Sunday, December 02, 2012

Saturday, December 01, 2012

Islamic Cover Photos





"There Is No God But Allah And Mohammad (P.B.U.H) Is The Last Messenger Of Allah"



Hazrat Mohammad (S.A.W) Ne Farmaya.
Jumma Ke Din Tum Muj Par Kasrat Se Darood Bejo Kyunki Tumhara Darood Mujhe Paish Kiya Jata Hai
Aur Allah Ne Zameen Par Haram Kar Diya Hai Ki Woh Anbiya Ke Jismoo Ko Khaye.




Wednesday, November 28, 2012

Navier–Stokes equations

General form of the equation

The general form of the Navier–Stokes equations for the conservation of momentum is:
\rho\frac{D\mathbf{v}}{D t} = \nabla\cdot\mathbb{P} + \rho\mathbf{f}
where
  • \rho\ is the fluid density,
  • \frac{D}{D t} is the substantive derivatives (also called the material derivative).
  • \mathbf{v} is the velocity vector,
  • \mathbf{f} is the body force vector, and
  • \mathbb{P} is a tensor that represents the surface forces applied on a fluid particle (the stress tensor).
Unless the fluid is made up of spinning degrees of freedom like vortices, \mathbb{P} is a symmetric tensor. In general, (in three dimensions) \mathbb{P} has the form:
\mathbb{P} = \begin{pmatrix}
\sigma_{xx} &  \tau_{xy} & \tau_{xz} \\
\tau_{yx} &  \sigma_{yy} & \tau_{yz} \\
\tau_{zx} &  \tau_{zy} & \sigma_{zz}
\end{pmatrix}
where
  • \sigma\ are normal stresses,
  • \tau\ are tangential stresses (shear stresses).
The above is actually a set of three equations, one per dimension. By themselves, these aren't sufficient to produce a solution. However, adding conservation of mass and appropriate boundary conditions to the system of equations produces a solvable set of equations.
.....