INTERNAL COMBUSTION ENGINE (IC ENGINE)

MECHANICAL ENGG : INTERNAL COMBUSTION ENGINE

fig: wankel engine

single cylinder IC engine

IC engine

Definition:

The internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber. In an internal combustion engine the expansion of the high temperature and pressure gases, which are produced by the combustion, directly applies force to a movable component of the engine, such as the pistons or turbine blades and by moving it over a distance, generate useful mechanical energy.

Combustion Type:

• Intermittent Combustion:

The term internal combustion engine usually refers to an engine in which combustion is intermittent, such as the more familiar four-stroke and two-stroke piston engines, along with variants, such as the Wankel rotary engine.

• Continuous Combustion:

A second class of internal combustion engines use continuous combustion: gas turbines, jet engines and most rocket engines, each of which are internal combustion engines on the same principle as previously described.

Uses and Applications:

Internal combustion engines are most commonly used for mobile propulsion in vehicles and portable machinery. In mobile equipment, internal combustion is advantageous since it can provide high power-to-weight ratios together with excellent fuel energy density. Generally using fossil fuel (mainly petroleum), these engines have appeared in transport in almost all vehicles (automobiles, trucks, motorcycles, boats, and in a wide variety of aircraft and locomotives).

Internal combustion engines appear in the form of gas turbines as well where a very high power is required, such as in jet aircraft, helicopters, and large ships. They are also frequently used for electric generators and by industry.

Combustion Mechanism:

All internal combustion engines depend on the exothermic chemical process of combustion: the reaction of a fuel, typically with oxygen from the air (though it is possible to inject nitrous oxide in order to do more of the same thing and gain a power boost). The combustion process typically results in the production of a great quantity of heat, as well as the production of steam and carbon dioxide and other chemicals at very high temperature; the temperature reached is determined by the chemical make up of the fuel and oxidisers.

Types of Fuels it uses:

The most common modern fuels are made up of hydrocarbons and are derived mostly from fossil fuels (petroleum). Fossil fuels include diesel fuel, gasoline and petroleum gas, and the rarer use of propane. Except for the fuel delivery components, most internal combustion engines that are designed for gasoline use can run on natural gas or liquefied petroleum gases without major modifications. Large diesels can run with air mixed with gases and a pilot diesel fuel ignition injection. Liquid and gaseous biofuels, such as ethanol and biodiesel (a form of diesel fuel that is produced from crops that yield triglycerides such as soybean oil), can also be used. Some engines with appropriate modifications can also run on hydrogen gas.

Comparison of IC Engine with Steam Engine:

a) Both IC engine and steam engine are basically heat engines used to convert heat energy into mechanical energy.

b) In IC engine, the combustion of fuel (liquid or gas) takes place inside the engine cylinder. Where as, in steam engine combustion occurs outside engine, in a boiler to raise the temperature which in turn is used in the heat engine.

c) The working temperature and pressure inside an IC engine are much higher than that of steam engine. It requires the design be robust and strong temperature and pressure resistant.

d) IC engines are mostly single acting while most of the steam engines are double acting. Hence, no need of stuffing box in IC engines.

e) IC engine produces high efficiency in the range of 35% to 40%, while steam engine can produce work with an efficiency in the range of 10% to 15%.

f) Compared to long starting procedure of a steam engine, an IC engine can be started instantenously.

Classification of IC engines:

IC engines can be classified on different characteristics basis.

a) Type of Ignition process: i) Spark Ignition or SI engine, ii) Compression Ignition or CI engine, iii) Hot spot ignition engine.	b) Type of Fuel used: i) Petrol/Gasoline engine, ii) Diesel engine, iii) Gas engine.	c) Number of Strokes per cycle: i) Four stroke engine, ii) Two stroke engine.
d) Type of Cooling system: i) Air cooled engine, ii) Water cooled engine, iii) Evaporative cooling engine.	e) Cycle of Operation: i) Otto cycle engine, ii) Diesel cycle engine, iii) Dual cycle engine.	f) Method of fuel injection: i) Carburettor engine, ii) Air injection engine, iii) Airless or solid injection engine.
g) Arrangement of Cylinders: i) Vertical engine, ii) Horizontal engine, iii) Radial engine, iv) V engine, v) Opposed cylinder engine, vi) Opposed piston engine.	h) Application fields: i) Stationary engine, ii) Automotive engine, iii) Marine engine, iv) Aircraft engine, v) Locomotive engine.	i) Valve Locations: i) Over-head valve engine, ii) Side valve engine.
j) Speed of the engine: i) Slow speed engine, ii) Medium speed engine, iii) High speed engine.	k) Method of Governing: i) Hit and Miss governed engine, ii) Qualitatively governed engine, iii) Quantatively governed engine.

