ME - Mechanical Engineering
Online resource for Mechanical Engineers

The application of First Law of Thermodynamics process led to the establishment of a new property named internal energy (U), the application of the second law to a process leads to the establishment of another new property names as entropy (S).
Entropy is defined as follows
Δ
S
=
Q
T
rev
Change in entropy for an reversible and irreversible cycle by second law of thermodynamics

For a reversible thermodynamic process between two states, from state 1 to state 2 in an open system, the change in entropy is given by


It is found by applying Clausius inequality that for for an irreversible process from state 1 to state 2, the change in entropy is given by

Below tables shows list of 112 Mechanical Inventions arranged in the order of invented year with inventor(s) name and inventor country they belong to.

Mechanical Inventions

If you want us to include any more Mechanical Inventions comment below.
The First Law of Thermodynamics states that energy is neither created nor destroyed, thus the total energy of the universe is a constant. However, energy can certainly be transferred from one form to another form.

The 1st Law of thermodynamics is mathematically stated as follows:
§dQ = §dW

During a thermodynamic cycle, a cyclic process the systems undergoes, the cyclic integral of heat added is equal to integral of work done. the first law equation can also be written in the form,
§(dQ – dW) = 0

Equation dU = dQ - dW is corollary for first law of thermodynamics. It shows that there exists a property internal energy (U) of the system, such that a change in its value is equal to the difference in heat entering and work leaving the system.
Sign convention for heat and work in  first law of thermodynamics is represented in picture below.
Another property named enthalpy (H) can also be defined now as a combination of properties U, p and V.
H = U + pV

For a reversible process, since dW = pdV, the first law of thermodynamics can also be written as
dQ = dU + pdV
properties of fluid
Understanding the properties of fluids is essential to analyse their behavior in working conditions.
In this post I have written the fluid properties namely mass density, specific weight, specific volume, specific gravity, viscosity, vapor pressure, compressibility and surface tension.


Mass Density:

Mass Density (ρ) is the property of a fluid is the mass per unit volume.

Specific Weight:

Specific Weight (w) of a fluid is the weight per unit volume.

Specific Volume:

Specific Volume (v) of a fluid is the volume of the fluid per unit mass.

Specific Gravity or Relative Density:

Specific Gravity (s) of a fluid is the ratio of the mass density of a fluid to the mass density of a standard fluid.

Viscosity:

Viscosity is property by virtue of which it offers resistance to the movement of one layer of fluid over the adjacent layer.

Vapor Pressure:

When a liquid is confined in a closed vessel, the ejected vapor molecules accumulated in the space between free liquid pressure and top of the vessel exert a partial pressure on the liquid surface. This pressure in liquid is known as vapor pressure.

Compressibility:

The normal compressive stress of any fluid element at rest is known as hydro static pressure which arises as a result of innumerable molecular collisions in the entire fluid. The degree of compressibility of a substance is characterized by bulk modulus of elasticity (K).

Surface Tension:

Surface is a measure of fluid tendency to take a spherical shape, caused by mutual attraction of the liquid molecules.
In this post We have written the top 15 most Popular automobile car manufacturing companies. We have given ranking to automobile companies by considering number of followers to company in social media. Social media that we have considered are google+, twitter and facebook. Calculation of number of followers is made on basis of calculating sum of total followers in facebook, google+ and twitter . Only the company's worldwide social accounts are considered (Regional social media accounts are not considered while making this analysis). If the company doesn't have worldwide account, USA accounts are considered for making analysis.

15. Volkswagen Group

Volkswagen is an German automobile manufacturer. Volkswagen group products are Automobiles, commercial vehicles, engines, motorcycles, turbomachinery. Vw stands 15th position in social media followers.







14. Mitsubishi

Mitsubishi is an autonomous Japanese multinational companies. Mitsubishi products are Mining, shipbuilding, telecom, financial services, insurance, electronics, automotive, construction, heavy industries, real estate, foods and beverages, chemicals, steel.etc. This company stands 14th position in social media followers with 2,299,000 fans as on 15th August.






13. Mazda

Mazda Motor Corporation is a Japanese automobile company. Mazda manufactures luxury vehicles, commercial vehicles, engines and motorcycles. It has 2720k fans with thirteenth position.









12. Toyota

Toyota is a Japanese Automotive Manufacturer. Toyota Motor Corporation manufactures luxury vehicles, commercial vehicles, engines and motorcycles. Toyota has 2771k fans on three social media.








11. Chrysler

Chrysler is an American Automobile Manufacturer owned by Italian company Fiat. Chrysler manufactures Commercial vehicles and Automotive parts. Chrysler and GM have nearly same number of followers in social media.








