## How the jet engine produce thrust ?

Thrust is the force which moves an aircraft through the air. Thrust is used to overcome the drag of an airplane, and to overcome the weight of a rocket. Thrust is generated by the engines of the aircraft through some kind of propulsion system.

Propulsion of a jet aircraft is accomplisshed by the principle of Newton’s 3^{rd} law; the principle of reaction: a jet gas exhausting at high velocity from a nozzle is the action which is accompanied by the reaction of forward motion of the aircraft. This reaction is termed to be the *thrust*.

The factors on which the thrust depends on are

- i) Mass of airflow through the engine
- ii) Exhaust velocity

These factors determine the momentum which is the product of mass and exhaust velocity. Any sudden variation in momentum a force is generated which is the underlying principle of jet propulsion giving rise to the *Thrust equation *or *Theorem of momentum*.

The Application is starightforward which allows us to calculate engine thrust easily with known engine boundary conditions, rather than having the knowledge of conditions within the engine.

__CALCULATION OF ENGINE THRUST__

**Step-1: **A control volume is to be defined as required for the momentum theorem.

**Step-2:** Forces acting on the boundaries are to be estimated such as at the open boundaries as of the passage of air through the components results in *pressure forces* whereas the solid boundaries as of the engine casing do not allow the airflow which results in *pressure & friction forces.*

The unknowns are the frictions forces which are also estimated to sum up to calculate the thrust, our main aim in the proceure.

The forces evaluated here are the *vector quantities* which has both magnitude and direction. Since thrust acts along the direction of flight, flow approaches the same direction, hence thrust is considered as -T

With the above assumptions, the other forces are resolved as follows:

Pressure force at entrance: +P_{0}A_{0 }( pressure force= pressure * Area)

Pressure forece at nozzle:( negative sign as in the direction of flight)

a)at area less exit of exhaust nozzle: -P_{0}(A_{0}-A_{9})

b) at exit area of exhaust nozzle: -P_{9}A_{9}

Thrust in the direction of flight: -T

Summing all the forces in the horizontal direcion; we obtain

Sum = P_{0}A_{0 }-P_{0}(A_{0}-A_{9}) -P_{9}A_{9 }-T

Sum = A_{9}(P_{0}-P_{9}) -T

**Step-3:** Determination of timewise variation of momentum which is equal to the sum of all forces

The time variation with momentum arises as the product of ‘*mass divided by time*‘ and ‘*exhaust velocity*‘. The term mass divided by time is the air flow passing through the engine at given time i.e., *‘mass flow rate’*. Hence the time variation of momentum is a product of mass flow rate and exhaust velocity which is exclusively valid only for the engines at rest i.e., before taking off the flight.

In the flight at velocity v_{0} , the airflow already carries an initial momentum while approaching the engine which is intake momentum ‘ṁ * v_{0}‘. this value has to be deducted while calculating thrust.

From the above considerations the thrust equation is assumed in a simplest form as follows:

**-T = ṁ (c _{9}-c_{0}) + A_{9 }(P_{9}-P_{0})**

**ṁ **is mass flow rate in kg/s

**c _{9}** is the exhaust velocity in m/s

**c _{0}** is the intake velocity in m/s

**p** is static pressure in N/m^{2}

**A** is the area** _{ }**in m

^{2}

**subscript 0 **is intake station

**subscript 9** is exhaust station

- Engine design process ends with sizing of the engine to achieve the required thrust for a given airflow (ṁ) through the engine, at the design point.
- When a power plant is installed or attached to the body of the aircraft and flown with it the Installed thrust (T
_{F}) as experienced by the aircraft, comes out to be different from the design uninstalled thrust(F) computed or bench tested for the isolated engine. - The difference between T
_{F }and F is often quite significant and may vary from one operating point to another of the engine or the aircraft.

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