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.^[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 . 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 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

See also

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

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