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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.
In the aircraft example, the observer on the ground will observe unsteady flow, and the observers in the aircraft will observe steady flow, with constant streamlines. When possible, fluid dynamicists try to find a reference frame in which the flow is steady, so that they can use experimental methods of creating streaklines to identify the ...
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:
The essential problem is modeled by nonlinear partial differential equations and the stability of known steady and unsteady solutions are examined. [1] The governing equations for almost all hydrodynamic stability problems are the Navier–Stokes equation and the continuity equation.
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.
The local derivative occurs during unsteady flow, and becomes zero for steady flow. The portion of the material derivative represented by the spatial derivatives is called the convective derivative. It accounts for the variation in fluid property, be it velocity or temperature for example, due to the motion of a fluid particle in space where ...
The steady-state flow of groundwater is described by a form of the Laplace equation, which is a form of potential flow and has analogs in numerous fields. The groundwater flow equation is often derived for a small representative elemental volume (REV), where the properties of the medium are assumed to be effectively constant.
Steady Bernoulli equation: Start with the Bernoulli Equation and assume a steady flow. [49] Or start with the EE and assume that the flow is steady and integrate the resulting equation along a streamline. [47] [46] Stokes Flow or creeping flow equations: Start with the C-NS or I-NS. Neglect the inertia of the flow.