Calculate Jet Engine Net Thrust (F(N))

[v_pino]

I was given some notes on aircraft performance that states the equation for finding the net thrust of a jet engine.

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It states (words in brackets are subscripts):

F(N) = m dot (air) + m dot (j) V(j) - m dot (air) V

F(N) = net thrust
m dot (air) = inlet mass flow
m dot (j) = fuel mass flow
V(j) = final velocity
V = initial velocity
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How is this equation obtained?

I know that Force = change in momentum / change in time

 

[rcgldr]

F(N) = m dot (air) + m dot (j) V(j) - m dot (air) V

I think this should be:

F(N) = (m dot (air) + m dot (j)) V(j) - m dot (air) V

This is obtained as follows (assumes average accelartion, ..., you'd really need to take the integral sum of all the affected components):

force = mass x acceleration = mass x (Vout-Vin)/(unit time) = (mass/(unit time)) x (Vout - Vin)

 

[v_pino]

Hi Jeff,

If I use F=ma, should I not get this:

( m dot (air) + m dot (j) ) ( V (j) - V )

thanks

 

[nucleus]

This is the way the formula is written in my book;
Gross Thrust (Static) F (gross) = m dot (V2-V1)
V2-V1 Final velocity – initial velocity.
F (net) = F (gross) – F (Drag)
F (Drag) is the ram drag or inlet momentum drag caused by forward speed effect. If engine is not moving forward F (net) = F (gross).
Adding fuel: F (net) = m dot (V2-V1) + m dot fuel V (f)
Note: fuel inlet velocity will be same as engine so no initial velocity. Some formulas do not include fuel flow effects because the effects of air leakage are approximately the same as fuel flow effects.

The fuel is added to mass air flow – if used.

Most nozzles are chocked and there is a formula for that I can give you if you are interested.

 

[FredGarvin]

It's simple...draw a control volume around an engine. The net force is the sum of all of the outgoing momentum minus the incoming momentum.

 

[rcgldr]

If I use F=ma, should I not get this:
( m dot (air) + m dot (j) ) ( V (j) - V )

Not quite, the initial fuel velocity is different than the initial air velocity. Using the plane as a frame of reference, the initial fuel velocity is zero:

force = mass x acceleration = mass x (Vout-Vin)/(unit time) = (mass/(unit time)) x (Vout - Vin)

F = mass x acceleration
F = (mass (air))(Vout - Vin)/(unit time) + (mass fuel (j))(Vout - 0)/(unit time)
let m dot = mass / (unit time)
F = ( m dot (air) ) ( Vout - Vin) + ( m dot (fuel) ) ( Vout - 0)