MIT OpenCourseWare http ocw mit edu Electromechanical Dynamics For any use or distribution of this textbook please cite as follows Woodson Herbert H and James R Melcher Electromechanical Dynamics 3 vols Massachusetts Institute of Technology MIT OpenCourseWare http ocw mit edu accessed MM DD YYYY License Creative Commons Attribution NonCommercial Share Alike For more information about citing these materials or our Terms of Use visit http ocw mit edu terms Electromechanical Coupling with Viscous Fluids PROBLEMS 14 1 Rework the example of Sec 14 2 1 with the applied flux density in the X2 direction Assume that no current can flow in the x3 direction In particular obtain expressions for velocity profile like Eq 14 2 4 voltage like Eq 14 2 7 traction like Eq 14 2 10 and total power per unit area like Eq 14 2 12 Make plots of voltage and loss per unit area for the constants of Table 14 2 1 and compare the results with those plotted in Fig 14 2 3 14 2 A viscous liquid flows through a circular pipe as shown in Fig 14P 2 At the inlet the pressure is uniform and equal top 1 and at the outlet it is still uniform butp2 The volume rate of flow is Qm lsec Under the assumption that the flow is axisymmetric and steady and that the velocity is low enough that the fluid can be considered incompressible find the velocity profile vz r Hint Look for solutions where v v2 r iz and p p z Fig 14P 2 14 3 The channel shown in Fig 14P 3 contains a viscous fluid of conductivity a moving in the xz direction You are to analyze this problem using the Hartmann flow solutions Section 14 2 2 The highly conducting electrodes are connected by a load resistance R a Given the pressure drop from inlet to outlet the dimensions of the system field B o and conductivity a what is the power dissipated in the resistance b What value of R should be used to dissipate the largest possible power in the load c If the fluid is mercury Bo 20 000 gauss d 1cm I 1 m and w 10 cm what is the Hartmann number What is the value of the optimum resistance found in part b Perfectly conducting Fig 14P 3
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