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Paddle wheel work or Stirring Work Transfer

 




As the weight is lowered, and the paddle wheel turns, there is work transfer into the fluid system which gets stirred. Since the Volume  of the system remains constant . Integral pdV = 0. If m is the mass of the weight lowered through a distance dz and T is the torque transmitted by the shaft in rotating through the angle d0. the differential work transfer to the fluid is given by 

dW = mgdz = Td0. 

and the total work transfer is 

W = Integral (mgdz) = Integral ( Td0 ). 

where W' is the weight lowered. 


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