TERMINOLOGY: IC ENGINE

BORE: The inside diameter of the cylinder is known as bore. It is always measured in mm. 

STROKE: The distance travelled by the piston from one of its dead center positions to the other dead center position. 

DEAD CENTERS: They correspond to the positions occupied by the piston at the end of its stroke where the center lines of the connecting rod and crank are in the same straight line. These conditions arise at two specific positions of the piston. At the start of the journey of stroke and at the end of the stroke are these two specific conditions, which are named as Top Dead Center (TDC) and Bottom Dead Center or BDC for vertical engines and IDC or Inner Dead Center and ODC or Outer Dead Center for horizontal engines. 

TDC: The top most position of the piston towards the cover end side of the cylinder of a vertical engine is called Top Dead Center or TDC. 

BDC: The lowest position of the piston towards the crank end side of the cylinder of a vertical engine is known as BDC. 

CRANK THROW/ CRANK RADIUS: The distance between the center of main shaft and center of crank pin is known as Crank Throw or Crank Radius. This distance will be equal to half the stroke length. 

PISTON DISPLACEMENT/ SWEPT VOLUME: It is the volume through which the piston sweeps for its one stroke. Swept Volume is represented by Vs and it is equal to cross-sectional area of the piston x stroke length. 

Vs = {(π x d²)/4} x stroke length (L)
∴ Vs = (π.d².L)/4
CLEARENCE VOLUME: It is the volume included between the piston and the cylinder head when it is at TDC (for vertical engines) or IDC (for horizonal engine). The piston can never enters this portion of the cylinder during its travel. Clearence volume (Vc) is generally expressed as percentage of the swept volume and is denoted by Vc. 

COMPRESSION RATIO: It is the ratio of the total cylinder volume to the clearance volume. If swept volume is (Vs) and clearance volume is (Vc) then total volume of the cylinder V = Vs + Vc and Compression Ratio will be equals to (Vs + Vc)/Vc. For petrol engine it varies from 5:1 to 9:1 and for diesel engines from 14 : 1 to 22 : 1. 

PISTON SPEED: It is the distance travelled by piston in one minute. If rpm of engine shaft is (N) and length of stroke is (L), then piston speed will be 2LN m/min. 

TERMINOLOGY:

(i) Internal combustion (IC): The internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber. In an internal combustion engine the expansion of the high temperature and pressure gases, which are produced by the combustion, directly applies force to a movable component of the engine, such as the pistons or turbine blades and by moving it over a distance, generate useful mechanical energy.

(ii) Spark Ignition(SI): An engine in which the combustion process in each cycle is started by use of a spark plug.

(iii) Compression Ignition(CI): An engine in which the combustion process starts when the air fuel mixture self ignites due to high temperature in the combustion chamber caused by the high compression. CI engines are often called diesel engines especially in the non technical community.

(iv) Top-Dead-Center (TDC): Position of the piston when it stops at the furthest point away from the crankshaft. Top because this position is at the top of most engines (not always) and dead because the piston stops at this point. Because in some engines top-dead-center is not at the top of the engine (e.g., horizontally opposed engines, radial engines, etc.,), some sources call this position Head-End-Dead-Center (HEDC). Some sources call this position Top-Center (TC). When an occurrence in a cycle happens before TDC, it is often abbreviated bTDC or bTC. When the occurrence happens after TDC or a TC. When the piston is at TDC, the volume in the cylinder is a minimum called the clearance volume.

(v) Bottom-Dead-Center (BDC): Position of the piston when it stops at the point closest to the crankshaft. Some sources call this Crank-End-Dead-Center(CEDC) because it is not always at the bottom of the engine. Some sources call this point Bottom-Center(BC). During an engine cycle things happen before Bottom-Dead-Center, bBDC or bBC, and after bottom-deadcenter, aBDC or aBC.

