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kinematic viscosity ν of the fluid, size of the body, expressed in terms of its wetted area A, and; drag force F d. Using the algorithm of the Buckingham π theorem, these five variables can be reduced to two dimensionless groups: drag coefficient c d and; Reynolds number Re.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Kinematics is often described as applied geometry, where the movement of a mechanical system is described using the rigid transformations of Euclidean geometry. The coordinates of points in a plane are two-dimensional vectors in R 2 (two dimensional space).
The definitions of the Kolmogorov microscales can be obtained using this idea and dimensional analysis. Since the dimension of kinematic viscosity is length 2 /time, and the dimension of the energy dissipation rate per unit mass is length 2 /time 3 , the only combination that has the dimension of time is τ η = ν ε {\displaystyle \tau _{\eta ...
The term 1 / ρ 2 ∇ρ × ∇p is the baroclinic term. It accounts for the changes in the vorticity due to the intersection of density and pressure surfaces. The term ∇ × ( ∇ ∙ τ / ρ ), accounts for the diffusion of vorticity due to the viscous effects. The term ∇ × B provides for changes due to external body forces.
From this point of view the kinematics equations can be used in two different ways. The first called forward kinematics uses specified values for the joint parameters to compute the end-effector position and orientation. The second called inverse kinematics uses the position and orientation of the end-effector to compute the joint parameters ...
In multi-dimensional Cartesian coordinate systems, acceleration is broken up into components that correspond with each dimensional axis of the coordinate system. In a two-dimensional system, where there is an x-axis and a y-axis, corresponding acceleration components are defined as [ 12 ] a x = d v x / d t = d 2 x / d t 2 , {\displaystyle a_{x ...
The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, [1] is defined for incompressible (divergence-free), two-dimensional flows. The Stokes stream function , named after George Gabriel Stokes , [ 2 ] is defined for incompressible, three-dimensional flows with axisymmetry .
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