The positive direction of rotation is taken, by convention, to be in the direction towards the y axis from the x axis. The angular velocity in two dimensions is a pseudoscalar, a quantity that changes its sign under a parity inversion (for example if one of the axes is inverted or if axes are swapped). In two dimensions, the angular velocity is a single number with an orientation but no direction. This is related to the cross-radial (tangential) velocity by: Īn explicit formula for v ⊥ in terms of v and θ is:Ĭombining the above equations gives a formula for ω: In two dimensions, the angular velocity ω is given by Therefore, the rotation is completely produced by the perpendicular motion around the origin, and the angular velocity is completely determined by this component. On the other hand, if there is no cross-radial component, then the particle moves along a straight line from the origin.Ī radial motion produces no change in the direction of the particle relative to the origin, so, for the purpose of finding the angular velocity, the radial component can be ignored. If there is no radial component, then the particle moves in a circle. As shown in the diagram (with angles ɸ and θ in radians), if a line is drawn from the origin (O) to the particle (P), then the velocity ( v) of the particle has a component along the radius (radial component, v ‖) and a component perpendicular to the radius (cross-radial component, v ⊥). The angular velocity of a particle is measured around or relative to a point, called the origin. The direction of the angular velocity pseudovector will be along the axis of rotation in this case (counter-clockwise rotation) the vector points up. If you select the Options button next to the Vectors check box you have further control over the display of the vectors.The angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. Once you have a vector data set you can adjust the display of the vectors by going to the Display Options dialog for the 3D grid and turning on the Vectors check box. To create a velocity vector data set from a MODFLOW CCF file in GMS you simply right click on the CCF data in the GMS Project Explorer and select the CCF -> Velocity Vectors command. Veloctiy.K = Flow.K / (Area.K * porosity) Velocity.J = Flow.J / (SaturatedArea.J * porosity) Velocity.I = Flow.I / (SaturatedArea.I * porosity) Once the flows, areas, and porosity are assembled the groundwater flow velocity is computed using the following equations: Although porosity is not part of the MODFLOW inputs, using GMS you can specify porosity on a per cell basis.

The final piece of information necessary for the calculation is porosity. If the particular cell is part of an unconfined aquifer then it is also necessary to get the computed head for the cell as the computed head is most likely below the top elevation of the cell. For the I and J directions it is necessary to use the top and bottom elevations that are specified in MODFLOW's discretization package. Next, the saturated area is calculated in the I, J, and K directions. If a particular cell contains a boundary condition that is withdrawing water (such as a well) then the flow in the I, J, and K directions is decreased based on the amount of flow leaving the cell through the boundary condition. First, the amount of flow in the I, J, and K directions for a given cell is read from the CCF file. Several pieces of information are required to compute groundwater flow velocity from a MODFLOW model. Beginning with version 8.2, GMS can now generate velocity vectors using information from the MODFLOW cell-to-cell flow (ccf) file.

Mtasa velocity with vectors