It is impossible to feel hair growing, because hair grows at a very slow rate on the scalp. The average rate of hair growth is about half a millimeter every day, or about 15 cm per year.
Hair growth rate differs slightly between the different human races. It is fastest among Asians, at 15cm per year, and slowest amongst Africans, at about 10 cm per year. Caucasian hair grows at a rate in between the two extremes. The actual growth rate in an individual can differ slightly from time to time, depending on age, genetics and hormonal state. Overall, though, the growth rate is much too slow for the individual to actually feel the hair growing.