(vi) Direct Injection:Fuel injection into the main combustion chamber of an engine. Engines either have one main combustion chamber (open chamber) or a divided combustion chamber made up of a main chamber and a smaller connected secondary chamber.

(vii) Indirect injection: Fuel injection into the secondary chamber of an engine with a divided combustion chamber.

(viii) Displacement volume: Volume displaced by the piston as it travels through one stroke. Displacement cans b given for one cylinder or for the entire engine (one cylinder time’s number of cylinders). Some literature calls this swept volume.

(ix) Gasoline Direct Injection (GDI): Spark ignition engine with fuel injectors mounted in combustion chambers. Gasoline fuel is injected directly into cylinders during compression stroke.

(x) Homogeneous Charge Compression Ignition (HCCI): Compression-Ignition engine operating with a homogeneous airfuel charge instead of the diffusion combustion mixture normally used in CI engines.

(xi) Smart Engine: either computer controls that regulate operating characteristics such as air fuel ratio, ignition timing, valve timing, exhaust control, intake tuning, etc.Computer inputs come from electronic, mechanical, thermal and chemical sensors located throughout the engine. Computers in some automobiles are even programmed to adjust engine operation for things like valve water and combustion chamber deposit build up as the engine ages. In automobiles, the same computers are used to make smart cars by controlling the steering, brakes, exhaust system, suspension, seats, anti-theft systems, sound-endear analysis navigation entertainment systems, shifting, doors, noise, suppression, environment, comfort,etc.(o) Engine Management System: Computer and electronics used to control smart engines.

(xii) Wide- Open throttle (WOT): Engine operated with throttle valve fully open when maximum power and/or speed is desired.

(xiii) Ignition Delay (ID): Time interval between ignition initiation and the actual start of combustion.

(r) Air Fuel Ratio: Ratio of mass air to mass of fuel input into engine.

(xiv) Fuel-Air ratio: Ratio of mass of fuel to mass of air input into engine.

(xv) Brake Maximum torque: (BMT): Speed at which maximum torque occurs.

(xvi) Overhead Valve (OHV): Valves mounted in engine head.

(xvii) Overhead Cam (OHC): Camshaft mounted in engine head, giving more direct control of valves which are also mounted in engine head.

(xviii) Fuel Injection (FI):

MAIN ENGINE COMPONENTS:

The following is the list of major components found in most reciprocating internal combustion engines.

• Block: Body of engine containing the cylinders made of cast iron or aluminum. In many older engines the valves and the valve ports were contained in the block. The block of water cooled engines includes a water jacket cast around the cylinders. On air cooled engines the exterior surface of the block has cooling fins. 

• Camshaft: Rotating shaft used to push open valves at the proper time in the engine cycle either directly or through mechanical or hydraulic linkage (push rods, rocker arms, and tappets). Most modern automobile engines have one or more camshafts mounted in the engine head (Overhead cam). Older engines had camshafts in the crank case. Crankshafts are generally made of forget steel or cast iron and driven off the crankshaft by means of a belt or chain (Timing chain). To reduce weight, some cams are made from a hollow shaft with the cam lobes press-fit on. In four stroke cycle engines the camshaft rotates at half engine speed.

• Carburetor: Venturi flow device that meters the proper amount of fuel into the air flow by means of pressure
  differential. For many decades it was the basic fuel metering system on all automobile (and other) engines. It is still used on low cost small engines like lawn mowers but is uncommon on new automobiles.

• Catalytic converter: Chamber mounted in exhaust flow containing catalytical material that promotes reduction of emission by chemical reaction.

• Choke: Butterfly valve at carburetor intake, used to create rich fuel-air mixture in intake system for cold weather starting.

• Combustion chamber: The end of the cylinder between the head and the piston face where the combustion occurs. The size of the combustion chamber continuously changes from a minimum volume when the piston is at TDC to a maximum when the piston is at BDC. The term cylinder is sometimes synonymous with combustion chamber (e.g., the engine was firing on all cylinders). Some engines have open combustion chambers which consist of one chamber for each cylinder.

• Other engines have divided chambers which consist of dual chambers on each cylinder connected by an orifice passage.

• CRANK CASE: In IC Engine terminology, Crank Case is the housing of Crank Shaft. It is the largest cavity in engine and is fixed to cylinder. 
  
  
  
  
  

OCTANE AND CETANE NUMBERS

Self ignition temperature (SIT) of a fuel is the temperature at which the fuel ignites on its own without spark. If large amount of mixture in an engine cylinder auto ignites, there will be a rapid rise in pressure causing direct blow on engine structure accompanied by thudding sound. This causes vibrations in the engine. The phenomenon is called knocking.

If however, a small pocket of fuel-air mixture auto ignites, pressure waves are generated which travel with the speed of sound across the cylinder. These pressure waves are of such small duration that indicator diagram mechanism fails to record them. These waves interact within themselves and with the cylinder walls, creating characteristics ping sound. The phenomenon is called pinking.

The engine runs rough, overheats and loses efficiency due to knocking and pinking.

The processes of knocking and pinking are related to the nature of the fuel and relative merits of the fuel are decided on the basis of their anti-pinking and anti-knock property. The merit is measured by octane number such that a fuel of high octane number will be liable to less pink or knock as compared to a fuel of low octane number in the same engine. It is important to note that the same fuel will show same tendency to pink or knock in all engines.

Commonly used fuel in SI engines is a mixture of iso-octane and n-heptane. Iso-octane has minimum tendency to knock and this fuel is arbitrarily assigned an octane number of 100 (ON = 100) where as n-heptane has maximum knocking tendency with ON = 0. The octane number of a given fuel is percentage of iso-octane in the mixture of iso-octane and n-heptane. Thus a fuel other than mixture of iso-octane and n-heptane if assigned an ON of 80, it means, it will knock under standard operating condition similar to the mixture of 80% iso-octane and 20% n-heptane.

The tendency to knock in an engine increases with the increase in compression ratio. The highest compression upto which no knocking occurs in a given engine is called highest useful compression ratio (HUCR).

Certain chemical compounds when added to the fuel successfully suppress the knocking tendency. Tetra-ethyl lead [Pb(C₂ H₅)₄] also commonly called TEL and tetra-methyl lead [Pb(CH₃)₄] also referred to as TML are effective dopes in the automobile fuel to check knocking. They are called as anti-knocking agents. However, because of lead poisoning effects TEL and TML are not being used now-a-days. In stead, some organic auto knocking agents have been developed to check the undesirable effects like knocking.

In CI engine air alone is compressed to a compression ratio of 15 to 20 (commonly). The fuel is injected under a pressure of 120 to 210 bars about 20° to 35° before TDC. As the fuel in the engine starts to evaporate the pressure in the cylinder drops and it delays the ignition process by a small amount. The time between beginning of injection and the beginning of combustion is known as the delay period which consists of time for atomization, vapourization and mixing along with time of chemical reaction prior to auto-ignition. The combustion of fuel continues in the expansion and is called after burning. Increased delay period causes accumulation of atomized fuel in the combustion chamber and as the pressure and temperature continue to rise at one instant, the bulk of fuel auto-ignites. This would result in high forces on the structure of the engine causing vibration and rough running.

The CI engine fuel rating is based on ignition delay and is measured in terms of cetane number. Cetane fuel [C₁₆ H₃₄] has very low delay period and is arbitrarily assigned a cetane number of 100. Another fuel a α-methyl-napthalene [C₁₁ H₁₀] has poor ignition quality and is assigned zero cetane number. The volume percentage of cetane in a mixture of cetane and a-methyl naphthalene is the cetane number of the fuel that produces same delay period as the mixture under specified test conditions. Additives such as methyl nitrate, ethyl thio-nitrate and amyl nitrate increase cetane number of a fuel respectively by 13.5%, 10% and 9% if added to the extent of 0.5%.

MOCK CLASS TEST: THERMODYNAMICS Sub: Code: EME-303; Mahamaya Technical University

Time: 2 hrs                                                                                                   Maximum Marks: 50 

Attempt all the questions: 

SECTION A: 

1) Attempt the following questions:                                                                        (5 x 2 = 10) 

a) Define system, surroundings and universe. 

b) Distinguish between Heat pump and Refrigerator. 

c) What is Exergy and Anergy? 

d) Explain the law of degradation of energy. 

e) What is triple point of water? 

