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Gradually Varied Flow

R. H. J. Sellin

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Abstract

2.1.1 General. Gradually varied flow is non-uniform flow in which the change of depth in the channel occurs but gradually, in the direction of flow. As a result the streamlines in any restricted locality can be considered straight and parallel and the resulting pressure distribution will therefore be hydrostatic. This restriction on the flow conditions also enables the Bernoulli equation to be used to evaluate the fluid energy. It is known that the Bernoulli equation, as well as the hydrostatic pressure distribution, breaks down when the streamlines become significantly curved. The criterion of streamline curvature will be used to distinguish between gradually varied flow and rapidly varied flow although in practice the exact point of distinction is indeterminate.

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2.1.1 General. Gradually varied flow is non-uniform flow in which the change of depth in the channel occurs but gradually, in the direction of flow. As a result the streamlines in any restricted locality can be considered straight and parallel and the resulting pressure distribution will therefore be hydrostatic. This restriction on the flow conditions also enables the Bernoulli equation to be used to evaluate the fluid energy. It is known that the Bernoulli equation, as well as the hydrostatic pressure distribution, breaks down when the streamlines become significantly curved. The criterion of streamline curvature will be used to distinguish between gradually varied flow and rapidly varied flow although in practice the exact point of distinction is indeterminate.

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Available abstract

2.1.1 General. Gradually varied flow is non-uniform flow in which the change of depth in the channel occurs but gradually, in the direction of flow. As a result the streamlines in any restricted locality can be considered straight and parallel and the resulting pressure distribution will therefore be hydrostatic. This restriction on the flow conditions also enables the Bernoulli equation to be used to evaluate the fluid energy. It is known that the Bernoulli equation, as well as the hydrostatic pressure distribution, breaks down when the streamlines become significantly curved. The criterion of streamline curvature will be used to distinguish between gradually varied flow and rapidly varied flow although in practice the exact point of distinction is indeterminate.

Key concepts: Streamlines, streaklines, and pathlines, Bernoulli's principle, Flow (mathematics), Mechanics, Curvature, Hydrostatic pressure, Energy–depth relationship in a rectangular channel, Isothermal flow

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