Inviscid flow

An inviscid flow is the flow of an ideal fluid that is assumed to have no viscosity. In fluid dynamics there are problems that are easily solved by using the simplifying assumption of an 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 the 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.

The Euler equation governing inviscid flow is:

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

which is admittedly Newton's second law applied on a flowing infinitesimal volume element. In the steady-state case, combined with the continuity equation of mass, this can be solved using potential flow theory.

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.

See also

• Viscosity
• Fluid dynamics
• Potential flow, a special case of inviscid flow
• Stokes flow, in which the viscous forces are much greater than inertial forces.
• Couette flow

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 0-12-178253-0, ISBN 978-0-12-178253-5