Fluids Lecture 02

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  • Stresses in a fluid consist of body (long range) and surface (short range) forces.
  • The stress in a fluid is described by a symmetric tensor of second order there are normal stresses and shear stresses, only the isotropic part survives in a fluid in equilibrium
  • in hydrostatic equilibrium every fluid element must be in equilibrium

Dynamics of Ideal Fluids

The continuity equation reads:


Euler’s Equation:

where is a velocity field. We can use the vector identity:

where describes vorticity, and describes the energy of the field. Vorticity is a uniform shear flow, which is to say that , or that in some direction, the velocity of the fluid tangential to that direction grows linearly with distance.

We may relate circulation and vorticity by stokes theorum:

Vorticity is the circulation per unit area perpendicular to the surface. It is a measure of local rotation, and has nothing to do with global rotation. An individual speck of dust in a liquid spins with angular velocity .