The straightening of a river meander such as cutting through the neck of a meander (as seen in the figures below) will allow the water to flow in a shorter and therefore quicker route, hence resulting in an increase in velocity (B).

Fig. 1: The neck of the meander is being eroded. Fig. 2: The river is straightened as the neck is cut.

The gradient (D), volume of water flowing in the river (A), and the risk of flooding (C) should stay relatively the same. Although if one built a home in the middle of the neck, the risk of flooding would be a major problem.