A pipe with a diameter of 15 cm carries hot air with a velocity 200 m/s and temperature 1000 K into a chamber. Surrounding the pipe, in an annulus of outer diameter 20 cm, is a flow of cooler air entering the chamber at 10 m/s with a temperature of 300 K. The mixing chamber operates at steady state with a single exit of diameter 20 cm. If the air exits at 646 K and the specific volume of air is proportional to the temperature (in K), determine:
(a) The exit velocity in m/s.
(b) The dm/dt for the mixing chamber in kg/s.