a) For a rocket with Isp = 500 s and cF_max = 2.0, what is the temperature in th
ID: 2086426 • Letter: A
Question
a) For a rocket with Isp = 500 s and cF_max = 2.0, what is the temperature in the combustion chamber [you may assume an exhaust gas with ? = 1.2 and R = 626 J/(kg K)]?
b) For a rocket with an initial weight of 25,000 kg and a propellant mass fraction of ? = 0.8, if over a 2 minute burn time a thrust of 680 kN is maintained using a conical expansion nozzle with a half angle of 45o , what is the exit velocity of the nozzle (you may neglect the pressure contribution to the thrust)? If you assume that the stagnation temperature is 4000 K and the gas specific heat at constant pressure is 3756 J/(kg K), what is the Mach number at the exit of the nozzle?
c) For a solid rocket booster to have a regressive burn, the burning surface area must i) get larger with time; ii) stay constant with time; iii) decrease with time?
d) In what liquid rocket cycle must the fuel be passed around the exhaust nozzle for the turbines driving the pumps to operate?
e) For a rocket with Isp = 500 s and an exit velocity of 5450 m/s but with a large particle solid phase in the exhaust, what is the percentage of the flow in solid phase?
Mearth = 5.975 x 1024 kg REarth = 6375 km G = 6.674 x 10-11 m3 /(kg s2 )
a) For a rocket with Isp500 s and max 2.0, what is the temperature in the combustion chamber [you may assume an exhaust gas with ? = 1.2 and R-626 J/(kg K)]? b) For a rocket with an initial weight of 25,000 kg and a propellant mass fraction of ? = 0.8, if over a 2 minute burn time a thrust of 680 kN is maintained using a conical expansion nozzle with a half angle of 45°, what is the exit velocity of the nozzle (you may neglect the pressure contribution to the thrust)? If you assume that the stagnation temperature is 4000 K and the gas specific heat at constant pressure is 3756 J/(kg K) what is the Mach number at the exit of the nozzle? c) For a solid rocket booster to have a regressive burn, the burning surface area must i) get larger with time; ii) stay constant with time; ) decrease with time? d) In what liquid rocket cycle must the fuel be passed around the exhaust nozzle for the turbines driving the pumps to operate? e) For a rocket with Isp500 s and an exit velocity of 5450 m/s but with a large particle solid phase in the exhaust, what is the percentage of the flow in solid phase?Explanation / Answer
Thrust coefficient, CF = ?[{2* ?2/( ?-1)}*{2/(?+1)}*{1 – (pe/pc)}] + [(Ae/At)*{( pe – pa)/ pc}] …(i)
Where, pe = exhaust pressure, pa = atmospheric pressure, pc = combustion chamber pressure, Ae = exhaust area, At = throat area
Tc/ Te = (pe/pc)(? -1)
Where, Tc = temperature at combustion chamber, Te = temperature at exhaust
Assume that pe = pa. Then the expression in equation (1) becomes
CF = ?[{2* ?2/( ?-1)}*{2/(?+1)}( ? +1/? -1)*{1 – (pe/pc) (? -1)/ ? }] = ?[{2* 1.22/( 1.2-1)}*{2/(1.2+1)} ( 1.2 +1/1.2 -1)*{1 – (pe/pc) (1.2 -1)/ 1.2}] = 2.24*(pe/pc)0.17 = 2.24*{( Tc/ Te)(1/0.2)} 0.17 = 2.24*{( Tc/ Te)0.85
Thrust, F = ISP*?*g; where, ? = mass flow rate, g = acceleration due to gravity
=> CF* At* pc = 2.24*{( Tc/ Te)0.85
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