Solving Shield’s diagram for the diameter to be mobilised
I once fitted a curve to the Shield’s diagram.
I’m sure this must have been done before, but anyway my version is:
Where the subscript ‘c’ refers the the critical condition – i.e. the line on the Shields diagram above. This line indicates that combination of average bed shear stress and sediment diameter in which noticeable movement of sediment is said to start occurring. If you solve the Shield’s diagram in the normal way, i.e.
… then you can set up a routine that keeps changing the sediment diameter until Equation (1) = Equation (2), giving the critical sediment diameter. Alternatively, you could solve for the critical bed shear stress for a given diameter. It just automates the otherwise laborious graphical process.
