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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]
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Reynolds number
The assumption of inviscid flow is generally valid where viscous forces are small in comparison to inertial forces. Such flow situations can be identified as flows with a Reynolds number much greater than one. 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:
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-field the effect of viscosity may be very small, a number of factors make the assumption of negligible viscosity invalid in many cases. Viscosity cannot be neglected near fluid boundaries because of the presence of 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 increasingly 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
See also
- Viscosity
- Fluid dynamics
- Stokes flow, in which the viscous forces are much greater than inertial forces.
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