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Task 1Newtons law of motion : Sir Isaac Newton provides Three Laws of Motion; these are:First law: An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This law is often called"the law of inertia". (1)Second law: The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.This law states the relationship between the force applied to an object and the resultant change of momentum in that direction. Normally, the mass of an object is constant and the relation becomes:

F = (mv-mu)/t = m(v-u)/t =ma

Where, m is the mass, u is the initial velocity, v is the velocity after t second, F is the applied force acting in the direction of motion, a is the acceleration, mu is the initial momentum, mv is the momentum after t seconds. This formula has direct application in mathematical treatment of jet-propulsion of an aircraft gas turbine engine. (2) Third law: For every action there is an equal and opposite reaction. (2)In this statement the term "action" means the force that one body exerts on a second, and "reaction" means the force that the second body exerts on the first. That is, if body A exerts a force on body B, then B must exert an equal and opposite force on A. Note that action and reaction, though equal in magnitude and opposite in direction, never neutralize or cancel each other for they always act on different objects.The recoil of a rifle demonstrates this law of action-reaction. The gunpowder in a charge is ignited by the ignition cap, combustion takes place, and the bullet is rapidly accelerated from the rifle. As a result of this action, the rifle is accelerated rearward against the shoulder of the person firing it. The recoil felt by the person is the reaction to the action which ejected the bullet. The principle of jet propulsion can be illustrated by a toy balloon (Figure). When inflated with the stem sealed, pressure is exerted equally on all internal surfaces. Boyles Law: For a fixed amount of an ideal gas, kept at a fixes temperature, pressure and volume are inversely proportional to each other. Robert Boyle studied the relation between the pressure (p) and the volume (V) of confined gas held at constant temperature, He noticed that the product of the pressure and volume was nearly constant. (2)PV=Constant =kP1V1=P2V2

Figure: Boyles Law explain Example: When you ride a bicycle then tire become narrower the contact point of the road, because, we give load on the tire for that the volume of the tire is reduced. It is a example of Boyles LawCharles Law: At a constant pressure, the volume occupied by a fixed mass of gas is directly proportional to its thermodynamic temperature this

Figure: Charles Law explainDirectly proportional relationship can be written as:VTOr, V/T=kwhere:V is the volume of the gasT is the temperature of the gas (measured in Kelvin).k is a constant.This law explains how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:V1/T1=V2/T2 or, V2/V1=T2/T1 or, T2V1=V2/T1 (3)Example: In hot season some time the tire become puncture because incising the temperature the volume also incise. For that the tire becomes puncture. It is the example of Charles Lawb) (i)Thrust Momentum Thrust: If the condition (area A, pressure P and velocity V) at the engine intake and exhaust are designated with the subscripts 'a' and 'j' respectively, then a mass of 'air (m) flowing per unit time through the engine will experience an: Increase in velocity = (Vj - Va). The momentum gain = m (Vj - Va), where m is the mass flow rate of air through the engine under steady condition. = rate of change of momentum= Applied force to the air mass flow as per Newtons 2nd Law of motion. According to Newton's Third Law, for every action, there is an equal and opposite reaction. Therefore as the air mass is accelerated through the engine, there will be an equal and opposite reaction (thrust) acting on the engine in the forward direction. Since the force is obtained due to a change in momentum of the air, this is called the Momentum Thrust of the engine. Momentum Thrust = m (Vj - Va) = m Vj - m VaConsideration may be given to the fuel mass flow rate (mf) that is mixing with air at combustion chamber with initial zero velocity relative to the engine, the thrust equation may be modified as follows: Momentum Thrust = (m + mf )Vj m Va = m (Vj- Va ) + mf Vj (4) Pressure Thrust: Considering the engine as a physical body in the air, it will be subjected to pressures acting at the intake (Pa) and the exhaust (Pj). The pressures will produce a pressure force of (Pj - Pa)Aj acting on the engine in the forward direction. This force is the result of an unbalanced pressure and is called the Pressure Thrust. Hence, Pressure Thrust = (Pj - Pa)AjIn most practical cases, pressure thrust exists because all of the pressure of the engine cannot be converted into velocity at the exhaust (i.e. gas does not fully expanded to atmospheric pressure). It becomes more pronounced and significant as the speed of the aircraft becomes supersonic and the exhaust nozzle becomes choked. At choked nozzle condition, velocity of exhaust gas cannot exceed M =1, unless it is a C-D duct and invariably there remains significant amount of unconverted pressure. (4) Total Thrust: The Total Thrust on a jet engine will be the sum of the momentum thrust and the pressure thrust. Total Thrust = Momentum Thrust + Pressure Thrust Tt = m (Vj- Va ) + mf Vj + (Pj Pa) Aj In actual practice, fuel flow is usually neglected when net thrust is computed, because the weight of the air that leaks from various section of the engine is assumed to the approximately equivalent to the weight of the fuel consumed. Therefore, the final equation for computing the thrust by a turbo-jet engine becomes: Tt = m (Vj- Va ) + (Pj Pa) Aj This is a general thrust equation and is applicable for all kinds of jet propulsion (4)

