<< Now from momentum considerations you can show that the tip speed should 
be equal to the exhaust velocity- in this case ~200 m/s >>

I may be missing part of this scenario, but there seems no reason for rotor 
tip speed to equal exhaust velocity.  I would think rotor tip speed would 
increase until the torque of the overall drag forces on the rotor equaled the 
torque produced by the engines.  IF this "terminal velocity" HAPPENS to equal the 
exhaust velocity of rocket, then additional energy from the rocket propellant 
would go mainly into the kinetic energy of the air moved by the rotor 
(downwash, shock waves, etc.), less an allowance for inefficiencies.  

In ordinary rockets, the classic rocket equation does link exhaust velocity 
to final vehicle velocity through total propellant mass. For instance, the 
burnout velocity of an ideal, free space, single stage is equal to its exhaust 
velocity when the propellant mass is "e-1" (1.718..) times the mass of everything 
else.   But I would think a rotor would reach its drag-limited "terminal 
velocity" long before fuel consumption becomes an issue.

--Best, Gerald 
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