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### Jet Engine, Exhaust Air Velocity?

Posted: **Wed Mar 27, 2002 6:43 am**

by **Mr Spaceman**

Hi guys.

I know that Newton stated.... "every action has an equal and opposite reaction".

However, in the case of a 747-400 weighing 850,000 pounds and cruising at 500 knots, I doubt it's 4 RollsRoyce RB211-524 engines are blasting air out of their tailpipes at a velocity of only 500 knots to push the 747 forward at that speed.

So, can anyone give me an idea of how fast the exhaust gases/air is moving when it leaves a 747's RR jet engine? Or its other types of jet engines.

Is the speed of a jet engine's exhaust flow several thousand mph?

The RollsRoyce RB211-524 engine is rated at 58,000 to 60,000 lbs of thrust. How do you calculate the velocity of that thrust?

Specific or general info would be great.

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Photo © Chris Sheldon
Chris

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Wed Mar 27, 2002 7:03 am**

by **pikachu**

According to the JT-8D operating manual the velocity immediately behind the engine is 200 mph at take-off power.

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Wed Mar 27, 2002 7:09 am**

by **777236ER**

It's not just the velocity of the air that's important, but also the mass of the air moved.

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Wed Mar 27, 2002 9:09 am**

by **lehpron**

**Mr Spaceman**: I'm sure you are familiar with Newton's law F=ma, well this can be written in another way:

F=(mass [of fuel] per second)x(velocity [of exhaust])

Which gives you an idea of how much fuel is being burned at takeoff!

Is this formula used with liquid flow?:

F= (1/2)x(density of mass)x(cross sectional area)x(velocity)

^{2}x(coeff of thrust)

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Wed Mar 27, 2002 9:25 am**

by **Guest**

The Galaxy that I fly has P&W PW306A engines that produce 6,040 pounds of static thrust each. Just for grins I went to the pilot training manual and got the following information:

Exhaust velocity at engine exhaust nozzle = 613 knots @ 1052 F

" " " " " " " " at 150 feet = +/- 100 knots @ 94 F

" " " " " " " " at 200 feet = =/- 50 knots @ 85 F

Anyone for a $20.0 million kerosene powered hair dryer?

Jetguy

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Wed Mar 27, 2002 6:07 pm**

by **kaddyuk**

I thought that pressure came in here somewhere?

It all good saying that air comes out at 600kts but If there is no pressure difference, it wont get a 300ton aircraft moving anywhere fast will it?

I am not a mechanic so I am probably wrong but that is what I always though mattered?!?!

KaDdYuK

C Ya L8r

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Wed Mar 27, 2002 7:29 pm**

by **FredT**

T = mdot_air * ( (1 +f) * u_e - u_a) + (p_e - p_a) * Ae

T - thrust

f - fuel mass flow per second / air mass flow per second

mdot_air - air mass flow per second

u_e - exhaust air velocity

u_a - ambient air velocity (speed of aircraft)

p_e - pressure in the exhaust

p_a - ambient pressure

Ae - exhaust area

Usually (1+f) will be close enough to unity to be ignored and you strive to have p_e = p_a.

Cheers,

Fred

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Thu Mar 28, 2002 3:35 am**

by **wingscrubber**

The air comes out slower than you might think, you have to take into account the high temperature and pressure...

Jet engines can't accelerate air to supersonic speeds. Even afterburning engines, they merely heat the air, which raises the speed of sound in the jetpipe, so the engine can propel the aircraft at mach1+ without ever inducing supersonic flow in the engine. That's about as fast as it gets before you start talking about ramjets and rocket engines....

As forementioned in this chain, it's the mass of air moved, not the speed at which it's moved, that gives you your thrust.

Pete

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Fri Mar 29, 2002 12:05 am**

by **aeroguy**

I'd have to disagree that engines cannot accelerate air to supersonic speeds. Afterburning engines certainly accelerate the exhaust gases to supersonic speeds. This occurs despite the fact that the speed of sound of the exhaust gases has increased due to the high temperature. By considering an afterburning engine with a convergent-divergent exhaust nozzle on it, why would it need such a nozzle if the flow were only subsonic? The entire purpose of a convergent-divergent nozzle is to accelerate flow to supersonic speed. If that doesn't convince anyone, consider an exhaust plume from an afterburning engine at max augmented thrust in which shock waves are visible. Shock waves can only exist if supersonic flow is present.

As far as thrust is concerned, when you've got your simplified equation

Thrust = (mass flow of **air**)x(exhaust velocity)

mass flow and exhaust velocity are both very important to how much thrust is produced, not one or the other.

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Mon Apr 01, 2002 12:17 am**

by **EssentialPowr**

Aeroguy's post is excellent.

Let's see....exhaust velocity of 200 mph out of a JT8d at takeoff thrust? That's not even close. How would the a/c be able to exceed that velocity (200mph), which it certainly can... (DC9, 727 , whatever.)

Total thrust = mdot * v. As a corollary to this equation, exhaust velocity is always equal to or great than the a/c's speed.

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Mon Apr 01, 2002 4:11 am**

by **delta-flyer**

Just a couple of more thoughts to add....

Let's get back to first principles and do a little sanity check.... FredT and others gave a good "formula" for thrust / velocity, but here is the "rest of the story":

Newton's famous second law actually states that force is equal to the "rate of change of momentum". The familiar F=ma is only a special case of this.

