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Math Help - fluid dynamics

  1. #1
    Junior Member
    Joined
    Oct 2008
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    57

    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.
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  2. #2
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
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    539
    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

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