Physical Properties of Fluids
Introduction: The study of properties of fluids is basic for the understanding of flow or static condition of fluids. The important properties are density, viscosity, surface tension, bulk modulus and vapor pressure. Viscosity causes resistance to flow. Surface tension leads to capillary effects. Bulk modulus is involved in the propagation of disturbances like sound waves in fluids. Vapor pressure can cause flow disturbances due to evaporation at locations of low pressure. It plays an important role in cavitation studies in fluid machinery. In this chapter various properties of fluids are discussed in detail, with stress on their effect on flow. Fairly elaborate treatment is attempted due to their importance in engineering applications. The basic laws used in the discussions are:
(i) Newton’s laws of motion,
(ii) Laws of conservation of mass and energy,
(iii) Laws of Thermodynamics, and
(iv) Newton’s law of viscosity.
A fluid is defined as a material which will continue to deform with the application of shear force however small the force may be
THREE PHASES OF MATTER: Generally matter exists in three phases namely
(i) Solid (ii) Liquid and (iii) Gas (includes vapor).
The last two together are also called by the common term fluids.
In solids atoms/molecules are closely spaced and the attractive (cohesive) forces between atoms/molecules are high. The shape is maintained by the cohesive forces binding the atoms. When an external force is applied on a solid component, slight rearrangement in atomic positions balances the force. Depending upon the nature of force the solid may elongate or shorten or bend. When the applied force is removed the atoms move back to the original position and the former shape is regained. Only when the forces exceed a certain value (yield), a small deformation called plastic deformation will be retained as the atoms are unable to move to their original positions. When the force exceeds a still higher value (ultimate), the cohesive forces are not adequate to resist the applied force and the component will break.
COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS: If the density of a fluid varies significantly due to moderate changes in pressure or temperature, then the fluid is called compressible fluid. Generally gases and vapors under normal conditions can be classified as compressible fluids. In these phases the distance between atoms or molecules is large and cohesive forces are small. So increase in pressure or temperature will change the density by a significant value.
If the change in density of a fluid is small due to changes in temperature and or pressure, then the fluid is called incompressible fluid. All liquids are classified under this category.
CONTINUUM: As gas molecules are far apart from each other and as there is empty space between molecules doubt arises as to whether a gas volume can be considered as a continuous matter like a solid for situations similar to application of forces.
Under normal pressure and temperature levels, gases are considered as a continuum (i.e., as if no empty spaces exist between atoms). The test for continuum is to measure properties like density by sampling at different locations and also reducing the sampling volume to low levels. If the property is constant irrespective of the location and size of sample volume, then the gas body can be considered as a continuum for purposes of mechanics (application of force, consideration of acceleration, velocity etc.) and for the gas volume to be considered as a single body or entity. This is a very important test for the application of all laws of mechanics to a gas volume as a whole. When the pressure is extremely low, and when there are only few molecules in a cubic meter of volume, then the laws of mechanics should be applied to the molecules as entities and not to the gas body as a whole. In this text, only systems satisfying continuum requirements are discussed.
DEFINITION OF SOME COMMON TERMINOLOGY:
Density (mass density):The mass per unit volume is defined as density. The unit used is kg/m3. The measurement is simple in the case of solids and liquids. In the case of gases and vapors it is rather involved. The symbol used is ρ. The characteristic equation for gases provides a means to estimate the density from the measurement of pressure, temperature and volume.
Specific Volume: The volume occupied by unit mass is called the specific volume of the material. The symbol used is v, the unit being m3 /kg. Specific volume is the reciprocal of density.
Weight Density or Specific Weight: The force due to gravity on the mass in unit volume is defined as Weight Density or Specific Weight. The unit used is N/m3. The symbol used is γ. At a location where g is the local acceleration due to gravity,
Specific weight, y= g ρ