Hjulström Diagram

The simplest experimental threshold graph for initiation of grain movement is the Hjulström diagram - the critical velocity for movement of quartz grains on a plane bed at a water depth of 1 m plotted against mean grain size (grain diameter). ^[1] In this diagram, the velocity at which grain movement begins as flow velocity increases above the bed is plotted against mean grain size. ^[1] The graph divides into two fields: points above the curve indicate conditions under which grains are in motion, and points below indicate no motion. ^[1]

The diagram is one of the most widely used tools in introductory sedimentology because it makes the entrainment threshold immediately intuitive - you can read off a critical velocity directly from the grain size. More rigorous treatment is possible with the Shields diagram, but the Hjulström diagram’s simplicity makes it valuable for field estimation and conceptual understanding.

Behaviour of Coarse Grains

Critical entrainment velocity for grains larger than about 0.5 mm increases gradually with increasing mean grain size. ^[1] This is the intuitively expected relationship: heavier particles require a stronger current to be lifted. As grain size increases from fine sand through coarse sand to gravel, progressively higher velocities are needed because each larger grain is heavier, sits in a more exposed position on the bed, and requires more force to overcome its inertial and gravitational resistance.

Anomalous Behaviour of Fine Grains - Cohesion

The entrainment velocity for consolidated clay and silt grains smaller than 0.05 mm increases with decreasing grain size - the opposite of what is expected for coarser particles. ^[1] This seemingly anomalous behaviour at smaller grain sizes is apparently due mainly to increasing cohesion of finer size particles, making them more difficult to erode than larger, noncohesive particles. ^[1] Also, extremely small grains may lie within the viscous sublayer, where little grain movement takes place. ^[1]

The result is a U-shaped erosion boundary - or more precisely, a curve that descends to a minimum at medium sand (~0.3-0.5 mm), then rises steeply again into the silt and clay fraction. Medium sand is the easiest grain size to erode. Finer particles are protected by cohesion and viscous forces; coarser particles resist by sheer weight. This shape has important consequences: a river that slows from flood to normal stage can deposit sand while still leaving fine silt and clay in suspension, yet those fine particles - once settled and consolidated - can be harder to re-erode than the sand itself.

Limitations

The Hjulström diagram is somewhat limited in its application because it is strictly valid only at a water depth of 1 m on a plane bed and only in water in which fluid and grain densities and dynamic viscosity are constant, as in freshwater streams in a given season during average flow. ^[1] These constraints limit direct application to saline water, deep ocean currents, wind flows, or conditions substantially different from a shallow freshwater stream. The Shields diagram, which uses dimensionless variables, has a more general application and can be used for wind as well as water and for a variety of conditions in water. ^[1]

Additionally, instantaneous fluctuations in boundary shear stress from local eddies or wave action superimposed on current flow may cause some particles to move before the general onset of grain movement predicted by the diagram. ^[1]

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