What is meant by convective derivative?
The convective derivative (also commonly known as the advective derivative, substantive derivative, or the material derivative) is a derivative taken with respect to a coordinate system moving with velocity u, and is often used in fluid mechanics and classical mechanics.
What is substantial time derivative?
Substantial derivative is an important concept in fluid mechanics which describes the change of fluid elements by physical properties such as temperature, density, and velocity components of flowing fluid along its trajectory .
What is the formula of the substantial derivative?
Δf = ∂f ∂t Δt + ∂f ∂x1 Δx1 + ∂f ∂x2 Δx2 + ∂f ∂x3 Δx3 (1.331) Page 3 120 Since the differential df is the limit of Δf as all changes of variable go to zero, we can take the limit of equation 1.331 to obtain df in terms of dx1, dx2, and dx3.
What is meant by the material derivative of a fluid property?
The material derivative computes the time rate of change of any quantity such as temperature or velocity (which gives acceleration) for a portion of a material moving with a velocity, v . If the material is a fluid, then the movement is simply the flow field.
What is convective time derivative?
Clearly, the so-called convective time derivative, , represents the time derivative seen in the local rest frame of the fluid. The continuity equation ( 1.37) can be rewritten in the form
What is the second derivative of time and velocity?
For example, for a changing position , its time derivative is its velocity, and its second derivative with respect to time, , is its acceleration. Even higher derivatives are sometimes also used: the third derivative of position with respect to time is known as the jerk. See motion graphs and derivatives .
What is the use of time derivative in economics?
Use in economics. The growth rate of the money supply is the time derivative of the money supply divided by the money supply itself. Sometimes the time derivative of a flow variable can appear in a model: The growth rate of output is the time derivative of the flow of output divided by output itself.
What is the time derivative of the displacement vector?
The time derivative of the displacement vector is the velocity vector. In general, the derivative of a vector is a vector made up of components each of which is the derivative of the corresponding component of the original vector. Thus, in this case, the velocity vector is: