Movement of a fluid

The critical discharge, critical velocity and the water depth describe a situation when the velocity of propagation of a wave is equal to the flow velocity. The pictures below show the effect of undulation when a stone drops into a river.

The relationship between h and hE for a constant discharge Q can be displayed in a diagram. In reference to the diagram, the following statements can be made: Under a given discharge Q a minimum height of energy hE,min exists. This statement is known as extremal principle.With an existing specific energy hE larger than hE,min, two conditions are possible:
Low water depth h, high flow velocity v:
This flow is supercritical. Enormous stress at the bottom is the result. Interferences do not spread out upstream, therefore the flowage is only calculated for a downstream flow.
Great water depth h, low flow velocity v:
This flow is subcritical. This type of movement is often found in open channels and rivers. Interferences such as a cross-section constriction have an effect on the upstream flow. The flowage is calculated for the upstream flow.

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