Torque calculation in pumping equipment

Kirill

Hello,

I am trying to calculate hydraulic/viscous/overall torques based on the simulation of a pump (Polyflow/Fieldview). The motion of the internal rotor is quite complex, so it's easier to calculate torques on the stationary pump stator relative to the center axis. While the overall procedure of torque calculation seems to be obviuous

T = integral[vec_R x tens_Sigma dot dA], where vec_R is the arm, and tens_Sigma is the stress tensor),

the result yields three torque components, which by themselves are difficult to relate to the hydraulic load of the pump. According to analytical prediction, the hydraulic torque is related to pressure load dP as

T = QdP/W, where Q is the flow rate and W is rotational speed in rad/s.

My question is how do I relate the vector_torque obtained by integration of the stresses on stator surface to the analitical torque, which is a scalar? The square root of the square sum of the components of the torque doesn't seem to yield good correlation... I guess the question is also valid for simulations in extrusion due to a similar nature of the problem. Thank you.