# Relationship between sediment concentration of flow and erosion - streampower equation

I am trying to understand how the sediment concentration of a flow affects erosion. I stumbled across this paper by Bagnold (1968) today that uses a form for the stream power equation that I had not seen before, and haven't yet managed to find anywhere else. Namely:

\Omega = Q g S [\rho + C (\sigma - \rho)]

where \Omega is the streampower, Q volumetric flux of the flow, g is gravity, S slope, \rho is the density of the flow, C is the volumetric sediment concentration of the flow, and \sigma is the density of the sediment.

This implies that the Stream power increases with increasing sediment concentration. I do not understand why this would be the case. I also haven't yet been able to find this relationship anywhere else to give me more context.

My (rather uninformed) intuition was that erosion would decrease as the flow is carrying more sediment - basically because at some point there has to be a limit to how much sediment a flow can carry and it's still a flowing river/stream etc. But if streampower increases with increased sediment then I would expect that erosion would also increase (since that is driven by streampower), which is quite a feedback loop (although obviously deposition would also increase so it's not a simple one).

Can anyone explain what is happening here? Or point me to resources that will help clear up my confusion? I suspect I'm missing something basic, but not sure.

• Not an answer but if the water has the sediment supported within the flow then the density of the combined fluid would be overall higher. In our part of the world we have creeks that occasionally develop what are called debris flows. When one of these flows down a drainage they can scour the banks right to the bedrock. Don't know if a debris flow would be considered in the equation above. – user824 Jun 24 '19 at 22:39
• Thanks Friddy - that makes perfect sense, neglecting the sediment part of the density would be problematic in those cases. There must be some other process that I'm not fully understanding that prevents every erosive event becoming choked with sediment. – Esme_ Jun 25 '19 at 2:12
• I just come across your question & like Friddy I don't know if I can give you a satisfactory answer. @Friddy is correct in stating the sediment would increase the density of the flow medium (water & sediment). Depending on the amount of sediment in the flow, the flow medium could be called a slurry. The other thing the sediment does is increase the mass of the flow medium. Kinetic energy, Ek = 0.5mv^2. A flow medium with a higher mass, due to sediment, would also have a higher kinetic energy, which would increase the erosion potential of the flow medium. Also, sediment is composed of solid ... – Fred Jul 6 '19 at 14:53
• ... particles which can impart a greater amount of energy/momentum into the river bank material thus accelerating/increasing erosion. Sand/Abrasive blasting is very analogous to this. Blast a painted surface with air or water & little will happen. Blast it with an air-sand or water-sand mixture & the paint is removed relatively quickly & easily. Sediment in the river water is the abrasive that scours the river bank material. – Fred Jul 6 '19 at 14:59