The undestanding and knowledge of the fluid are essential for the analysis and design of a aircraft because aircraft move through fluids. This page introduces the fluid - What is the fluid and what are its properties?

Written by Sang-in Park

## Definition of FluidEdit

A** fluid **is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude. [1]

All gases and all liquids are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas, and to some extent, plastic solids.[4]

- Gas and Liquid

- The molecules of a gas are much farther apart than those of a liquid. Hence a gas is very compressible and when all external pressure is removed, it tends to expand indefinitely. A gas, therefore, is in equilibrium only when it is completely enclosed. A liquid is relatively incompressible, and if all pressure is removed the cohesion between molecules holds them together, so that the liquid does not expand indefinitely. Therefore a liquid may have a free surface. [2]

- Fluid as a continuum [5]

Continuum | Solid | Elastic solid |

Plastic solid | ||

Fluid | Newtonian fluid | |

Non-Newtonian fluid |

## Distinction Between a Solid and a FluidEdit

### In Macroscopic ViewEdit

The fluid deforms continuously** **under the influence of a shear force - i.e., the fluid particles continuously change their position relative to one another when subjected to a shear force. On the other hand, a solid may resist a shear force when at rest and if it deforms, it does not continue to deform indefinitely. Fig.1 shows the behavior of a solid and a fluid under influence of shear force. In case of a solid, the deformation is small and the angular deformation is not a continuous function of time, but in the case of a fluid the deformation is large and the angular deformation is continuous function of time. [3]

### In Microscopic ViewEdit

The molecules of a solid are usually much closer together than those of a fluid. The attractive forces between the molecules is inversely proportional to the square of the distance between them. Since the molecules of a solid are located close to one another, the forces are large and, therefore, they offer a great resistance to any external force. In a fluid, the force of attraction between molecules is only large enough to hold them together to give a definite shape (liquid) or is negligible (gas). Therefore, when an external force is applied to a fluid, its molecules get rearranged continuously until the force is removed and do not go back to their original positions after the force is removed.[3]

- Example

- A lump of tar may look like a solid. When placed on the ground, it does not spread quickly as water does. However, it does start to deform as soon as placed on the ground. After sufficient time, perhaps a few days, it will spread just like any other fluid. [3]

## Classification of Fluid Edit

### Compressible vs Incompressible Fluid Edit

The specific weight is equal to the product of fluid density and acceleration of gravity. Thus changes in specific weight are caused by a change of density or acceleration of gravity. Since in most engineering applications the variation of gravity is negligible, the density is a major factor. The density of a compressible fluid can change with changes in pressure or temperature. However, the density of an incompressible fluid is constant. [2]

### Ideal(Inviscid) vs Real(Viscous) FluidEdit

The ideal fluid is a fluid in which there is no friction; it is inviscid (its viscosity is zero). Thus the internal forces at any section within it are normal to the section, even during motion. The **real** fluid contains tangential or shearing forces, which always come into being whenever motion relative to a body takes place, thus giving rise to fluid, because these forces oppose the motion of one particle past another. This friction gives rise to a fluid property called viscosity. [2]

### Newtonian vs Non-Newtonian FluidEdit

Sir Isaac Newton showed how stress and the rate of strain are very close to **linearly** related for many familiar fluids, such as water and air. These Newtonian fluids are modeled by a coefficient called viscosity, which depends on the specific fluid. However, some of the other materials, such as emulsions and slurries and some visco-elastic materials (e.g. blood, some polymers), have more complicated non-Newtonian stress-strain behaviors. [6]

## Newton's Law of ViscosityEdit

### Newton's Observation from the Two Parallel Plate Experiment Edit

- Keeping the area A and the distance
*Y*constant, the velocity*U*attained by the plate is directly proportional to the applied force*F.**F*∞*U*

- Keeping the velocity
*U*and the distance*Y*constant, the force required to move the plate with a velocity*U*, is directly proportional to the area of plate.*F*∞*A*

- Keeping the velocity
*U*and the distance*Y*constant, the force required is inversely proportional to the distance between the plates.*F*∞ 1/*Y*[2]

### Newton's Equation of Viscosity Edit

- In the case of two parallel plates, the lower surface is assumed to be stationary while the upper surface is moved parallel to the it with velocity
*U*. If the separation distance*Y*is not too great, the velocity profile is will be linear as Fig. 2. - This relationship can be expressed by following equation:
- In above equation, the constant is a measure of internal fluid resistance to relative motion between layers. This constant is called fluid
**viscosity**. The viscosity is generated by the frictional forces in the flowing fluid resulting from the cohesion and momentum interchange between molecules. Thus, it is dependent on temperature. As Fig. 4 the viscosities of liquids decrease as the temperature increases while the viscosities of all gases increase. [2]

### Non-Newtonian FluidEdit

- For most fluids, viscosity is independent of the velocity gradient; hence the relationship between shear stress and velocity gradient is linear. Such a fluid is called a
*Newtonian fluid*. However, there are fluids that are not independent of velocity gradient and they are called*Non-Newtonian*fluids. Fig. 3 shows the difference between Newtonian and Non-Newtonian fluid. [2-3]

## Reference Edit

[1]* Fundamentals of Fluid Mechanics*, Bruce R. Munson. Donald F. Young and Theodore H. Okiishi, 5th edition, John Wiley & sons.

[2]* Fluid Mechanics With Engineering Application*, Joseph B. Franzini and E. john Finnemore, 9th edition, McGraw-Hill.

[3]* Fluid Mechanics*, Irfan A. Khan, 1st edition, Holt, Rinehart and Winston.

[4] http://www.absoluteastronomy.com/topics/Fluid