The pressure, temperature and velocity of air flowing in a pipe are $$5$$ $$bar,$$ $$500$$ $$K$$ and $$50$$ $$m/s,$$ respectively. The specific heats of air at constant pressure and at constant volume are $$1.005kJ/kgK$$ and $$0.718$$ $$kJ/kgK,$$ respectively. Neglect potential energy. If the pressure and temperature of the surroundings are $$1$$ bar and $$300$$ $$K,$$ respectively, the available energy in $$kJ/kg$$ of the air stream is

In order to have maximum power from a Pelton turbine, the bucket speed must be