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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.¹

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.² 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:

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

$\nabla \cdot \mathbf{u} = 0,$

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.

1 Problems with the inviscid flow model
2 References
- 2.1 Notes
3 See also

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

^ Clancy, L.J., Aerodynamics, p.xviii
^ Kundu, P.K., Cohen, I.M., & Hu, H.H., Fluid Mechanics, Chapter 10, sub-chapter 1

Inviscid flow.html

Contents

Problems with the inviscid flow model

References

Notes

See also