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Bhutan - River Systems
Bhutan has four major river systems: the Drangme Chhu; the Puna Tsang Chhu, also called the Sankosh; the Wang Chhu; and the Amo Chhu. Each flows swiftly out of the Himalayas, southerly through the Duars to join the Brahmaputra River in India, and thence through Bangladesh where the Brahmaputra (or Jamuna in Bangladesh) joins the mighty Ganges (or Padma in Bangladesh) to flow into the Bay of Bengal. The largest river system, the Drangme Chhu, flows southwesterly from India's state of Arunachal Pradesh and has three major branches: the Drangme Chhu, Mangde Chhu, and Bumthang Chhu. These branches form the Drangme Chhu basin, which spreads over most of eastern Bhutan and drains the Tongsa and Bumthang valleys. In the Duars, where eight tributaries join it, the Drangme Chhu is called the Manas Chhu. The 320-kilometer-long Puna Tsang Chhu rises in northwestern Bhutan as the Mo Chhu and Pho Chhu, which are fed by the snows from the Great Himalayan Range. They flow southerly to Punakha, where they join to form the Puna Tsang Chhu, which flows southerly into India's state of West Bengal. The tributaries of the 370-kilometer-long Wang Chhu rise in Tibet. The Wang Chhu itself flows southeasterly through west-central Bhutan, drains the Ha, Paro, and Thimphu valleys, and continues into the Duars, where it enters West Bengal as the Raigye Chhu. The smallest river system, the Torsa Chhu, known as the Amo Chhu in its northern reaches, also flows out of Tibet into the Chumbi Valley and swiftly through western Bhutan before broadening near Phuntsholing and then flowing into India.
You can read more regarding this subject on the following websites:
Geography of Bhutan - Wikipedia
Bhutan Country Studies index
Country Studies main page