Search results
Results from the WOW.Com Content Network
Sink flow is the opposite of source flow. The streamlines are radial, directed inwards to the line source. As we get closer to the sink, area of flow decreases. In order to satisfy the continuity equation, the streamlines get bunched closer and the velocity increases as we get closer to the source. As with source flow, the velocity at all ...
The velocity satisfies the continuity equation for incompressible flow: ∇ ⋅ u = 0. {\displaystyle \quad \nabla \cdot \mathbf {u} =0.} Although in principle the stream function doesn't require the use of a particular coordinate system, for convenience the description presented here uses a right-handed Cartesian coordinate system with ...
In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates. It is named after the British physicist and mathematician Geoffrey Ingram Taylor and his collaborator A. E. Green. [1]
Continuity in the Eulerian description is expressed by the spatial and temporal continuity and continuous differentiability of the flow velocity field. All physical quantities are defined this way at each instant of time, in the current configuration, as a function of the vector position x {\displaystyle \mathbf {x} } .
() then provides the governing equation for pressure computation. The idea of pressure-correction also exists in the case of variable density and high Mach numbers, although in this case there is a real physical meaning behind the coupling of dynamic pressure and velocity as arising from the continuity equation
Schematic view of an SPH convolution Flow around cylinder with free surface modelled with SPH. See [1] for similar simulations.. Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows.
For example, in the mass continuity equation for flowing water, if 1 gram per second of water is flowing through a pipe with cross-sectional area 1 cm 2, then the average mass flux j inside the pipe is (1 g/s) / cm 2, and its direction is along the pipe in the direction that the water is flowing. Outside the pipe, where there is no water, the ...
The assumptions for the stream function equation are: The flow is incompressible and Newtonian. Coordinates are orthogonal. Flow is 2D: u 3 = ∂u 1 / ∂x 3 = ∂u 2 / ∂x 3 = 0; The first two scale factors of the coordinate system are independent of the last coordinate: ∂h 1 / ∂x 3 = ∂h 2 / ∂x 3 = 0 ...