A Synchronous Turbo Generator is otating at 1800rpm, has acylindrical rotor(the

Question

A Synchronous Turbo Generator is otating at 1800rpm, has acylindrical rotor(the rotor is the rotating component of the Turbogenerator) 3meters long, 1m in diameter, whose mass has a volumedensity of 7800 Kg/m3 . a) What is the kinetic energy possessed by the spinningrotor? b) Determine the required torque to bring the Turbo Generatorfrom rest to its rated speed of 1800rpm in 2 hrs.. I promise to rate. Any assistance is appreciated. A Synchronous Turbo Generator is otating at 1800rpm, has acylindrical rotor(the rotor is the rotating component of the Turbogenerator) 3meters long, 1m in diameter, whose mass has a volumedensity of 7800 Kg/m3 . a) What is the kinetic energy possessed by the spinningrotor? b) Determine the required torque to bring the Turbo Generatorfrom rest to its rated speed of 1800rpm in 2 hrs.. I promise to rate. Any assistance is appreciated.

Explanation / Answer

          Givne that the length of the rotating cylinder is L = 3m           Diameter of the cylinder is d = 1 m           then radius of the cylinder is r = d /2 = 0.5 m            volumedensity of the cylinder is = 7800 Kg/m3.           final angular speed of the cylinder is 2 = 1800 rpm =(1800rpm)(2rad/rev)(min /60s)                                                                        =188.4 rad/s           time taken is t = 2hr = 2*3600s = 7200 s       -----------------------------------------------------------------------------            The mass of the rotator is m = *V                                                         =* r2h                                                              =----------- kg                      Thekinetic energy of the turbo genarator is K =(1/2)I*22                                                                                  = -------------- J        where I= mr2/2 is the moment of inertia of the rotor           The torque to bring the turbo fromthe rest to finalspeed is = I                                                                                                       =I *(2 -1) /t                                                                                                       = I*(2 -0) /t                                                                                                       =----------- N.m         where 1 =0 is the initial angular speed of the turbo                                

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