Inviscid flow

In fluid dynamics there are problems that are easily solved by using the simplifying assumption of an ideal fluid that has no viscosity. The flow of a fluid that is assumed to have no viscosity is called inviscid flow. [Clancy, L.J., "Aerodynamics", p.xviii]

The flow of fluids with low values of viscosity agree closely with inviscid flow everywhere except close to the fluid boundary where the boundary layer plays a significant role. [Kundu, P.K., Cohen, I.M., & Hu, H.H., "Fluid Mechanics", Chapter 10, sub-chapter 1] This is generally true where viscous (friction) forces are small in comparison to inertial forces, i.e. a flow with a Reynolds number $mathit\{Re\}\; gg\; 1$. The assumption that viscous forces are negligible can be used to simplify the Navier-Stokes solution to the Euler equations.

In the case of incompressible flow, the Euler equations governing inviscid flow are:

:

:$abla\; cdot\; mathbf\{u\}\; =\; 0,$

which, in the steady-state case, can be solved using potential flow theory. More generally, Bernoulli's principle can be used to analyse certain time-dependent compressible and incompressible flows.

Problems with the inviscid flow model

While throughout much of a flow the effect of viscosity may be small, a number of factors make the assumption of negligible viscosity invalid in many cases. Viscosity often cannot be neglected near boundaries because the no-slip condition can generate a region of large strain rate (a boundary layer) which enhances the effect of even a small amount of viscosity. Turbulence is also observed in some high Reynolds number flows, and is a process through which energy is transferred to decreasingly small scales of motion until it is dissipated by viscosity.

References

* Clancy, L.J. (1975), "Aerodynamics", Pitman Publishing Limited, London. ISBN 0 273 01120 0
* Kundu, P.K., Cohen, I.M., & Hu, H.H. (2004), "Fluid Mechanics", 3rd edition, Academic Press. ISBN 0121782530, 9780121782535

Notes

ee also

*Viscosity
*Fluid dynamics
*Stokes flow, in which the viscous forces are much greater than inertial forces.