What does the terms in Navier-Stokes equation mean?
The Navier-Stokes equation, in modern notation, is. , where u is the fluid velocity vector, P is the fluid pressure, ρ is the fluid density, υ is the kinematic viscosity, and ∇2 is the Laplacian operator (see Laplace’s equation).
What are the assumptions of the Navier-Stokes equations?
The Navier–Stokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum, in other words is not made up of discrete particles but rather a continuous substance.
What are the basic 3 Conservation of laws in which Navier-Stokes equation is based that relate to CFD?
The Navier-Stokes equations consists of a time-dependent continuity equation for conservation of mass, three time-dependent conservation of momentum equations and a time-dependent conservation of energy equation.
What’s the hardest math problem in the world?
These Are the 10 Toughest Math Problems Ever Solved
- The Collatz Conjecture. Dave Linkletter.
- Goldbach’s Conjecture Creative Commons.
- The Twin Prime Conjecture.
- The Riemann Hypothesis.
- The Birch and Swinnerton-Dyer Conjecture.
- The Kissing Number Problem.
- The Unknotting Problem.
- The Large Cardinal Project.
How is the stress tensor used in the Navier Stokes equations?
The Stress Tensor for a Fluid and the Navier Stokes Equations 3.1 Putting the stress tensor in diagonal form A key step in formulating the equations of motion for a fluid requires specifying the stress tensor in terms of the properties of the flow, in particular the velocity field, so that the
What are the two terms in the Navier Stokes equation?
The stress tensor σ denoted above is often divided into two terms of interest in the general form of the Navier-Stokes equation. The two terms are the volumetric stress tensor, which tends to change the volume of the body, and the stress deviator tensor]
How is the stress tensor related to the equations of motion?
A key step in formulating the equations of motion for a fluid requires specifying the stress tensor in terms of the properties of the flow (and in particular the velocity field) so that the theory becomes closed. That is, the number of variables is reduced to the number of governing equations.
Which is the correct formula for the tensor?
The tensor can be represented as σ = (σxx τxy τxz τyx σyy τyz τzx τzy σzz). A tensor is a generalization of the concept of the higher-order quantity; a vector is represented as a first order tensor, a matrix as a second order tensor, a 3D matrix is a third order tensor, and so on.