10. General Motors

General Motors is known as GM. It is an American Multinational corporation. General Motors manufactures are Automobile parts Commercial Vehicles. GM couldn't be successful in getting followers from facebook it stands 10th position with 2883k  fans.







9. Fiat

Fiat is the main Italian car manufacturer, founded in 1900. It owns the company Chrysler. Fiat products are Automobiles, commercial vehicles, auto parts, newspapers. Fiat company has 30 lakh followers in social media which makes it to stand in ninth position.








8. Honda

Honda Motor Company Ltd. is a Japanese company famously known as a manufacturer of automobiles, motorcycles and power equipment. Honda is the world largest two wheeler manufacture from the past 50 years. Honda has nearly 40 lakh fans.







7. Hyundai

Hyundai Group is a multinational chaebol headquartered in Seoul, South Korea. Honda was founded in 1947 as a construction. Hyundai products are Automobiles, Heavy industry, Finance and Insurance, Construction, Engineering, Retail, Aerospace, Defense and Steel. Hyundai has good number of fans in social media which sums up to 4,411,000 including facebook, google+, twitter.




6. Kia

Kia Motors Corporation is South Korea's second-largest automobile manufacturer. Kia's products are automobiles, Luxury cars and Commercial vehicles. It stands sixth in position in social media following with around 5 billion followers.





5. Ford Motor

Ford Motor company is an American multinational Automaker. Ford Motor Company Automobile products are Luxury Vehicles Commercial Vehicles Automotive parts. Ford stands fifth in social media fans with 4,988,000 followers.





4. Audi

Audi is a German automobile manufacturer that designs, engineers, produces, markets and distributes automobiles. Audi manufactures only luxury cars. It has clear leader on twitter with 810,000 fans, with overall 11,667,000 fans.







3. Nissan Group

Nissan Group products are Industrial machinery, telecommunications, power plants, information systems, electronics, automotive, materials, financial services, construction. It is third position with 13,791,000 followers.







2. Mercedes-Benz


Mercedes-Benz is a German automobile manufacturer, a multinational division of the German manufacturer Daimler AG. Mercedes-Benz is used for luxury automobiles, buses, coaches and trucks. Benz stands second in social network with 19,857,000 fans.






1. BMW Group

BMW (Bayerische Motoren Werke AG) is a German automobile company. BMW products are luxury vehicles, motorcycles and bicycles.
It stands first position in the social media with 23,276,000 followers.








Below table shows the social media fans count to top 15 automobile manufacturing companies.

There is no positive correlation between increase in sales and increase in social media fans.
All these data were collected on August 15th, 2014.
A temperature scale is established by assigning numerical values to certain reproducible states. It is customary to use the fixed points ice point and steam point.
Ice point is the equilibrium temperature of ice with air-saturated water at a pressure of 101.325 kPa which assigned a value of 0 degree centigrade.
Steam point is the equilibrium temperature of pure water with its own vapor at 101.325 kPa which is assigned a value of 100 deg C.
The temperature scale with the above fixed points is called Celsius scale.

Relationship between different temperature scales
temperature conversion from one scale to another scale
Where,
LPF = Lower Fixed Point,
UPF = Upper Fixed Point.
F = Fahrenhiet scale,
C = Centigrade scale,
K = Kelvin scale
R = Reaumer’s scale,
ρ = Our defined scale,
temperature conversion formulae
Below I have given the program for converting temperature from one scale to another scale. Write the value of any one scale and then press 'Calculate' then you will get corresponding values in the remaining scales.

Temperature Scale Converter

Fahrenheit Scale(F): 
Celsius Scale (C): 
Reaumer Scale (R): 
Kelvin Scale (K): 
    

Welding, Soldering and Brazing are the process used for joining separate pieces of metal. Each type of joining process has its own significance. Type of joining process to be used depends on many factors. In this article I have written the three major differences the welding, soldering and brazing joints.

S.No
Welding
 Soldering
Brazing
1
Welding joints are strongest joints used to bear the load. Strength of the welded portion of joint is usually more than the strength of base metal.

Soldering joints are weakest joints out of three. Not meant to bear the load. Use to make electrical contacts generally.

Brazing are weaker than welding joints but stronger than soldering joints. This can be used to bear the load up to some extent.

2 Temperature required is 3800 degree Centigrade in Welding joints.

Temperature requirement is up to 450 degree Centigrade in Soldering joints.

Temperature may go to 600 degree Centigrade in Brazing joints.

