Energy Dissipation and Channel Temperature for Barrel Rotation

2 Energy Dissipation and Channel Temperature for Barrel Rotation 

The dissipation is calculated for barrel rotation in the screw pump device in a similar manner. For this case, the velocities Vozl, and are used for the calculations, and they are provided by Eqs. 7.21,7.23, and 7.27, respectively. The rate of work input for barrel rotation tv, is obtained by multiplying the normal shear stress for the barrel surface by the velocity of the barrel surface integrated over the barrel surface area. The traditional method for calculation of dissipation for barrel rotation is as follows  

The velocity component in the z direction for drag flow and pressure flow are provided in Eqs. 7.86 and 7.87. This equation uses Eqs. 7.23 and 7.27 for N/Ws that are less than 0.1. If the channel aspect ratio H/Wli, greater than 0.1, then Eqs. 7.23 and 7.27 should be used. The generalized solution using Eqs. 7.23 and 7.27 is provided in Appendix A7. 

Here Ffeis a positive value for barrel rotation. For the z component of pressure flow for///FT less than 0.1  

Substituting the shear stresses and velocities and then integrating provides the rate of work for the channel as Eq. 7.88 for barrel rotation. As before for screw rotation, dissipation is a positive definite quantity, and thus the absolute value of the pressure gradient is used. The dissipation between the flight lands and barrel wall is the same for barrel and screw rotation. 

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