The energy slope, also known as the hydraulic gradient, represents the change in total energy per unit length of the channel. It is equal to the difference in height between two points in the channel, divided by the distance between those points. The energy slope determines the pressure head and velocity of the flow, and is used to calculate the discharge (volume flow rate) in open channel flow.
The friction slope, on the other hand, represents the energy lost due to friction between the fluid and the channel walls. It is proportional to the velocity of the flow, and increases as the flow velocity increases. The friction slope influences the resistance to flow, and must be taken into account when determining the discharge in an open channel.
In summary, the energy slope determines the flow rate, while the friction slope determines the resistance to flow. Together, they control the behavior of the flow in an open channel.