SECTION B: 

2) Attempt any three questions:                                                                               (3 x 5 = 15) 

a) Distinguish between macroscopic and microscopic approaches of thermodynamics. 

b) Discuss the neccessity of 2nd law of thermodynamics. 

c) 2 kg of a gas at 10 bar expands adiabatically and reversibly till its pressure drops to 5 bar. During the process 120 kJ of non-flow work is done by the system and the temperature drops from 377°C centigrade to 257°C. Calculate the value of the index of expansion and the characteristics gas constants. 

d) Steam at a pressure of 4 bar absolute and having dryness fraction 0.8, is heated at constant volume to a pressure of 8 bar absolute. Find the final temperature of the steam. Also, find the total heat absorbed by 1 kg of steam. 

e) 2 kg of air at NTP is heated at constant volume untill the pressure becomes 6 bar. Find the change of entropy of the system. 

SECTION C: 

Attempt part (a) or part (b) of the following questions                                                 (5 x 5 = 25) 

3) (a) Explain the thermodynamic equilibrium and quasi-static process. 

(b) Prove the equivalence of Kelvin-Planck statement and Clausius statement. 

4) (a) A steam turbine developing 110 kW is supplied steam at 17.5 bar with an internal energy of 2600 kJ/min, specific volume = 15.5 m³/kg and velocity of 275 m/s. Heat loss from the steam turbine  37.6 kJ/kg. Neglecting the changes in potential energy, determine the steam flow rate in kg/hr. 

(b) A reversible engine takes 2400 kJ/min from a reservoir at 750 K develops 400 kJ/min of work during cycle. The engine rejects heat at two reservoir at 650 K and 550 K. Find the heat rejected to each sink. 

5) (a) Explain the causes of internal and external irreversibility. 

(b) Explain the importance of Gibb's function and Gibb's free energy. 

6) (a) 5 kg steam at pressure 8 bar and temperature 300°C is adiabatically mixed with 4 kg steam at 6 bar and 250°C. Find the final condition of the mixture. Also find the change in entropy. 

(b) Hot steam is flowing through a perfectly adiabatic pipe. At point A the temperature of the steam is 250°C and pressure is 4 bar, while at the point B, its temperature is 275°C and pressure is 3.5 bar. Find the direction of the flow. 

7) (a) 5 kg of Oxygen is enclosed within a vessel of 0.05 m³ at a temperature 200°C, is being supplied 120 kJ of energy through heating. Find the final pressure and temperature. 

(b) One kg of an ideal gas is heated from 18.3°C to 93.4°C. Assuming R = 287 J/kg-K and  γ  = 1.18 for the gas. Find out (i) specific heats, (ii) change in internal energy, and (iii) change in enthalpy and entropy.

BEAMS, JOINTS AND SUPPORTS

KINEMATICS ANALYSIS : MOVING BODIES......

KINEMATICS ANALYSIS: MOVING BODIES......
Mechanics, physics, mechanical engineering

What makes a body moving?

OBSERVATION ONE:

"From our perception, we can say, a body moves if we apply either a push or a pull on the body. There are several  instances, when after applying push or pull, the body still doesn't move. What is the exact reason behind this?"

OBSERVATION TWO:

"Almost to apply a push or pull on a body, a physical contact is needed, with out any physical contact it is not possible to exert push/pull on a body, although there are exceptions too.

(i) We know on every material body existing on earth experience a downward pull towards the center of Earth and to exert this pull, the object and the earth don't need any physical contact. This phenomena is aptly named as the 'Force of Gravity.'

(ii) The second option is Magnet. A magnet can pull as well as push another magnet from a distance with out any physical contact.

(iii) When we place a charged particle near another charged particle, we watch the particles can exert push as well as pull without any physical contact. Like a proton repels another proton, ie they exert push on each other. But a proton attracts an electron by pulling each other to come close.

So there are two types of motion. Type one is the example of a Cricket ball going to boundary after being hit by the bat. So, here impact is the driver of the motion.

But an apple falling from a tree is also in motion, but for this no impact is there. In fact the attraction between the apple and the earth is responsible for the motion. By attraction, it means the tendency of going closer in two objects. Here motion of apple occurs without being hit.