3 Work piece to be joined need to be heated till their melting point. Heating of the work pieces is not required Work pieces are heated but below their melting point.
The Wien's Displacement Law states that a black body having a wavelength (λmax) carrying the maximum energy is inversely proportional to the absolute temperature (T).

λmax * T = b

Where, λmax  =  Wavelength of maximum intensity in meters,
T  =  Temperature of the black body in kelvins,
b  = Wien's displacement constant  =  2.898 × 10^(-3) meter.kelvins

weins Displacement law graph of power density vs wavelength
Image Credits : Hyperphysics

Wien's Displacement law equation is useful for the find the temperatures of hot radiant bodies such as stars and used for a finding of the temperature of any radiant object which is far above that of its surroundings.

The LMTD is a logarithmic average of the temperature difference between the hot and cold fluid streams at each end of the heat exchanger. The larger the value of LMTD, the higher heat is transferred.
The rate of heat transfer can be expressed as q = U*A*ΔTm
Where ∆Tm is the log mean temperature difference given as
log mean temperature difference

Parallel Flow Heat Exchanger
Parallel Flow Heat Exchanger LMTD

Counter Flow Heat Exchanger
Counter Flow Heat Exchanger LMTD

Assumptions made in LMTD method are

  • The Internal Energy (U) is constant throughout the Heat Energy
  • Cp and m are constant.
  • The Heat Exchanger is perfectly insulated
  • The Cross Section of stream is uniform
  • No conduction of heat along the tubes of Heat Exchanger
  • The Kinetic Energy and Potential Energy changes are negligible
  • The flow conditions are steady
Gas Laws explain the behavior of an ideal gas in terms of Temperature, Pressure, Volume. The following are some of the important gas laws are
  • Boyle’s Law
  • Charles Law
  • Gay-Lussac’s Law
  • Avogadro’s law
  • Universal Gas Law

Boyle’s Law:

Boyle’s law states that the volume of a given mass of gas (V) is inversely proportional to its absolute pressure (P), provided the temperature of the gas (T) remains constant.
Boyle’s law formula
boyles law equation

Charles Law:

According to Charles law, the volume of a given mass of gas (V) is directly proportional to its absolute temperature (T), when its pressure remains constant.
Charles law formula
Charles law equation

Gay-Lussac’s Law:

Gay-Lussac's Law is also know as Amontons’ law. It states that if the volume of a given mass of a gas (V) is kept constant, then the pressure of the gas (P) is directly proportional to its absolute temperature (T).
Gay-Lussac's Law Formula

gay lussacs law equation

Avogadro’s Law:

Avogadro's law states that equal volumes of different perfect gases, at the same temperature (T) and pressure (P), contain equal number of molecules (n).
Avogadro’s law equation
avogadros law formula

Universal Gas Law:

Combined Gas law is derived from the three gas laws Boyles law, Charles law and Gay-Lussacs law.
Universal Gas Law Formula
universal gas law equation
free body diagram of body sliding in friction
The sliding of a solid body in contact with another solid body is always opposed by  force of friction. Friction acts in the direction opposite to that of relative motion and it is tangential to the surface of two bodies at the point of contact.
Friction is a necessary in every machine because it involves wearing of machine component and consumes energy that transfers into heat. In come cases friction is desirable in case for functioning of a machine, such as belt drives, friction clutches.

The Five Laws of Friction:

  1. When a body is moving, the friction is directly proportional to normal force and frictional force direction is perpendicular to the normal force.
  2. Friction doesn't depend on the area of contact so long as there is an area of contact.
  3. The coefficient of static friction is slightly higher the value than the coefficient of kinetic friction.
  4. Kinetic friction is independent of velocity of the body.
  5. Friction depends upon the type of the surfaces in contact.
A manometer is a device used for measure the pressure of a fluid by balancing it with against a column of a liquid. Five different types of manometers are shown with pictures below.

U-Tube Manometer :

It consist a U – shaped bend whose one end is attached to the gauge point ‘A’ and other end is open to the atmosphere. It can measure both positive and negative (suction) pressures. It contains liquid of specific gravity greater than that of a liquid of which the pressure is to be measured.
U-Tube Manometer
where 'γ' is Specific weight, 'P' is Pressure at A.
Pressure at A is P = γ2h2 – γ1h1

Differential Manometer :

A U-Tube manometric liquid heavier than the liquid for which the pressure difference is to be measured and is not immiscible with it.

