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Homework answers / question archive / Starting from the definition of Specific Enthalpy, ? = ? + ??, show that:     ?     ??   = ?−1 ?           Explain the meaning of the word “Adiabatic” and give an example of non-adiabatic flow in the engine

Starting from the definition of Specific Enthalpy, ? = ? + ??, show that:     ?     ??   = ?−1 ?           Explain the meaning of the word “Adiabatic” and give an example of non-adiabatic flow in the engine

Mechanical Engineering

  1. Starting from the definition of Specific Enthalpy, ? = ? + ??, show that:

 

 

?

 

 

??

 

= ?−1

?

 

 

 

 

 

  1. Explain the meaning of the word “Adiabatic” and give an example of non-adiabatic flow in the engine.

 

  1. Air flowing through a control volume is used to drive an output shaft. If the air enters at a static temperature of 500 K and a velocity of 250 m/s and leaves at a total temperature of 400 K, calculate the specific power output down the shaft, ensuring that you include the appropriate units in your answer.

 

 

  1. At 7km ISA conditions, air is simulated at Mach 2 and passes through a normal shockwave.

 

    1. Calculate the static pressure and velocity of the flow in units of metres per second after the shock wave.                                                                   

 

    1. Calculate the change in specific entropy across the shockwave. Make sure you include the appropriate units in your answer.                               

 

  1. Explain the different purposes of primary, secondary and tertiary air within the combustion chamber.

 

 

 

 

End of Part A Continue to Part B

 

 

Part B

Answer any two questions from Part B

 

  1. An aircraft flying at an altitude of 9 km at Mach 0.75 in ISA conditions has an engine which is producing 45 kN of thrust when the mass flow rate of air through the engine is 40 kg/s and the fuel to air ratio is 0.06. Assume that the exit pressure is equal to the ambient pressure.

 

  1. Calculate the thrust specific fuel consumption, giving your answer in units of hr-1.

 

  1. Calculate the flow exit velocity.                            

 

  1. Calculate the thermal efficiency.                         

 

  1. Calculate the propulsive efficiency.                    

 

  1. Calculate the overall efficiency.                                                   

 

  1. In a convergent divergent nozzle:
  1. Explain what happens to the subsonic air flow if it passes through a convergent nozzle.                                                                         
  2. Explain why subsonic air passing through a convergent nozzle cannot accelerate past Mach 1, illustrate your answer with suitable diagram and data from formula sheet.                                                                
  3. Air at a static temperature of 300K and static pressure of 400 kPa enters a convergent divergent nozzle at a velocity of 250 m/s. The area of the nozzle throat is 64% of the nozzle exit.

 

    1. Calculate the total temperature and pressure of the flow entering the nozzle.                                                                            
    2. Calculate both the maximum ambient pressure at the nozzle exit which generate supersonic flow at the exit and the flow Mach number generated.                                                             

iii         Calculate the temperature and pressure at the throat for the flow generated in part ii above.                                          

 

 

 

 

 

 

Continued…

 

 

 

 

 

  1. An experiment in the wind tunnel is set up to produce conditions where the flow of air is travelling at Mach 2 at an altitude of 9km ISA. An oblique shockwave is formed on a wedge with a half angle of 15°.

 

 

  1. Determine the total temperature and total pressure upstream of the shockwave.

 

 

  1. Determine the Mach number of the flow downstream of the shockwave.

 

 

  1. Determine the static temperature, total pressure, static pressure and flow velocity downstream of the shockwave.                                                    

 

 

 

 

  1. Rockets

 

  1. The propulsion requirements for space vehicles are frequently expressed in terms of the Velocity Increment that the propulsion system must supply. Explain how the Velocity Increment is calculated, giving details of the energy components that it is made up from.

 

 

  1. A spacecraft is to be designed to deliver a 500 kg satellite payload in a low earth orbit for which the required velocity increment is 9.140 km/s. The planned propulsion system for the rocket engine has a specific impulse of 310.91s for single stage. Calculate the velocity increment for the single stage launch and then calculate the difference in initial take-off mass of the spacecraft if a single stage rocket is used compared to that of a two-stage rocket. In both cases, assume that the dead-weight ratio is 3%. For the two-stage rocket, assume that half the velocity increment is delivered by each stage. You are to neglect gravitational and drag effects.

