The river that flows out of Lake Tana and later joins the White Nile at Khartoum is the Blue Nile.
The Blue Nile begins in Ethiopia, with its headwaters associated with Lake Tana and the outlet near Bahir Dar. Known as the Abay in Ethiopia, it travels roughly 1,450 kilometres through Ethiopia and Sudan before meeting the White Nile in Khartoum. From that confluence, the combined river is generally called the Nile.
Seasonal rainfall in the Ethiopian highlands gives the Blue Nile a powerful wet-season surge. Historically, its floodwaters carried fertile sediment into the Nile valley, helping support agriculture in Egypt and Sudan. Today, the river is also important for hydropower, irrigation and regional water politics.
The White Nile is not the answer because it is the river that meets the Blue Nile at Khartoum. The Atbara also rises in Ethiopia and joins the Nile farther north, while the Sobat joins the White Nile upstream in South Sudan. During the rainy season, the Blue Nile contributes most of the Nile’s flow at Khartoum.