Differential Manometer
Pressure difference between A and B is given by equation
PA – PB = γ2h2 – γ3h3 – γ1h1

Inverted U-Tube Manometer :

Inverted U-Tube manometer consists of an inverted U - Tube containing a light liquid. This is used to measure the differences of low pressures between two points where where better accuracy is required. It generally consists of an air cock at top of manometric fluid type.
Inverted U-Tube Manometer
Pressure difference can be calculated from equation
P1 - ρ1*g*H1 – ρm*g(H2 – H1) = P2 – ρ2*gH2

Micro Manometer :

Micro Manometer is is the modified form of a simple manometer whose one limb is made of larger cross sectional area. It measures very small pressure differences with high precision.
Micro Manometer
Let 'a' = area of the tube,
A = area of the reservoir,
h3 = Falling liquid level reservoir,
h2 = Rise of the liquid in the tube,
By conversation of mass we get A*h3 = a*h2
Equating pressure heads at datum we get 
P1 = (ρm ρ1)*gh3 + ρm*gh2 - ρ1*gh1

Inclined Manometer :

Inclined manometer is used for the measurement of small pressures and is to measure more accurately than the vertical tube type manometer. Due to inclination the distance moved by the fluid in manometer is more.
Inclined Manometer
Pressure difference between A and B is give by equation
Governor is a device used to maintain the speed of an engine within specified limits when the engine works in varying of different loads.
Based on the source of controlling force, the governors can be classified into two types. They are centrifugal governors and inertia governors.

Centrifugal Governors :

In centrifugal governors, multiple masses know as governor balls, are responsible to revolve about the axis of a shaft, which is driven through suitable gearing from the engine crankshaft. Each ball is acted upon by a force which acts in the radially inward direction and is provided by dead weight, a spring or a combination of two. This force is commonly called as the controlling force and it will increase as the distance of the ball from the axis of rotation increases. The inward or outward movement of the ball is transmitted by the governor mechanism to the valve which controls the amount of energy supplied to the engine.

Centrifugal governor
Image Source : flickr.com

Inertia Governor :

In inertia governors, the balls are arranged in manner that the inertia forces caused by angular acceleration or retardation of the governor shaft tend to change their position. The obvious advantage of inertia governor lies in its rapid response to the effect of a change of load. This advantage is small, however by the practical difficulty of arranging for the complete balance of the revolving parts of the governor. For this reason Centrifugal governors are preferred over the inertia governors.
In statics, Lami's theorem is an equation that relates the magnitudes of three coplanar, concurrent and non-collinear forces, that keeps a body in static equilibrium.
Lami’s theorem states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces A, B, C acting on a particle or rigid body making angles α, β and γ with each other.

Lami's Theorem

According to Lami’s theorem , the particle shall be in equilibrium if
Lami's Theorem condition
The angle between the force vectors is taken when all the three vectors are emerging from the particle.

A belt is a looped strip of flexible material used to mechanically link two or more rotating shafts. A belt drive offers smooth transmission of power between shafts at considerable distance. Belt drives are used as source of motion to transfer to efficiently transmit power or to track relative movement.

Image source : wwag.com

Types of Belt Drives:

In a two pulley system, depending upon direction the belt drives the pulley, the belt drives are divided into two types. They are open belt drive and crossed belt drive. The two types of belt drives are discussed below in brief.

Open belt drives :

open belt drive
An open belt drive is used to rotate the driven pulley in the same direction of driving pulley.  In motion of belt drive, power transmission results makes one side of pulley more tightened compared to the other side.  In horizontal drives, tightened side is always kept in the lower side of two pulleys because the sag of the upper side slightly increases the angle of folding of the belt on the two pulleys.

Crossed belt drive
Crossed belt drives :

A crossed belt drive is used to rotate driven pulley in the opposite direction of driving pulley. Higher the value of wrap enables more power can be transmitted than an open belt drive. However, bending and wear of the belt are important concerns.

Advantages of belt drives :

  • Belt drives are simple are economical.
  • They don't require Parallel shafts.
  • Belts drives are provided with overload and jam protection.
  • Noise and vibration are damped out. Machinery life is increased because load fluctuations are shock-absorbed.
  • They are lubrication-free. They require less maintenance cost.
  • Belt drives are highly efficient in use (up to 98%, usually 95%).
  • They are very economical, when distance between shafts is very large.

Disadvantages of belt drives :

  • In Belt drives, angular velocity ratio is not necessarily constant or equal to the ratio of pulley diameters, because of slipping and stretching.
  • Heat buildup occurs. Speed is limited to usually 35 meters per second. Power transmission is limited to 370 kilowatts.
  • Operating temperatures are usually restricted to –35 to 85°C.
  • Some adjustment of center distance or use of an idler pulley is necessary for wearing and stretching of belt drive compensation.