Question

Discuss the differences between the fluid mechanics and other mechanics from the perspectives of properties, kinematics, and conservation laws.

( 1500-2000 words )

Answer 1

Fluid mechanics :

Fluid Mechanics is the study of fluids at rest (fluid statics) and in motion (fluid dynamics). A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. Whereas a solid can resist an applied force by static deformation.

The following are some of the important basic properties of fluids:

1. Density
2. Viscosity
3. Temperature
4. Pressure
5. Specific Volume
6. Specific Weight
7. Specific Gravity

1. Density:

Density is the mass per unit volume of a fluid. In other words, it is the ratio between mass (m) and volume (V) of a fluid.

Density is denoted by the symbol ‘ρ’. Its unit is kg/m3.

$Density,~rho~=~{Mass}/{Volume}~kg/m^3$

In general, density of a fluid decreases with increase in temperature. It increases with increase in pressure.

The ideal gas equation is given by:

$P~=~(m/V)RT$

The above equation is used to find the density of any fluid, if the pressure (P) and temperature (T) are known.

Note: The density of standard liquid (water) is 1000 kg/m3.

2. Viscosity

Viscosity is the fluid property that determines the amount of resistance of the fluid to shear stress. It is the property of the fluid due to which the fluid offers resistance to flow of one layer of the fluid over another adjacent layer.

In a liquid, viscosity decreases with increase in temperature. In a gas, viscosity increases with increase in temperature.

3. Temperature:

It is the property that determines the degree of hotness or coldness or the level of heat intensity of a fluid. Temperature is measured by using temperature scales.There are 3 commonly used temperature scales. They are

1. Celsius (or centigrade) scale
2. Fahrenheit scale
3. Kelvin scale (or absolute temperature scale)

Kelvin scale is widely used in engineering. This is because, this scale is independent of properties of a substance.

4. Pressure:

Pressure of a fluid is the force per unit area of the fluid. In other words, it is the ratio of force on a fluid to the area of the fluid held perpendicular to the direction of the force.

Pressure is denoted by the letter ‘P’. Its unit is N/m2.

5. Specific Volume:

Specific volume is the volume of a fluid (V) occupied per unit mass (m). It is the reciprocal of density.

Specific volume is denoted by the symbol ‘v’. Its unit is m3/kg.

$Specific~Volume,~v~=~V/m~{m^3}/kg$

6. Specific Weight:

Specific weight is the weight possessed by unit volume of a fluid. It is denoted by ‘w’. Its unit is N/m3.

Specific weight varies from place to place due to the change of acceleration due to gravity (g).

$Specific~weight,w~=~Weight/Volume~N/m^3$

7. Specific Gravity:

Specific gravity is the ratio of specific weight of the given fluid to the specific weight of standard fluid. It is denoted by the letter ‘S’. It has no unit.

$Specific~Gravity,~S~=~{Specific~Weight~of~Given~Fluid}/{Specific~Weight~of~Standard~Fluid}$

Specific gravity may also be defined as the ratio between density of the given fluid to the density of standard fluid.

Fluid kinematics is a term from fluid mechanics, usually referring to a mere mathematical description or specification of a flow field, divorced from any account of the forces and conditions that might actually create such a flow. The term fluids includes liquids or gases, but also may refer to materials that behave with fluid-like properties, including crowds of people or large numbers of grains if those are describable approximately under the continuum hypothesis as used in continuum mechanics.

Three conservation laws are used to solve fluid dynamics problems, and may be written in integral or differential form. The conservation laws may be applied to a region of the flow called a control volume. A control volume is a discrete volume in space through which fluid is assumed to flow.Mass, momentum, and energy are assumed conserved.

Solid mechanics :

Solid mechanics, also known as mechanics ofsolids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.

The mechanical properties of a material are those which affect the mechanical strength and ability of a material to be molded in suitable shape. Some of the typical mechanical properties of a material include:

• Strength
• Toughness
• Hardness
• Hardenability
• Brittleness
• Malleability
• Ductility
• Creep and Slip
• Resilience
• Fatigue

Strength

It is the property of a material which opposes the deformation or breakdown of material in presence of external forces or load. Materials which we finalize for our engineering products, must have suitable mechanical strength to be capable to work under different mechanical forces or loads.

Toughness

It is the ability of a material to absorb the energy and gets plastically deformed without fracturing. Its numerical value is determined by the amount of energy per unit volume. Its unit is Joule/ m3. Value of toughness of a material can be determined by stress-strain characteristics of a material. For good toughness, materials should have good strength as well as ductlity.

For example: brittle materials, having good strength but limited ductility are not tough enough. Conversely, materials having good ductility but low strength are also not tough enough. Therefore, to be tough, a material should be capable to withstand both high stress and strain.

Hardness

It is the ability of a material to resist to permanent shape change due to external stress. There are various measure of hardness – Scratch Hardness, Indentation Hardness and Rebound Hardness.

1. Scratch Hardness
   Scratch Hardness is the ability of materials to the oppose the scratches to outer surface layer due to external force.
2. Indentation Hardness
   It is the ability of materials to oppose the dent due to punch of external hard and sharp objects.
3. Rebound Hardness
   Rebound hardness is also called as dynamic hardness. It is determined by the height of “bounce” of a diamond tipped hammer dropped from a fixed height on the material.

Hardenability

It is the ability of a material to attain the hardness by heat treatment processing. It is determined by the depth up to which the material becomes hard. The SI unit of hardenability is meter (similar to length). Hardenability of material is inversely proportional to the weld-ability of material.

Brittleness

Brittleness of a material indicates that how easily it gets fractured when it is subjected to a force or load. When a brittle material is subjected to a stress it observes very less energy and gets fractures without significant strain. Brittleness is converse to ductility of material. Brittleness of material is temperature dependent. Some metals which are ductile at normal temperature become brittle at low temperature.

Malleability

Malleability is a property of solid materials which indicates that how easily a material gets deformed under compressive stress. Malleability is often categorized by the ability of material to be formed in the form of a thin sheet by hammering or rolling. This mechanical property is an aspect of plasticity of material. Malleability of material is temperature dependent. With rise in temperature, the malleability of material increases.

Ductility

Ductility is a property of a solid material which indicates that how easily a material gets deformed under tensile stress. Ductility is often categorized by the ability of material to get stretched into a wire by pulling or drawing. This mechanical property is also an aspect of plasticity of material and is temperature dependent. With rise in temperature, the ductility of material increases.

Creep and Slip

Creep is the property of a material which indicates the tendency of material to move slowly and deform permanently under the influence of external mechanical stress. It results due to long time exposure to large external mechanical stress with in limit of yielding. Creep is more severe in material that are subjected to heat for long time. Slip in material is a plane with high density of atoms.

Resilience

Resilience is the ability of material to absorb the energy when it is deformed elastically by applying stress and release the energy when stress is removed. Proof resilience is defined as the maximum energy that can be absorbed without permanent deformation. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without permanent deformation. It can be determined by integrating the stress-strain cure from zero to elastic limit. Its unit is joule/m3.

Fatigue

Fatigue is the weakening of material caused by the repeated loading of the material. When a material is subjected to cyclic loading, and loading greater than certain threshold value but much below the strength of material (ultimate tensile strength limit or yield stress limit), microscopic cracks begin to form at grain boundaries and interfaces. Eventually the crack reaches to a critical size. This crack propagates suddenly and the structure gets fractured. The shape of structure affects the fatigue very much. Square holes and sharp corners lead to elevated stresses where the fatigue crack initiates.

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