A small permanent magnet motor has a torque constant kT=0.1 Nm/A and a back e. m.f. constant ke=2.50 V/krpm. The total internal resistance is R=10 Ω. Determine the torque for maximum power and the maximum rotational speed if the applied voltage is V=5V. Sketch the characteristic curves of a generic permanent magnet motor.

Apiping systems consists of 6 m of 6-std type k and 12 m of 4-std type k, both drawn copper tubing. the system conveys ethylene glycol at a rate of 0.013 m3/s. the pressure drop across the system is to be calculated. there are two 90° elbows in the 6-in pipe, a reduction from the 6-in pipe to the 4-in pipe and four 90° elbows in the 4-in pipe. all fittings are soldered (same as flanged) and regular. the inlet and outlet of the system are at the same height.