For situations where the viscous terms in the Navier-Stokes equations were dropped because the flow was ideal (irrotational and of constant density) or the effects of viscosity were small, the underlying assumptions were either that

• viscous forces and rotational flow were spatially confined to a small portion of the flow domain (thin boundary layers near solid surfaces)
• fluid particle accelerations caused by fluid inertia ~\(U²/L\) were much larger than those caused by viscosity ~\(μU/ρL²\), where \(U\) is a characteristic velocity, \(L\) is a characteristic length, \(ρ\) is the fluid’s density, and \(μ\) is the fluid’s viscosity

However, for low values of the Reynolds number, the entire flow may be influenced by viscosity, and inviscid flow theory is no longer even approximately correct