Which world river has the largest elevation drop?

The source of the Yarlung Zangbo River lies some 6,020 m (19,750 ft) above sea level at the foot of the Angsi Glacier in Tibet, China. No continuously flowing river has a higher origin. It flows east across the Tibetan Plateau, falling to 3,000 m (9,800 ft) before crossing into India, where it is known as the Brahmaputra River.

The mean elevation of the river has been estimated to be around 4,000 m (13,123 ft).

How steep does it get? 2,000 feet per mile, approximately – and make no mistake, that's steep. Not to mention the 20m+ waterfalls.

Stream gradient (or stream slope) is the grade (or slope) of a stream. It is measured by the ratio of drop in elevation and horizontal distance. It is a dimensionless quantity, usually expressed in units of meters per kilometer (m/km) or feet per mile (ft/mi); it may also be expressed in percent (%). The world average river reach slope is 2.6 m/km or 0.26%; a slope smaller than 1% and greater than 4% is considered gentle and steep, respectively.