LINEAR MOTION:

We know that Force is a kind of physical quantity having both magnitude as well as direction. So, force is a vector quantity. We also know that applying triangle's law or parallelogram law of forces addition, we can add two forces to get an equivalent force which is known Resultant force.

So, application of force on an object brings a change in position of the object. This change is position is called displacement. An object in a coordinate system has a position vector to define the position vector. Any change of position will bring change in its position vector.

Suppose in a coordinate system we have an object at a position vector (r). Let after a time interval of (dt), the object changes its position by an amount (dr). Hence, the rate of change of position will be (dr)/(dt). Rate of change of position

means the change of position in unit time. Rate of change of position is called velocity of the object. It is denoted by (v).

Hence, (v) = (dr)/(dt).
The unit of velocity is m/s in SI units and cm/s in cgs system. The most popular unit is km/hr.

A velocity may change, it may change in direction or it may change in magnitude. Suppose, we have an object moving with a velocity (v) at any instant. Suppose after an interval of time (dt), its new velocity becomes (v + dv), where (dv) is the change in velocity. Hence (dv)/(dt) will be the rate of change of velocity and it indicates the change of velocity per unit time. This physical quantity is called acceleration. Negative acceleration which is rate of decrease in velocity is called retardation or deacceleration too.

Acceleration may be changed; the rate of change of acceleration is called impulse. Like when a bat touches a moving ball, it has an impact and this changes its acceleration due to this magnitude and direction of the ball changes. If a large magnitude of force act on a body for a very short period of time, it is called impulse.

Free falling under the forces of gravity is a case of constant acceleration and that is denoted by (g) and it is equal to g = 9.81  m/s ² .

THREE EQUATIONS OF MOTION

These three equations are valid only in the case of constant acceleration. Every particle falling under the gravity will satisfy these equations.

We know (dv)/(dt) = a,
hence, (dv) = a(dt) or by integrating both side from initial state t = 0; v = u to final t = t; v = v,
we get,
v - u = a(t - 0) or v = u + at

Again, a = (dv)/(dt)
a = {(dv)/(dx)}.{(dx)/(dt)}
a = v.(dv)/(dx)
hence, v.dv = a.dx
Integrating both sides from initial v= u, x = 0 to final v = v, x = s
we get,
v² - u² = 2 a (s - 0)
v² - u² = 2as

From the defination of velocity, we get
v = (dx)/(dt)
but, v = u + at
hence,
u + at = (dx)/(dt)
dx = (u +at). dt
Integrating both sides of the equation from initial condition t = 0, x = 0 and final condition t = t, x = s, we get

(s - 0) = u(t - 0) + (a.t²)/2
s = ut + (at²)/2

Average Velocity = (u + v)/2
= (u + u + at)/2 = u + at/2

Total distance, s = Average Velocity x time

s = (u + at/2) x t
s = ut + (at²)/2

Uses of these equations:

1) Suppose we have a particle travelling with 5 m/s and an acceleration of 1 m/s^2 is applied on the body. What will be the

velocity after a time of 10 s?

Ans: Here, u = 5 m/s, a = 1 m/s ²  and t = 10 s, then

velocity after 10 s,
v = u + at
v = 5 + 1 x 10 = 15 m/s

2) A car moving with a velocity 60 km/hr suddenly applies the brake. As a result, the car comes to a halt after running 50 m

after applying brake. What will the value of retardation? Find the time it needs to come to rest after the application of brake.

Ans: Here, initial velocity u = 60 km/hr = (60 x 1000)/(60 x 60) m/s = 16.67 m/s
final veloity, v = 0 m/s
Total distance travelled s = 50 m
a = (v² - u²)/2s
a = (0 - 16.67²)/(2 x 50)
a = - 2.78 m/s²

again time, t = (v - u)/a
t = (0 - 16.67)/(-2.78)
t = 5.99 s

The Concept of Relative Velocity:

Suppose in a road two car is moving. The faster car at 40 km/hr and the slower car at 30 km/hr in the same direction. Now, if anyone watches the faster car from the slower car, he won't be see it running at 40 km/hr, in stead he will see the velocity at 15 km/hr. When we watch from a moving body or better we say moving reference frame, the velocity of other bodies seem be reduced. Again if we take the same two cars running in opposite directions to each other, the velocity of the each car will be at 55 km/hr as seen from the other. This is due to relative velocity. The relative velocity of a body is the velocity of the body relative to an observer.

