Bhagirathi River
The Bhagirathi at Gangotri
The Bhagirathi (Hindi: भागीरथी Bhagirathi ) is the longer of the two sources of the Ganges in India. Your source called Gaumukh, is located in the Himalayas in the state of Uttarakhand. The other source river, called Alaknanda is shorter but more watery.
The Bhagirathi is dammed in the Tehri Dam for power generation and irrigation.