 

 

 

End of Part B. End of Question Paper

 

Formula Sheet – Aeroengines & rocket Science

ISA Table

 

H

T

P

r

a

n

m

km

K

N.m-2

kg.m-3

m.s-1

m2.s-1

N.s.m-2

0

288.2

1.0133E+05

1.2252

340.3

1.4634E-05

1.7930E-05

1

281.7

8.9866E+04

1.1117

336.4

1.5837E-05

1.7607E-05

2

275.2

7.9480E+04

1.0065

332.5

1.7169E-05

1.7280E-05

3

268.7

7.0088E+04

0.9090

328.5

1.8647E-05

1.6950E-05

4

262.2

6.1616E+04

0.8190

324.5

2.0290E-05

1.6617E-05

5

255.7

5.3993E+04

0.7359

320.5

2.2122E-05

1.6280E-05

6

249.2

4.7153E+04

0.6594

316.4

2.4170E-05

1.5939E-05

7

242.7

4.1032E+04

0.5892

312.2

2.6466E-05

1.5593E-05

8

236.2

3.5571E+04

0.5248

308.0

2.9046E-05

1.5244E-05

9

229.7

3.0714E+04

0.4660

303.8

3.1955E-05

1.4891E-05

10

223.2

2.6408E+04

0.4123

299.4

3.5246E-05

1.4534E-05

11

216.7

2.2605E+04

0.3636

295.0

3.8980E-05

1.4172E-05

12

216.7

1.9308E+04

0.3105

295.0

4.5638E-05

1.4172E-05

13

216.7

1.6491E+04

0.2652

295.0

5.3434E-05

1.4172E-05

14

216.7

1.4085E+04

0.2265

295.0

6.2560E-05

1.4172E-05

15

216.7

1.2030E+04

0.1935

295.0

7.3246E-05

1.4172E-05

16

216.7

1.0275E+04

0.1653

295.0

8.5756E-05

1.4172E-05

17

216.7

8.7763E+03

0.1411

295.0

1.0040E-04

1.4172E-05

18

216.7

7.4959E+03

0.1206

295.0

1.1755E-04

1.4172E-05

19

216.7

6.4024E+03

0.1030

295.0

1.3763E-04

1.4172E-05

20

216.7

5.4684E+03

0.0879

295.0

1.6114E-04

1.4172E-05

 

Data:

 

1bar = 105 N/m2

Patm = 1.01325x105 Pa

Air density = 1.2252 kg/m3

 

? (??????) = ?° (???????) + 273               ????????? = ?????? + ??????

For air:

γ = 1.4, R= 287 J/kg.K, CP= 1004 J/kg K

For the combustion products:

γ = 1.3, CP= 1140 J/Kg K, R=283 J/Kg.K

The Lower Calorific Value of hydrocarbon aviation fuel: hPR= 45,000KJ/kg

Thermodynamics:

1 ??? = 100,000 ??             1 ??? = 101,325 ??

 

Ideal Gas

 

?? = ???                 ?? = ??                     Polytropic process: ??? = ????????

 

Adiabatic process: ??? = ????????

 

 

Work Done

 

 

? = ?2 ???

?1

 

Isothermal:

 

 

Polytropic:     ? = ?1?1−?2?2

?−1

 

?2

 

? = ?1?1?? ( )

?1

 

Specific Heat Capacities

 

 

??

 

= ??

??

 

??

 

= ??

??

 

? = ??

??

 

??

 

??

 

= ?

 

 

Non Flow Energy Equation

 

? − ? = ??             ? − ? = ??

 

 

Steady Flow Energy Equation

 

 

?? − ?? = ?? + ??? + ???

 

 

 

?? − ?? = ?? (? + ?2 + ??)

2

 

 

 

???

 

− ?? (? + ?2 + ??)

2

 

 

 

??

 

Where ? = ????????

 

 

?? = ???        ? = ? + ??    or         ? = ? + ??

 

 

Second Law of Thermodynamics

 

2 ??

?? = ?2 − ?1 =

1        ?

 

 

Gibbs Equation:

 

 

 

 

 

Isentropic Relationships:

 

 

??? = ?? − ??? = ?? + ???

 

 
 
 

 

 

 

?2 =

?1

 

 

?2 ( )

 

 

?−1

 

1

?

 

 

 

 

 

2

?

?2 − ?1 = ???? (

?1

 

 

) − ? ?? (

 

 

?2

?1

 

 

)     (Ideal Gas Only)

 

 

 

Thrust Equation:

? = (??0 + ??? )? − ??0?0 + (?? − ?0)??

 

 

 

 
   
 

 

Speed of Sound:                                          ? = √???

Mach number:                                                 ? = ?

?

 

Total Temperature:                            ??

Isentropic Area Ratio:

 

 

 

 

 

Mass Flow Parameter:

 

= (1 + ?−1 ?2)

2

 

 

 

 

 

Normal Shock Relations:

Subscript 1 refers to conditions before the shock and 2 to conditions after the shock.

 

 
 
 

 

 

Engine Efficiencies:

Propulsive efficiency:

 

 
 
 

 

Thermal efficiency:

 

 
 
 

 

 

Overall efficiency:

?? = ?? × ??

 

 

 

 

Rockets

Effective Exhaust velocity:

 

 

??

 

 ??? 

=

?? ????

 

 

 

(??  ??)??

 

? = ?? +

 

 

 

???

 

Specific Impulse:                                             ???

 

= ?

?? ?

 

 

 

 

?                           ?0

 ?2

Orbital speed:                                                 ? = √?

??+?

Velocity increment:

 

 
 
 

 

 

Table for gas flow

Massey, B.S., Mechanics of fluids, Spon press, 9th Edition, 2012

 

 
   
 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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