# Math Help - fluid dynamics

1. ## fluid dynamics

any help would be much appreciated.

consider an inviscid fluid with the velocity field:

1. u(x,y,x,t)=(1,z,y)

2. u(x,y,z,t)=(0,0,w) x (x,y,z)

Find the pressure of the fluid as a function of the density p and the gravitational acceleration g in each case, if pressure at the origin is Po.

2. You need the Eulerian equation for ideal fluid:
$\boxed{\displaystyle{\rho\frac{d\bold{v}}{dt} = \bold{f} - \nabla p}}$
,where $\rho$ is the fluid density, $\bold{f}$ is the volume density of mass forces( $\bold{f} = \rho\bold{g}$ in case of gravity), $\nabla p$ is the pressure gradient.

Other forms: (Refer Wikipedia)
$\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho\bold u)=0$

$\frac{\partial\rho{\bold u}}{\partial t}+ \nabla\cdot(\bold u\otimes(\rho \bold \bold u))+\nabla p=0$
$\frac{\partial E}{\partial t}+\nabla\cdot(\bold u(E+p))=0$