Rivers are not static — they continuously adjust their shape in response to the water and sediment moving through them. In 1956, engineer Emory Lane captured this with a simple proportionality:
The left side is the river’s transport capacity: how much sediment the flow can carry, set by discharge (Qw) and channel slope (S). The right side is the sediment supply: how much material is delivered, characterised by its load (Qs) and grain size (Ds). On the balance below, bar height encodes discharge and load; pan position along the arm encodes slope and grain size.
When the sides balance, the channel is in dynamic equilibrium. Tip the balance and the river responds: excess transport capacity causes degradation (the bed erodes downward); excess sediment supply causes aggradation (the bed fills up). Try changing one parameter at a time — then consider what happens downstream of a dam, or after widespread deforestation.