# Difference between inviscid and viscous flow

In my lecture notes, I have a load of examples and I want to sort out which egs are viscous flow and which are inviscid flow. It is not always said if the flow is viscous or inviscid. Please can someone tell me what other things determines the difference rather than just the words.

I do know that a gas bubble inviscid flow since there is no viscosity but gas isn't even a fluid which confuses me.

Quite simply, a viscous flow is a flow where viscosity is important, while an inviscid flow is a flow where viscosity is not important.

Gases and liquids alike are considered fluids and any fluid has a viscosity. So a gas bubble surely has a viscosity, albeit relatively low compared to some liquids; liquids are generally more viscous by a factor of 1000. Especially if the gas bubble is moving in a more viscous liquid, generally we must consider the viscosity of the liquid, but may neglect the viscosity of the bubble. The result of this is that no velocity gradients are present inside the bubble.

Determining if a flow is (in)viscid in my opinion is best characterized through the Reynolds number, $\mathrm{Re}$. If $\mathrm{Re}\ll1$, the flow may be considered viscous, i.e. Stokes flow. If $\mathrm{Re}\gg1$, the viscous forces may be negligble compared to inertial forces, much like in turbulence. Note that for $\mathrm{Re}\gg1$, if there are any boundaries in the flow, near any of those boundaries a viscous boundary layer may be formed, which is considered a viscous flow. So in reality, inviscid flow doesn't exist but is a useful model for certain applications.

In fluid mechanics, a gas (like air) is considered a fluid and operates under the mathematical formulae developed in this field. I believe the very essence of viscosity is displayed in the deformation characteristics of a fluid with regard to shear stresses. For example, the shear stress for a Newtonian fluid with respect to a flat plate is given by Newton's formula:

$$\tau = \mu\frac{\partial u}{\partial y}$$

Where $$\mu$$ is the dynamic viscosity and $$\partial u/\partial y$$ is the local shear velocity.

However, a lot of fluids do not follow this formula, and are called Non-Newtonian fluids. They follow equations that are mathematically similar, but with some variations.

Essentially when it comes down to solving physics problems in terms of engineering, you should know the degree of effects of certain phenomena. For example, in airplane wings, lift occurs due to the presence of viscosity; however, in terms of calculations, we tend to neglect freestream viscous effects at Mach numbers below 0.3 because Bernoulli's principle can then be applied, which seems to provide answers with enough accuracy.

However, when it comes to analyzing things like skin-friction drag across the wing, we must take into account the viscous effects because they play a huge role in the flow characteristics across the surface.

So, when it comes to problem-solving, I believe you should check the flow parameters and boundary conditions (Reynolds number $$Re$$, Mach number $$M$$, etc.) of the system/control volume to check if viscous effects will require consideration in the calculations. A little research into viscosity of different kinds of fluids and their mathematical development (such as the formula for the Newtonian fluid above) will come a long way as you develop the ability to decide what approximations suit which conditions.