(ii)Break Horse power: Horsepower at the output shaft of an engine, turbine, or motor is termed brake horsepower or shaft horsepower, depending on what kind of instrument is used to measure it. Horsepower of reciprocating engines, particularly in the larger sizes, is often expressed as indicated horsepower, which is determined from the pressure in the cylinders. Brake or shaft horsepower is less than indicated...

The actual horsepower a fan requires because no fan is 100% efficient. BHP can be expressed asPBHP= qdpinWG / 6356 Where,PBHP= Brake Horse Power (hp)= efficiency(5)

(iii)Thrust horse power: The force-velocity equivalent of the thrust developed by a jet or rocket engine.The thrust of an engine-propeller combination expressed in horsepower; it differs from the shaft horsepower of the engine by the amount the propeller efficiency varies from 100%. (naval architecture) The product of the speed of advance of a marine propeller through the water, in feet per second, and the thrust delivered by the propeller, in pounds, divided by 550.THP =( Forward velocity of aircraft Thrust) /550

(iv)Equivalent shaft horse power: A measure of the efficiency of a turboprop engine. It is the number of pounds of fuel burned per hour to produce one equivalent shaft horsepower (ESHP) and is found by dividing the fuel flow, in pounds per hour, by the ESHP)(6)

Reference: 1) http://teachertech.rice.edu/Participants/louviere/Newton/2) https://en.wikipedia.org/wiki/ Boyles Law )3) https://en.wikipedia.org/wiki/Charles's_law4) (83-UnitGas Turbine Engine and Propellers, Week 1.page-09, 10, 11)5) http://www.britannica.com/EBchecked/topic/77449/brake-horsepower6) http://www.datwiki.net/page.php?id=3196&find=ESHP%20(equivalent%20shaft%20horsepower)&searching=yes

Figure: Main part of Gas turbine Engine

Mainly gas turbine engine has three parts; there are Compressor, Combustion Chamber and turbine

Compressor: The compressor is the first component in the jet engine core. The compressor is made up of fans with many blades and attached to a shaft. The compressor squeezes the air that enters it into progressively smaller areas, resulting in an increase in the air pressure. This results in an increase in the energy potential of the air. The squashed air is forced into the combustion chamber. In Compressor temperature incises at 65 -70 degree. (7) Combustor - In the combustor the air is mixed with fuel and then ignited. There are as many as 20 nozzles to spray fuel into the airstream. The mixture of air and fuel catches fire. This

provides a high temperature, high-energy airflow. The fuel burns with the oxygen in the compressed air, producing hot expanding gases. The inside of the combustor is often made of ceramic materials to provide a heat-resistant chamber. The heat can reach 2700.(9)Turbine - The high-energy airflow coming out of the combustor goes into the turbine, causing the turbine blades to rotate. The turbines are linked by a shaft to turn the blades in the compressor and to spin the intake fan at the front. This rotation takes some energy from the high-energy flow that is used to drive the fan and the compressor. The gases produced in the combustion chamber move through the turbine and spin its blades. The turbines of the jet spin around thousands of times. They are fixed on shafts which have several sets of ball-bearing in between them.(9)Reference: 9) http://inventors.about.com/library/inventors/blhowajetengineparts.htm

Task 04 a) Working cycle of the gas turbine engine: The working cycle upon which the gas turbine operates is known as the Brayton cycle. This cycle is illustrated in Figure 1, and consists of the following processes:

Figure:1

12 Frictionless adiabatic compression where at point 1 atmospheric air is compressed along the line 1-2.

23 Frictionless constant pressure heating. Where heat is added from the burnt fuel at constant pressure, thus increasing volume.

