Tuesday, May 22, 2012

Applications in Fluid Dynamics


Influid dynamics, complex functions are used to describe potential flow in two dimensions. Fractals.
Certain fractals are plotted in the complex plane, e.g. the Mandelbrot set
Fluid Dynamics and its sub disciplines aerodynamics, hydrodynamics, and hydraulics have a wide range of applications. For example, they are used in calculating forces and moments onaircraft, the mass flow of petroleum through pipelines, and prediction of weather patterns.
The concept of a fluid is surprisingly general. For example, some of the basic mathematical concepts in traffic engineering are derived from considering traffic as a continuous fluids.

Relativity

Inspecialandgeneral relativity, some formulas for the metric onspacetimebecome simpler if one takes the time variable to be imaginary. (This is no longer standard in classical relativity, but isused in an essential wayinquantum field theory.) Complex numbers are essential tospinors, which are a generalization of thetensorsused in relativity.

Applied mathematics

In differential equations, it is common to first find all complex roots r of the characteristic equation of a linear differential equation and then attempt to solve the system in terms of base functions of the form f(t) = ert.

In Electromagnetism:

Instead of taking electrical and magnetic part as a two different real numbers, we can represent it as in one complex number

In Civil and Mechanical Engineering:

The concept of complex geometry and Argand plane is very much useful in constructing buildings and cars. This concept is used in 2-D designing of buildings and cars. It is also very useful in cutting of tools. Another possibility to use complex numbers in simple mechanics might be to use them to represent rotations.

0 comments:

Post a Comment