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


Fig.1 Effect of shear stress on a solid and fluid [3]

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

Newtoneq fig

Fig. 2 velocity profile in two plate [2]

Viscosity graph

Fig.3 viscosity in fluid [2]


Fig.4 Viscosities in various fluid [2]


Newton's Observation from the Two Parallel Plate Experiment Edit

  1. 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
  2. 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.
    • FA
  3. Keeping the velocity U and the distance Y constant, the force required is inversely proportional to the distance between the plates.
    • F ∞ 1/ [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:
Newton eq3 
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.