Momentum = m.v (mass x velocity)

Rate of change of momentum = d/dt (m.v)

= v.dm/dt + m.dv/dt

(you need to know a bit of calculus to follow the above step)

In words, force is equal to mass flow rate (dm/dt) times velocity plus mass times acceleration (dv/dt). The second part, m.dv/dt = m.a (mass times acceleration) is the familiar form of Newton but is only true if there is no mass flow component.

Now, is 200 mph air velocity reasonable? Consider a control volume enclosing a moving aircraft at a single instant of time. The air in front of the a/c is at rest. The air behind the a/c is moving at 200 mph. The force exerted on the control volume is v.dm/dt, where v is 200 mph and dm/dt is mass flow. What is the mass airflow required to generate 60,000 lb thrust?

dm/dt = F/v = 60,000 lbf/293.3 ft/s = 204.8 lbf-s/ft

I use lbf to indicate pounds-force units. To get it into pounds-mass, multiply by g = 32.2 ft/s^2. This yields

dm/dt = 6595 lbm/s.

Is this reasonable for a large engine?

Actually, no. For a JT9D engine, the velocity behind the fan is 885 ft/s, while out of the turbine it is 1190 ft/s. This is at sea level, static conditions, at 43,500 lb thrust. The mass flows are 1248 lb/s at the fan, and 247 lb/s at the turbine.

What about pressure? It doesn't really matter! Velocity and pressure are related by the Bernouli equation: P = 0.5 rho.v^2, where rho is air density. If you take the air at 200 mph velocity and stick a wall behind it to make it stop, you will get a pressure rise according to half-rho-v-squared. If you integrate this pressure over a large area behind the a/c, you will get the same 60,000 pounds as you get with Newton. That's the beauty of physics -- everything is related, and there are many ways to get to the same result.

Cheers,

Pete

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Mon Apr 01, 2002 4:33 am**

by **EssentialPowr**

Nice job above.

I have been reluctanct to reference calc b/c in a lot of cases, fundamental math and associated basic physics are neglected. Since 200 mph doesn't pass a sanity check, and mass flow rate involves the mass of the working fluid, not fuel, that tends to imply a rather basic approach is necessary.

Having said this, I certainly don't want to offend anyone, (my apologies if I have) but I offer that even a basic text on a/c design would provide a solid basis for most of these topics. Thrust comes up regularly, and I always uses the thrust = mdot *v to establish the basics.

Cheers

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Tue Apr 02, 2002 3:23 pm**

by **SailorOrion**

Normally, at least the core exhaust nozzle has so-called "critical conditions", meaning the exhaust temperature IN THE NOZZLE is exactly Mach 1.

SailorOrion

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Wed Apr 03, 2002 2:22 pm**

by **delta-flyer**

SailorOrion, I suspect you are right, although the data I have on the JT9D engine does not show the maximum speed in the nozzle.

Just downstream the nozzle, the gas temp is 850F, so 1190 ft/s is way less than mach 1. But at the hp turbine, the speed is much higher (as is the temp), and since mach varies as the square root of temp and directly as speed, thus mach 1 is very likely there.

Essential, I appreciate the compliment above. I always like to do a quick sanity check, to verify my analysis. It has pointed up many an obvious error - misplaced decimal, multiplying vs. dividing by "g", etc.

Cheers,

Pete

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Thu Apr 04, 2002 4:19 am**

by **Mr Spaceman**

Hello gentlemen.

Thanks, for your replies. I'm sorry for my delayed response, a family emergency forced me to travel. I've been very busy.

Regarding your answers & discussions about my question I have this to add..."HOLY SMOKES!!!" I knew there would be some equations and formulas to mention, however, they're mostly over my head! Heavy duty math never did please my grey matter.

When I'm watching an airliner starting it's takeoff roll, I always find the hot, blurry column of air that's streaming out the engines impressive. Who doesn't? I was always sure that the "volume" of air being forced out the exhaust was an important part of the thrust, although I was surprised to read that this jet blast could be moving as slow as 200 mph in the case of a JT8D, even if the tricky magic of scientific equations can explain why.

As mentioned above, I understand that if you can see shock waves in an exhaust streak....that exhaust is moving super sonic. Or am I confused about that?

Click for large version

Photo © Andrew Brooks
Chris

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Thu Apr 04, 2002 9:01 am**

by **prebennorholm**

A few years ago I was walking on the footpath outside the northern fence of LHR, parallel and close to RWY 27R. An Aeroflot Il-86 took off.

It is of course an extremely loud aircraft. But I noticed that on top of the very loud roar there was the sound like hundreds of very loud firecracker explosions. The frequency was something like 2, 3 or 4 "firecrackers" per second, but highly irregular.

I cannot explain that firecracker sound as anything else but "sometimes" turbulences make it so that the core exhaust meets other air at supersonic speed.

My assumption was that poor blending of core and fan exhaust made the extremely high velocity and hot core exhaust interfere directly with still and cold air at "cold air supersonic speed". Even if the hot core exhaust left the nozzle at "hot air subsonic speed".

Could my assumption be correct?

Has anybody else noticed that firecracker sound from an Il-86 take-off?

Regards, Preben Norholm

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Thu Apr 04, 2002 5:46 pm**

by **katekebo**

go to this link and have fun

http://www.grc.nasa.gov/WWW/K-12/airplane/ngnsim.html

this will answer ALL your questions

### RE: Jet Engine, Exhaust Air Velocity?

Posted: **Thu Apr 04, 2002 6:17 pm**

by **SailorOrion**

As long as a nozzle is convergent, the velocity of the fluid cannot exceed Mach 1. To do so, it is required to have a Lavall-nozzle (convergent + divergent part)

SailorOrion