Suppose, a car is moving with a velocity V_c and a train is moving with a velocity V_t. Then velocity of car with respect to a person sitting in the train will be V_ct = V_c – V_t and velocity of the train to a person in the car will be  V_tc = V_t – V_c  .

3) A train is moving towards east with a velocity 120 km/hr and wind is blowing towards west with a velocity 20 km/hr. What will the velocity of the wind to an observer in the train?

Ans: We shall take towards east direction as positive and towards west direction as negative.
Let the velocity of train is (V_t) and velocity of wind is (V_w)

So,  V_t  = 120 km/hr and
V_w = - 20 km/hr

V_wt =  V_w  - V_t
V_wt = - 20 - 120 = - 140 m/s and it means wind is flowing from west.

4) A car is moving on a horizontal road at 40 km/hr. Suddenly rain started to pour down at a velocity 30 km/hr. Find the

velocity of the rain drops with rest to an observer in the car. Also find the angle with which rain drops would appear to strike the car.

Ans: Let the velocity of the car be V_c = 40 km/hr and rain drop velocity is  V_r = - 30 km/hr. The angle between them is θ = 90°.
(V_rc) = (V_r) - (V_c)
(V_rc)² = (V_r)² + (V_c)² - 2(V_r)(V_c) cos θ
= 30² + 40² + 0
= 2500
(V_rc) = 50 m/s

ANGULAR MOTION:

Suppose a line AB displaces side wise such that A remains at same point, but the other end B comes to new position C. This is an angular displacement. Angles are measured in radian. 1 radian is the angle formed by an arc equals to magnitude of radius (r). A full circle produces 2π.

Suppose, a line of length (r) makes an angular displacement of (dθ) in time (dt). Then the rate of change of angular displacement is given by (dθ)/(dt) and it is called angular velocity, (w). Hence, (w) = (dθ)/(dt).

If we apply torque or moment in the line, the angular velocity will be changed. Let during the time interval, (dt), the change in angular velocity be (dω). The rate of change of angular velocity will (dω)/(dt) and it is called as angular acceleration and denoted as α.

α = (dω)/(dt)
(dω) = α.(dt)
Taking initial value ω = ωₒ, t = 0, to final value ω = ω, t = t and integrating both side, we get,
ω - ωₒ = α.(t - 0)
ω = ωₒ + αt

angular velocity ω = (dθ)/(dt)
ωₒ + αt = (dθ)/(dt)
(ωₒ + αt)(dt) = dθ
Taking initial value θ = 0, t = 0, to final value, θ = θ, t = t, and integrating both side we get,

ωₒ.(t - 0) + (α/2)(t² - 0) = θ - 0

θ = ωₒt + (αt²/2)

α = (dω)/(dt)
= {(dω)/(dθ)}.{(dθ)/(dt)}
α = ω.(dω)/(dθ)
ω.(dω) = α.(dθ)
taking the initial value ω = ωₒ, θ = 0 and final value ω =ω, θ = θ and integrating both sides,
(ω²)/2 - (ωₒ²)/2 = α.(θ - 0)
(ω²) = (ωₒ²) + 2.α.θ



MOTION OF A RIGID BODY

Plane Motion:

A rigid body is said to be in plane motion when all parts of the body move in parallel planes. The plane motion of a rigid body may be classified into several categories like :

1) Translation
2) Rotation
3) General plane motion.

Translation:

ENGINEERING MECHANICS CLASS TEST: ONE

CLASS TEST: ONE

Time: 1 hr 30 min                                                                                        Max. Marks: 30

                                                                                                                         

1) Answer the following question in brief                                                              2 x 6 = 12   

                                                                 

a)      Distinguish clearly between composition of forces and resolution of forces.

b)      Show that the algebraic sum of the resolved part of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction.

c)      Differentiate between coplanar forces and concurrent forces clearly.

d)     State and explain the laws of transmissibility of forces.

e)      Explain Newton’s third law of motion.

f)       What is a couple? Explain its characteristics.

