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direction: unitless impact parameter meter (m) differential (e.g. ) varied depending on context differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S: square meter (m 2) differential element of volume V enclosed by surface S
Velocity is the speed in combination with the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it.
Diffusion is of fundamental importance in many disciplines of physics, chemistry, and biology. Some example applications of diffusion: Sintering to produce solid materials (powder metallurgy, production of ceramics) Chemical reactor design; Catalyst design in chemical industry; Steel can be diffused (e.g., with carbon or nitrogen) to modify its ...
The two blue vectors represent velocities after the collision and add vectorially to get the initial (red) velocity. Real motion has both direction and velocity and must be represented by a vector. In a coordinate system with x, y, z axes, velocity has components v x in the x-direction, v y in the y-direction, v z in the z-direction.
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.
For example, for a macroscopic scalar field φ(x, t) and a macroscopic vector field A(x, t) the definition becomes: +, +. In the scalar case ∇ φ is simply the gradient of a scalar, while ∇ A is the covariant derivative of the macroscopic vector (which can also be thought of as the Jacobian matrix of A as a function of x ).
The x direction may be chosen to point down the ramp in an inclined plane problem, for example. In that case the friction force only has an x component, and the normal force only has a y component. The force of gravity would then have components in both the x and y directions: mg sin( θ ) in the x and mg cos( θ ) in the y , where θ is the ...
is the partial derivative in the direction x of the flow velocity component v that is oriented along the direction y. We can now generalize to the case of an incompressible flow with a general direction in the 3D space, the above constitutive equation becomes τ i j = μ ( ∂ v i ∂ x j + ∂ v j ∂ x i ) {\displaystyle \tau _{ij}=\mu \left ...