34 Frictionless adiabatic expansion of the gases through the turbine.

41 Frictionless constant pressure heat rejection, through the jet pipe nozzle to atmosphere.

To ensure maximum thermal efficiency (see explanation of the second law) we require the highest temperature of combustion (heat in) to give the greatest expansion of the gases. There has to be a limit on the temperature of the combusted gases as they enter the turbine, which is dictated by the turbine materials. Additional cooling within the turbine, helps maximize the gas entry temperature to the turbine.

Description of gas turbine engine working cycle: A gas turbine engine, as mentioned earlier, consists of three principal parts or sections: compressor, combustion chamber and turbine. These are the basic parts of the engine to which an air intake and an exhaust system with propelling nozzle (with or without an afterburner) are to be attached. In the Compressor chamber the pressure is increases. Compressor section ensures availability of adequate mass of pressurized air in the combustion chamber. In the combustion chamber, heat is added by burning fuel. A large number of heat produce there. The combustion gas with high energy passes through the turbine section. Turbine extracts energy required to give drive input to the compressor, fan, propeller and the gearbox as the case may be, and the gas with remaining energy is expanded across the propelling nozzle, achieving high velocity issuing as a kinetic-jet resulting in jet-reaction to the engine.

The relationship between pressure temperature and velocity: Air is normally thought of in relation to its temperature, pressure, and velocity. Within a gas turbine engine the air is put into motion and another factor must be considered, velocity. Consider a constant airflow through a duct. As long as the duct cross-sectional area remains unchanged, air will continue to flow at the same rate (disregard frictional loss). If the cross-sectional area of the duet should become smaller (convergent area), the airflow must increase velocity if it is to continue to flow the same number of pounds per second of airflow (Bernoulli's Principle). In order to obtain the necessary velocity energy to accomplish this, the air must give up some pressure and temperature energy (law of conservation of energy). The net result of flow through this restriction would be a decrease in pressure and temperature and an increase in velocity. The opposite would be true if air were to flow from a smaller into a larger duct (divergent area); velocity would then decrease, and pressure and temperature would increase.

_

Figure: A closed-cycle gas-turbine engine.

_The T-s and P-v diagrams of an ideal Brayton cycle are shown :

T-s and P-v diagrams ()+ ()=

=1-=1-=1-(8)

b)Relationship of pressure temperature ,volume and velocity : Ideal Gas Law:

PV = nRT where P is pressure and T is temperature. Therefore, pressure and temperature are directly related.That is to say, as P increases, so does T. Note that this is talking about the pressure within the gas.

Density is: D = M/V where M is mass and V is volume. Plug that into the ideal gas law above and you get:

PM/D = nRT so the D is on the bottom and therefore is inversely proportional to both temperature and pressure.

Velocity v: According to the Bernoulli's principle velocity is inversely proportional to the pressure, so v

In other words, as temperature and/or pressure goes up, the density will go down. And vice-versa. Velocity incise pressure descries.

Reference: 8) http://inventors.about.com/library/inventors/blhowajetengineparts.htm

Reference: (1) http://teachertech.rice.edu/Participants/louviere/Newton/(2) https://en.wikipedia.org/wiki/ Boyles Law )(3) https://en.wikipedia.org/wiki/Charles's_law(4) (83-UnitGas Turbine Engine and Propellers, Week 1.page-09, 10, 11)(5) http://www.britannica.com/EBchecked/topic/77449/brake-horsepower(6) http://www.datwiki.net/page.php?id=3196&find=ESHP%20(equivalent%20shaft%20horsepower)&searching=yes(7) http://inventors.about.com/library/inventors/blhowajetengineparts.htm(8) http://www.google.com.bd/#sclient=psyab&q=The+working+cycleName: Haraykrishna Biswas Unite title: Principle of Gus Turbine propulsion ID: ABC12-09-05 Assignment no: 01