A jet-engine thrust reverser to reduce an aircraft speed of...

A jet-engine thrust reverser to reduce an aircraft speed of $200 \mathrm{km} / \mathrm{h}$ after landing employs folding vanes which deflect the exhaust gases in the direction indicated. If the engine is consuming $50 \mathrm{kg}$ of air and 0.65 kg of fuel per second, calculate the braking thrust as a fraction $n$ of the engine thrust without the deflector vanes. The exhaust gases have a velocity of $650 \mathrm{m} / \mathrm{s}$ relative to the nozzle.

Transcript

00:01 Okay, so in this question we have a jet engine and this jet engine is moving at a speed of 200 km per hour.

00:12 Okay, this is the engine of jet and it's moving at 2 km 200 km per hour and it is also producing exhaust.

00:29 So this exhaust is actually the thrust that it is generating and for this exhaust it is consuming 50 kg.

00:38 Mass of air and 0 .65 kg of fuel and this exhaust gases are discharged at a rate of 650 meter per second.

00:54 Then at the time of stoppage we'll be using a deflector here.

01:00 This deflector is throwing this exhaust gases back into the channel and and this angle is 30 degree.

01:13 So the question asked about what would be the ratio of this breaking thrust without and breaking thrust with deflector.

01:26 Okay, so we'll calculate this step by step, we'll see what is required in this question.

01:32 First we'll calculate the initial case when the engine, when the thrust is in full throttle and there is a thrust by the air okay so we have here the exhaust that is actually generating the flow okay and causing the thrust so because of this thrust it is moving in the front direction so that thrust is actually contributing to the speed so that will be mass of fuel plus mass of air into the exhaust velocity so that velocity is six feet meter per second.

02:16 This is actually the back flow is actually causing the front motion and the resistance is provided by the air.

02:24 Okay, so that will be in negative direction and that is the mass of air is given as 50 kg and that 50 kg will be given at 200 kilometers per hour.

02:41 Since this is also in meter per second and here also we need it to be having in meter per second so we'll multiply it by thousand because this is a kilometer per hour so this will be multiplied by thousand and for r to convert it into seconds we'll multiply by 36000 so this will be the initial case when there is no deflector veins so the mass of fuel is 50 now mass of air is 50 mass of fuel is 0 .65 this will be multiplied by 650 subtracting that will be the mass of air into 200 into thousand divided by 3600 so step by step we'll calculate this out of the value 50 .65 into 650 that will be how much 3292 .5 minus this value this is 50 into 200 into thousand divided by 36 that gives you 27777 .77 so we'll be subtracting this from this we are getting 1314 .72 newtons...

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