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Spatially-varied flow. The discharge of a steady flow is non-uniform along a channel. This happens when water enters and/or leaves the channel along the course of flow. An example of flow entering a channel would be a road side gutter. An example of flow leaving a channel would be an irrigation channel.
Gradually varied flow occurs when the change in flow depth per change in flow distance is very small. In this case, hydrostatic relationships developed for uniform flow still apply. Examples of this include the backwater behind an in-stream structure (e.g. dam, sluice gate, weir, etc.), when there is a constriction in the channel, and when ...
Superposition of uniform flow and source flow yields the Rankine half body flow. A practical example of this type of flow is a bridge pier or a strut placed in a uniform stream. The resulting stream function and velocity potential are obtained by simply adding the stream function and velocity potential for each individual flow.
A flow that is not a function of time is called steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Time dependent flow is known as unsteady (also called transient [8]). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference.
n = 1: a trivial case of uniform flow, n = 2: flow through a corner, or near a stagnation point, and; n = −1: flow due to a source doublet; The constant A is a scaling parameter: its absolute value | A | determines the scale, while its argument arg(A) introduces a rotation (if non-zero).
Typical examples of such flows are flow in circular and Δ shaped channels. Closed conduit flow differs from open channel flow only in the fact that in closed channel flow there is a closing top width while open channels have one side exposed to its immediate surroundings.
The Chézy Formula is a semi-empirical resistance equation [1] [2] which estimates mean flow velocity in open channel conduits. [3] The relationship was conceptualized and developed in 1768 by French physicist and engineer Antoine de Chézy (1718–1798) while designing Paris's water canal system.
This equation applies to a steady, uniform, isentropic flow. There are several observations that can be made from an analysis of Eq. (9.26). They are: For a subsonic flow in an expanding conduit (M < 1 and dA > 0), the flow is decelerating (dV < 0). For a subsonic flow in a converging conduit (M < 1 and dA < 0), the flow is accelerating (dV > 0).