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.

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.

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:

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

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

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.

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

See also

• Viscosity
• Fluid Dynamics
• Stokes Flow, in which the viscous forces are much greater than inertial forces.
• Couette Flow
• Source code for an animation demonstrating this principle is available as the Euler2D module of the XScreenSaver collection for Unix and Mac OS X.