sin β1)    

 

V1  =   ( ˗r1 ω ˗  w1 cos β1 ) et  +   w1 (sin β1 ) er       V2  =   (˗ r2 ω + w2 sin β1) et   +  w2  (cos β1 ) er

 

Click here for a display of the vector diagrams.

 

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