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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.
The unsteady flow equation solver was adapted from Dr. Robert L. Barkau's UNET package. HEC-RAS is equipped to model a network of channels, a dendritic system or a single river reach. Certain simplifications must be made in order to model some complex flow situations using the HEC-RAS one-dimensional approach.
In this model the red fluid – initially on top, and afterwards below – represents a more dense fluid and the blue fluid represents one which is less dense. The Rayleigh–Taylor instability is another application of hydrodynamic stability and also occurs between two fluids but this time the densities of the fluids are different. [ 6 ]
In the case of steady flow, it is convenient to choose the Frenet–Serret frame along a streamline as the coordinate system for describing the steady momentum Euler equation: [24] =, where u {\displaystyle \mathbf {u} } , p {\displaystyle p} and ρ {\displaystyle \rho } denote the flow velocity , the pressure and the density , respectively.
Start with the 1D-EE. Assume a steady flow, no gravity effects, and introduce in the momentum-conservation equation an empirical term to recover the effect of wall friction (neglected in the EE). To close the Fanno flow equation, a model for this friction term is needed. Such a closure involves problem-dependent assumptions. [54] Rayleigh flow ...
For a given flow rate and channel geometry, there is a relationship between flow depth and total energy. This is illustrated below in the plot of energy vs. flow depth, widely known as an E-y diagram. In this plot, the depth where the minimum energy occurs is known as the critical depth.
The control volume integration of the steady part of the equation is similar to the steady state governing equation's integration. We need to focus on the integration of the unsteady component of the equation. To get a feel of the integration technique, we refer to the one-dimensional unsteady heat conduction equation. [3]
Uniform flow can be steady or unsteady, depending on whether or not the depth changes with time, (although unsteady uniform flow is rare). Varied flow. The depth of flow changes along the length of the channel. Varied flow technically may be either steady or unsteady. Varied flow can be further classified as either rapidly or gradually-varied: