Fluid Mechanics

What is Fluid Mechanics?

Fluid mechanics, the branch of science that deals with the study of fluids (liquids and gases) in a state of rest or motion is an important subject of Civil, Mechanical and Chemical Engineering. Its various branches are fluid statics, fluid kinematics and fluid dynamics.
A susbstance that flows is called as fluid. All liquid and gaseous substances are considered to be fluids. Water, oil, and others are very important in our day-to-day life as they are used for various applications. For instance water is used for generation of electricity in hydroelectric power plants and thermal power plants, water is also used as the coolant in nuclear power plants, oil is used for the lubrication of automobiles etc.
Fluid Mechanics is the branch of science that studies the behavior of fluids when they are in state of motion or rest. Whether the fluid is at rest or motion, it is subjected to different forces and different climatic conditions and it behaves in these conditions as per its physical properties. Fluid mechanics deals with three aspects of the fluid: static, kinematics, and dynamics aspects:

1) Fluid statics: The fluid which is in state of rest is called as static fluid and its study is called as fluid statics.

2) Fluid kinematics: The fluid which is in state of motion is called as moving fluid. The study of moving fluid without considering the effect of external pressures is called as fluid kinematics.

3) Fluid dynamics: The branch of science which studies the effect of all pressures including the external pressures on the moving fluid is called as fluid dynamics.

Why Study Fluid Mechanics

What is the necessity of stuying fluids as an aspect of engineering? Fluids are already an integral part of our day-to-day life. Engineering allows us to explore the potential of fluids for a number of new applications and various functions. Some of these include:

1) There are number of fluids that when burnt, produce lots of heat, which can be used for various applications. Examples of these fluids includes petrol and diesel for vehicles.

2) There are some fluids like oil that have a tendency to exert very high pressure or force. These fluids can be used for lifting various heavy loads. The fluids used in hydraulic machines and hydraulic lifters are an example.

3) Some fluids have excellent flow properties which can be used for the lubrication of various machines.

4) Fluids like water posses kinetic and potential energy, which is used for generation of electricity as in hydroelectric power plants.
Fluid mechanics helps us understand the behavior of fluid under various forces and at different atmospheric conditions, and to select the proper fluid for various applications.
This field is studied in detail within Civil Engineering and also to great extent in Mechanical Engineering and Chemical Engineering. It is in these branches of engineering where there is maximum use of the fluids.

Common Applications of Fluids

1) Hydroelectric Power Plants
In hydroelectric power plants, water is used to generate electricity on a large-scale basis. Water stored in the dam possesses potential energy, which is converted into the electrical energy in the power generation unit of the plant. Hydroelectric power plants are one of the major suppliers of power throughout the world. In some countries power requirements are fulfilled entirely by these plants.

2) Hydraulic machines
Machines that operate on a fluid like water and oil are called hydraulic machines. The fluid as the capacity to lift heavy loads and exert extremely high pressures. Some hydraulic machines are used to perform various machining operations. In most of these machines, oil is used as the fluid. The oil is passed through the hydraulic motor which transfers large amounts of energy to the fluid. This high energy fluid enters the piston and cylinder arrangement where it can be used to lift heavy loads or apply large forces.

3) Automobiles
No automobile can run without fluid. Fluids perform three crucial operations in automobiles: generation of power, lubrication, and cooling of the engine. Petrol or diesel generates power on combustion in the engine. This is commonly referred to as fuel. Oil is used for the lubrication of the engine and the gearbox and also various other moving parts of the vehicle. In larger automobiles like cars, busses and trucks, water is used for cooling the engine.

4) Refrigerators and Air Conditioners
This is another important area where fluids play a crucial role. In refrigerators and air-conditioners, the fluids are known as refrigerants. The refrigerant absorbs the heat from whatever is being kept in the chiller or evaporator, which is at a low temperature, and delivers that heat to the atmosphere, which is at a high temperature. In air conditioners, the refrigerant absorbs room heat and throws it in to the atmosphere, thereby keeping the room cool. The entire operation of refrigerators and air-conditioners depends on the use of a refrigerant.

5) Thermal Power Plants
In thermal power plants, water is used as the working fluid. After getting heated in a boiler, water is converted into superheated steam which is passes through the blades of turbines, thus rotating them. The shaft of the turbine rotates in the generator, where electricity is produced. Thermal power plants are one of the major suppliers of power in various parts of the world, and water working as the fluid is their most important component.

6) Nuclear power plants
Water is again a crucial power plant component. Here it is both the working fluid and a coolant. In some nuclear power plants, heat produced within the nuclear reactor is used to directly heat water, which is converted into steam. This steam is passed through the turbines similar to thermal power plants, rotating turbine blades to generate power. This is an application of water as the working fluid.
In other nuclear power plants, the heat from nuclear reactors is not used to generate steam directly. Heat is first used to heat the water, which acts as the coolant. This coolant then transfers the heat to a secondary coolant or the working fluid, which is again water and it is passed through the turbine to generate electricity.

7) Fluids as a Renewable Energy Source
There are number of fluids that are being used as a renewable energy source. Air or wind is one of the most popular sources of renewable energy. Wind is used for generation of electricity on a small as well as large scale basis. Water is used in tidal power plants to generate electricity on a small scale basis. Ocean waves are used to rotate turbine blades within the power generation unit. Biodiesel, a type of the vegetable oil, is used as a fuel for vehicles along with traditional diesel.

8) Operating Various Instruments
Compressed air is used for the operation of various types of instruments and automatic valves. These valves can be activated and deactivated by applying the pressure of compressed air. The pneumatic tools which work on compressed air are used for various applications like grinding, screwing and unscrewing various machinery parts, etc.

9) Heat Engines
In previous heat engine designs, air was used as a fluid to generate power in automobiles. Earlier it was thought that the efficiency of an engine is dependent on the type of fluid used, but later it was shown by Sadi Carnot, that the efficiency of an engine is not dependent on the type of the fluid, but rather, the temperature of the fluid.
Fluids are used in a wide range of applications, often playing a vital role, without which, these applications will just cease to exist. The important thing to note is that most of the crucial applications of fluids are for generation of electricity or power. In hydroelectric power plants and automobiles, fluids are directly used to generate power or electricity. In thermal and nuclear power plants, fluids are indirectly used for generation of power, and still they are the dominant parts of these applications. It is not an overstatement to say that without fluids, the progress of the human race would stop.


The Types of Fluids


The viscosity is a very important property of the fluid. The viscosity of the fluid at various conditions decides whether the fluid will be suitable for operating at certain temperature operating conditions or not. The viscosity of the liquid fluid reduces as their temperature increases, hence at higher temperatures the viscosity of the lubricating fluid becomes very important especially if it is used for the lubrication of the engines and compressors since lubricating properties of the fluid reduce as its viscosity reduces.
Based on how the property of viscosity of the fluid changes in various fluids, they are classified into five types, these are: ideal fluid, real fluid, Newtonian fluid, non-Newtonian fluid, and ideal plastic fluid. These have been described in more details as below (see the fig below):

1) Ideal fluids:
The fluid which is incompressible and has no viscosity is known as the ideal fluid. Since the ideal fluid has no viscosity there won’t be any effect of temperature on it. However, the ideal fluid is only an imaginary fluid, because all the fluids have viscosity and there is no fluid that doesn’t have viscosity (see the fig below).

2) Real fluid:
The fluid which has certain values of the viscosity is called as the real fluid. In practice all the fluids are real fluids because all of them have viscosity, small or high. For the real fluids which are liquids the viscosity reduces as the temperature increases and for the real fluids which are gases, the viscosity increases as the temperature increases (see the fig below).

3) Newtonian fluid:
The real fluid that obeys that Newton’s law of viscosity is called as Newtonian fluid. As per the Newton’s law of viscosity the shear stress between various layers of the fluid is proportional to the rate of shear strain or the velocity gradient (see the fig below).

4) Non-Newtonian fluids:
 The real fluids that do not obey the Newton’s law of viscosity are called as non-Newtonian fluids. In such fluids the shear stress between the various layers of fluid is not proportional to the rate of shear strain or the velocity gradient (see the fig below).

5) Ideal plastic fluid:
The fluid in which the shear stress is more than the yield value and shear stress is proportional to the rate of shear strain or velocity gradient is known as ideal plastic fluid (see fig below).

Properties of the Fluid:
Some of the important properties of the fluid are: density or mass density of the fluid, specific weight or weight density of the fluid, specific volume of the fluid, specific gravity or relative density of the fluid, viscosity of the fluid and others. All these are discussed in this two-part series

Introduction

Fluid is the substance that has tendency to flow; it can be any liquid or gas. Fluid mechanics is the branch of science that deals with the study of behavior of fluids whether they are at rest or are moving.

Here are some important properties of fluids:

1) Density or Mass Density of fluid

Mass density or simply density of the fluid is defined as the ratio of the mass of fluid to its volume. Density of the fluid can also be defined as the mass per unit volume of the fluid. Density of the fluid is denoted by the symbol ρ (rho).

2) Specific Weight or Weight Density of the fluid

The specific weight or the weight density of the fluid is defined as the ratio of the weight of the fluid to the volume of the fluid. The weight density of the fluid is also defined as the weight of the fluid per unit volume of the fluid. Weight density of the fluid is denoted by the symbol w.
In SI system the unit of measurement of the weight of the fluid is N (Newton) and that of volume is cubic meter m3, hence the unit of measurement of specific weight is N/m3 (Newton per meter cube).

The value of the specific density of water in SI unit is 9.81 x 1000 Newton/m3.

3) Specific Volume of the fluid

The specific volume of the fluid is defined as the volume of the fluid occupied by the unit mass of the fluid. Specific volume can also be defined as the volume per unit mass of the fluid.

Specific volume of the fluid is reciprocal of the density of the fluid so its unit of measurement in SI system is m3/kg. This term is important for the gases.

4) Specific gravity of the fluid

Specific gravity of the fluid is defined as the ratio of the density of the fluid to the density of the standard fluid. For the liquids the standard fluid is water and for the gases the standard fluid is air. Specific gravity is also called as relative density. Since specific density is the ration of the two densities, it is a dimensionless quantity and has not unit of measurement. It is denoted by symbol S.

Viscosity of the Fluid

The fluids like water or oil, flow on the surface in the form of layers with the top layer moving at the fastest speed and the bottom layer moving at slow speed. This shows that as we move from the top layer to the bottom layer the speed of the flow of fluid reduces. There is some sort of resistance to the flow of various layers of the fluid, which is offered by the adjoining layers, this property of the fluids is called as viscosity of the fluid.
The viscosity of the fluid is defined as the property of the fluids that offers resistance to the movement of one layer of the fluid over another adjacent layer of the fluid.

In the figure various layers of the liquid are shown. There will be viscous forces between various layers that will resist the movement of the adjoining layers. Let us consider the two layers separated by small distance dy. If the velocity of the lower layer is u, the velocity of the layer just above it will be u+du, where du is the small incremental velocity. This is because the velocity of the upper layer of the fluid is more than the velocity of the lower layers of the fluid.

The SI unit of measurement of viscosity of the fluid is Ns/m2.

What is the Viscosity of the Fluid?


Viscosity is one of the most important properties of the fluid and it has to be considered while selecting the fluid for particular application. This article describes what is viscosity and derives the formula for viscosity from Newton's law of viscosity.
What is Viscosity of the Fluid?


Viscosity is very important property of the fluids. While considering the fluid for various applications it is crucial to consider the viscosity of the fluid. The fluid flows in the form of various layers as shown in figure below. The top layer of the fluid flows at higher speeds, while the layers below it move at slightly lesser speed. Thus the layers of the fluid offer resistance to the flow of the adjoining layers. This property of the fluid is called as the viscosity of the fluid.

Viscosity of the fluid is defined as the property of the fluid that tends to resist the movement of one layer of the fluid over adjacent layer of the fluid.
Derivation of Viscosity Formula from Newton’s Law of Viscosity
In the figure shown above, let us consider two layers separated by small distance dy. Let us suppose that the velocity of the lower layer is u, so the velocity of the upper layer will be u+du, where du is the small incremental velocity. Now, the top layer tends to offer resistance to the flow of bottom layer and bottom layer offers resistance to the flow of top layer.
The resistance to the flow is offered in the form of shear stress. Thus the adjoining layers of the fluid cause shear stress on the adjoining layers. The shear stress among the various layers of the fluid depends on rate of change of the velocity of the fluid with respect to its distance ‘y’ from the lowest layer of the fluid. Shear stress is denoted by τ (tau). This is also called as Newton’s law of viscosity. It states that shear stress between various layers of the fluid is directly proportional to rate of shear strain.
Shear stress τ (tau) is given by: (refer the fig)

Here µ (mu) is called as the coefficient of dynamic viscosity or merely viscosity. The term du/dy is the rate of shear strain or rate of shear deformation or velocity gradient. Thus viscosity is also defined as the shear stress required to produce unit rate of shear strain.

Unit of Measurement of Viscosity
The unit of measurement of viscosity in various systems is given below:
SI system: Newton-sec/square meter or Ns/m2
MKS system: kgf-sec/m2.
CGS system: dyne-sec/square centimeter or dyne.s/cm2. The unit of measurement of viscosity in CGS system is also called as Poise.
Kinematic Viscosity of the Fluid
The ratio between dynamic viscosity of the fluid and the density of the fluid is called as kinematic viscosity of the fluid.

Effect of Temperature on the Viscosity of the Fluid

Understanding the effect of temperature on the viscosity of the fluid is very important. As the temperature of the liquid fluid increases its viscosity decreases. In gases its opposite, the viscosity of the gases fluids increases as the temperature of the gas increases.

Importance of Temperature for the Fluids

The viscosity is the property of the fluid that resists the flow of the fluids like liquids and gases. Understanding the effect of temperature on the viscosity of the fluid is very important. In engines the lubricating oil is heated to very high temperatures due to combustion of the fuel, hence it is vital to know whether the lubricating oil, which is a fluid, will be viscous enough to be able to carry out the lubrication of the moving parts of the engine at those high temperatures.

There are chances that at high temperature the fluid may loose its viscosity, which may render it useless when used in high temperature applications like lubrication of the engine. In some cases the fluid may even start evaporating at high temperature. On the other hand, in the refrigerating compressors there is very low temperature on the suction side of the compressor and high temperature on the discharge side of the compressor. Hence the fluid used as the lubricant in the refrigerating compressors should be able to maintain its viscosity as high as well as low temperatures.

Whenever the fluid is used for any application, operating temperature should be given due considerations. The fluid that can sustain those operating temperatures should only be selected for those applications; otherwise the very purpose of using the fluid will be lost.

Effect of Temperature on Liquid and Gas Fluids

Let us see the effect of temperature on liquids and gases fluid:

1) Liquids: 

As the temperature of the liquid fluid increases its viscosity decreases. In the liquids the cohesive forces between the molecules predominates the molecular momentum transfer between the molecules, mainly because the molecules are closely packed (it is this reason that liquids have lesser volume than gases. The cohesive forces are maximum in solids so the molecules are even more closely packed in them). When the liquid is heated the cohesive forces between the molecules reduce thus the forces of attraction between them reduce, which eventually reduces the viscosity of the liquids.

The liquids used as the lubrication fluid and for number of other applications should be selected properly considering the operating temperatures. At high temperatures the liquids loose viscosity; hence in the engine the fluid used for lubrication should be such that it should be able maintain its viscosity even at the high temperatures. At low temperatures the viscosity of the fluid increases, hence in the refrigerating compressor the fluid selected for the lubrication should be such that it is able to maintain value of viscosity at the lowest and highest temperatures inside the compressor.

For liquids: µ = µo/ (1 + αt + βt2)

Where: µ - Viscosity of the liquid at t degree Celsius n poise

µo – Viscosity of the fluid at 0o Celsius in poise

α, β – are the constants

2) Gases: 

In gases there is opposite phenomenon. The viscosity of the gases increases as the temperature of the gas increases. The reason behind this is again the movement of the molecules and the forces between them. In the gases the cohesive forces between the molecules is lesser, while molecular momentum transfer is high. As the temperature of the gas is increased the molecular momentum transfer rate increases further which increases the viscosity of the gas.

For gases: µ = µo + αt + βt2

Reference:

Book: Fluid Mechanics and Hydraulic Machines by Dr. R. K. Bansal