## 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 3rd 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

1. i) Mass of airflow through the engine
2. 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:  +P0A0 ( pressure force= pressure * Area)

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

a)at area less exit of exhaust nozzle:  -P0(A0-A9)

b) at exit area of exhaust nozzle: -P9A9

Thrust in the direction of flight:  -T

Summing all the forces in the horizontal direcion; we obtain

Sum =  P0A0 -P0(A0-A9) -P9A9 -T

Sum = A9(P0-P9) -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 v0 , the airflow already carries an initial momentum while approaching the engine which is intake momentum ‘ṁ * v0‘. 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 (c9-c0) + A(P9-P0)

is mass flow rate in kg/s

c9 is the exhaust velocity in m/s

c0 is the intake velocity in m/s

p is static pressure in N/m2

A is the area  in m2

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 (TF) 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 TF and F is often quite significant and may vary from one operating point to another of the engine or the aircraft.