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Inviscid flow is simply the flow of an inviscid fluid, in which the viscosity of the fluid is equal to zero. (BSL) The Reynolds number of inviscid flow approaches infinity, as the viscosity approaches zero. (BSL)   Though only a small number of true inviscid fluids have been discovered, known as superfluids, inviscid flow has great significance in fluid mechanics (BSL).  When viscous forces are neglected, such as the case of inviscid flow, the Navier-Stokes equation can be simplified to a form known as the Euler equation (BSL). This simplified equation is applicable to inviscid flow as well as flow with low viscosity and a Reynolds number much greater than one (BSL).   Using the Euler equation, many fluid mechanics problems involving low viscosity are easily solved, however, the assumed negligible viscosity is no longer valid in the region of fluid near a solid boundary (BSL).

Reynolds Number

The Reynolds number is a dimensionless group, having no distinct units, that is commonly used in fluid mechanics (BSL).  Originally described by Gabriel Stokes in 1850, it became popularized by Osborne Reynolds, who the concept was specifically named after in 1908 by Arnold Sommerfeld (History, Reynolds, Stokes).  The Reynolds number is calculated as:

Where:

L is a characteristic length (m)

Rho is the density (kg/m^3)

Mew is the viscosity (kg/(s*m))

V is the velocity (m/s)

It represents the ratio of inertial forces to viscous forces in a fluid, and is useful in determining the relative importance of viscosity (BSL).  In inviscid flow, since the viscous forces are zero, the Reynolds number approaches infinity (BSL).  In low viscosity fluids, the Reynolds number is much greater than one (BSL).

Euler equations

In a 1757 publication, Leonhard Euler described a set of equations governing inviscid flow (Euler).  Later in 1845, Gabriel Stokes published another important set of equations, today known as the Navier-Stokes equations (BSL).  Navier developed the equations first using molecular theory, and they were further confirmed by Stokes using continuum theory (BSL).  The Navier Stokes equations describe the motion of fluids(BSL):

Where:

T is time (s)

Rho is density (kg/m^3)

P is pressure (kg/(m*s^2))

V is the velocity (m/s)

When the flow is inviscid, or the viscosity can be assumed to be negligible, the Navier Stokes equation simplifies to the Euler equation: (BSL)

This simplification is much easier to solve, and can apply to many types of low viscosity flows (BSL). Some examples include flow around an airplane wing, upstream flow around bridge supports in a river, and ocean currents (BSL).  It is important to note, that negligible viscosity can no longer be assumed near solid boundaries, such as the case of the airplane wing (BSL). YADADADA talk about viscous sublayer

Air plane wing, ocean etc…

Viscous Sublayer

Applications

Two major applications of inviscid fluid, He 3 and He 4, are cooling of larger superconductor systems or RF cavities for high energy physics accelerators and instruments involving space systems such as infrared astronomy.

Spectrometers are kept at a very low temperature using He as the coolant. This allows for minimal background flux in far-infrared readings. Some of the designs for the spectrometers may be simple, but even the frame is at its warmest less than 20 Kelvin.  These devices are not commonly used as it is very expensive to use liquid helium over other coolants.

An industry that also relies on this fluid is the rocket propulsion industry. These companies includes NASA, SpaceX and other companies that launch rockets. The primary use is cooling oxygen and hydrogen to be used as liquid fuel.

Superfluid He3 and He4 have a very high thermal conductivity which makes it very useful for cooling superconductors. Superconductors such as the ones used at the LHC (Large Hadron Collidor) are cooled to temperatures approximately 1.9 Kelvin. This temperature allows the niobium-titanium magnets to reach a superconductor state. Without the use of the superfluid Helium this temperature would not be possible. Cooling to these temperatures, with this fluid, is a very expensive system and there are few compared to other cooling systems.

Another application of the superfluid He is its uses in understanding quantum mechanics. Using lasers to look at small droplets allows scientists to view behavior’s that may not normally be viewable. This is due to all the helium in each droplet being at the same quantum state. This application does not have any practical uses by itself, but it gives a look into better understand quantum mechanics which will have later applications.

Inviscid Flow describes flow that is at zero viscosity. Assuming a viscosity of zero allows for the calculation and examination of flow through and around objects. Inviscid flow calculations are governed by Euler's equation. Currently using the assumption of an Inviscid Fluid is used to simplify and model complex problems. Some inviscid fluids exhist but exhist under extreme conditions such as near absolute zero temperature which is obtained only in labs. Flow without viscosity present, inviscid flow, is also known as superfluidity. In 1938 the first and only example of an elemental material with inviscid flow was discovered as He at 2.18 Kelvin.