2) Answer any two of the following questions                                                     6 x 3 = 18

a)      A smooth circular cylinder of radius 1500 mm is lying in a triangular groove, the right side of which makes 20° angle and left side makes 40° angle with horizontal. Find the reaction at each contact if there is no friction and the cylinder weight is 400 N.

                                                                                             

b)      A right circular cylinder of weight 5 kN rests on a smooth inclined plane and is held in position by a cord AC as shown in the figure. Find the tension in the cord if there is a horizontal force of magnitude 1 kN acting at C.

c)      Four forces of magnitude 10 kN, 18 kN, 15 kN and 12 kN are acting along the diagonals and sides of a regular pentagon as shown in the figure. Find the resultant force of the given force system.

d)     Prove that if a body is at equilibrium under three forces, then the forces are concurrent forces.

SMALL ENGINEERING COLLEGES OF GHAZIABAD: A BLEAK FUTURE

Economics says "When Supply is more than the Demand of a product, the Price falls." This is particularly true in the case of Technical Education in U.P. and perhaps upto some extent in the country itself.

Over the past few years the supply is outstripping the demand for Engineering and Management seats in the country. Just take the example of Uttar Pradesh, the most populous state of India is home to about 333 Engineering colleges which cumulatively offer a total seats of 1,15,379 in Engineering Education where as according to University datas the total number of students took admission in various engineering colleges after qualifying SEE amounts to mere 25,903. So, what happens to the vacant seats? And this year the figures are not going to be improved it seems.

This year a total 1,60,561 candidates had registered for the State Entrance Examination, out of whom, 1,29,924 have qualified. But, there are approximately 1.33 lakh B.Tech seats in the Engineering colleges affiliated to GBTU and MTU.

There are clearly a huge gap between the supply and demand of Engineering seats. In this situation, it has been believed that many small colleges will be bankrupt due to the lack of students. Many colleges have defered the salaries of the teachers and other employees due to the revenue crunch. It seems a grim scenario ahead for those colleges.

Due to the revenue crunch, promoters of small colleges are taking the refuge of cost cutting, and as a part of that they are trying to trim their faculty strength. Surely, this will affect the quality of the education as the each teacher will be over burdened and perhaps have to take five classes per day, where as the AICTE limits the load at best 18 classes per week. Also, most of the colleges don't follow the exact teacher students ratio of 1:20 prescribed by the apex body.

Many promoters are planning to opt out by selling their stakes in the colleges. The causes of their exits are the facts that running colleges in western U.P. is no longer a profitable business. They have cited that due to lack of students in taking admission, the colleges are no longer the chickens that lay gold eggs, which were in fact so just three years ago. So, why these colleges suddenly loss their values? What are the reasons behind these failures?

There are several reasons for the fall in numbers of students opting B.Tech courses. The most vital reason is the very high tution fees in colleges under MTU and GBTU compared to colleges in other states like Karnataka, Punjab and Rajasthan. Most of the colleges here charge more than 90,000.00 in the first year B.Tech where as colleges in other states charges below 60,000.00, even colleges in Punjab and West Bengal charge below 50 thousand and this is going to be a major factor.

The 2nd factor is the placement after the completion of the degree. Although many colleges claim tall, citing a long list of companies taking interest to place their students in very good packages, but reality always bites hard. The negative publicity by the ex students are also eating the pie here and there is no solution other than boosting the placement record by making a good relation with the HR of these companies by the respective college authorities.

The third most important factor is the sagging quality of the available faculty members. Many teachers although possess M.Tech degrees are not competent to impart quality education due to lack of depth of required knowledge as well as the essential communicating power required to be a good teacher. In some cases, due to over burdened schedule, a good teacher becomes unable to teach in the class. Just imagine the mental fatigue a teacher experienced while taking 5th or 6th class in a day when each class is of 55 min. duration.

A college has to show money to run the next three years during the visits from AICTE. So all the colleges have to show enough balance to pay the salaries of the employees for atleast three years, otherwise they won't get the permission to run the colleges, still some of them couldn't pay the salaries of the teachers and staffs. Why? Becouse they must have showed enough balances to acquire the clearences during the AICTE visits. Where does the money go? Vanished! Or siphoned off? There are several "skips" of the rules and regulations these college authorities used to practise.