3.3.9 · D5 · HinglishRocket Propulsion
Question bank — Thrust coefficient C_F = F - (P_c A - ) — derivation
3.3.9 · D5· Physics › Rocket Propulsion › Thrust coefficient C_F = F - (P_c A - ) — derivation
True or false — justify
Doubling chamber temperature (same gas, same nozzle) roughly doubles .
False. mein appear hota hai ( ke roop mein) aur mein bhi ( ke roop mein), aur product mein cancel ho jaata hai; zyada hot gas thrust sirf aur $c^*$ ke through badhata hai, unchanged rehta hai.
dimensionless hai kyunki ye thrust ko ek genuine force se divide karta hai.
True. Pressure × area ek force hai, toh force/force hai — ek pure number, ek amplification factor.
Ek fixed engine ke liye, vacuum mein hamesha sea level ke se zyada hota hai.
True. Sea level ko pressure term se subtract karta hai; set karne se wo penalty hat jaati hai (ya ek bonus add hoti hai), toh vacuum strictly bada hota hai.
Agar ek nozzle perfectly expanded hai (), toh apne momentum term ke barabar hota hai.
True. Factor zero ho jaata hai, poora pressure term khatam ho jaata hai, sirf bachta hai.
kabhi bhi roughly se zyada nahi ho sakta.
False in general. Ceiling par depend karti hai: chote ke saath (jaise ) ; vacuum mein bada expansion practical values ko se upar push kar sakta hai.
Bada hamesha badhata hai.
False. Vacuum mein bada area hamesha help karta hai, lekin sea level par bahut bada nozzle ko over-expanded bana sakta hai (), toh negative pressure term gira deta hai.
Momentum term propellant ke gas constant par depend karta hai.
False. cancellation ke baad sirf aur pressure ratio bachta hai; bilkul gayab ho jaata hai.
Agar exit pressure zero ho jaaye (infinite expansion), toh pressure term bhi vanish ho jaata hai.
True. aur ke saath term ho jaata hai, aur apne purely momentum-set maximum tak pahunch jaata hai.
Do engines jinke paas same aur same pressure ratios hain unka same hoga chahe ek zyada hot, heavier-molecule propellant jalata ho.
True. sirf ratios aur geometry jaanta hai; propellant ka difference aur mein dikhta hai, nozzle report card mein nahi.
Spot the error
"Kyunki aur , ek bada engine zyada thrust nahi le sakta — coefficient capped hai."
Cap par hai, par nahi. Thrust ke saath scale karta hai; bada throat ya zyada chamber pressure ko freely badhata hai chahe fixed ho.
"Pressure thrust hamesha thrust add karta hai kyunki gas exit par baahir ki taraf push kar rahi hai."
Term hai: jab over-expanded ho () toh ambient wapas push karta hai, ise negative banata hai aur thrust ghatata hai.
"Main combustor ke andar static chamber pressure ko ke liye use karunga."
stagnation pressure hona chahiye (gas essentially at rest). Static aur stagnation values mix karne se isentropic relations toot jaate hain jo pane ke liye use hote hain.
" par depend karta hai kyunki main ko exit-velocity formula mein dekhta hun."
mein hai, lekin mein bhi ke through hai; product mein cancel ho jaata hai, toh mein koi nahi hai.
"Sea-level of impossible hai, toh measurement galat hai."
Impossible nahi — ek well-expanded, thoda under-expanded engine () ek positive pressure term gain karta hai aur high read kar sakta hai; number ek well-matched nozzle flag karta hai, koi error nahi.
" aur same performance measure karte hain, toh sirf ek chahiye."
Ye complementary hain: [[Characteristic Velocity c-star|]] combustion/propellant ko grade karta hai, nozzle ko grade karta hai. Unka product deta hai .
"Kyunki throat choked hai, thrust throat par set hai, toh exit conditions ke liye matter nahi karte."
Throat ko choked flow ke zariye fix karta hai, lekin momentum term phir bhi par depend karta hai (flow downstream kitna expand karta hai), aur pressure term ko chahiye.
Why questions
(throat), (exit) nahi, reference force mein kyun appear karta hai?
Kyunki jab flow choked hoti hai, poori tarah throat par set hoti hai; engine ki mass-flow capacity ka natural "size" hai, jisse ek clean reference force banta hai.
ko "nozzle report card" kyun kaha jaata hai?
Ye isolate karta hai ki nozzle shape aur expansion chamber pressure ko directed thrust mein kitni achhi tarah convert karta hai, is baat se independent ki propellant kitna hot ya heavy hai.
Momentum term sirf aur par kyun depend karta hai?
Energy conservation exit speed ko pressure ratio raised to se link karti hai, aur se divide karne ke baad har dimensional quantity (, ) cancel ho jaati hai, sirf ratio aur bachta hai.
Space engines bade bell nozzles kyun use karte hain jabki sea-level engines nahi?
Vacuum mein pressure term hamesha add karta hai, toh zyada area zyada deta hai; sea level par bahut zyada area over-expand karta hai aur ambient wapas push karta hai.
badhane se momentum-limit kyun girta hai?
Bada matlab gas expansion per apni internal energy kam release karti hai (zyada steep enthalpy drop chahiye), toh kam enthalpy directed kinetic energy mein convert hoti hai, ko lower cap karta hai. Dekho Nozzle Expansion Ratio Ae-over-Astar ki area kaise set karta hai.
bilkul alag sizes ke engines compare karne ke liye kyun useful hai?
Dimensionless hone ki wajah se, ye raw scale (, ) ko strip out karta hai aur ek pure efficiency grade deta hai — ek tiny thruster aur ek giant booster ko directly compare kiya ja sakta hai.
Thrust Equation naturally ek momentum part aur ek pressure part mein kyun split hota hai jab form karte hain?
Thrust khud hai; har piece ko se divide karne par wo split preserve hota hai, ek term mass-motion se aur ek unbalanced exit pressure se milta hai.
Edge cases
Exact optimum expansion point par, pressure term ka kya hota hai aur kya us ambient ke liye maximise hota hai?
Pressure term zero hota hai (), aur ek given ke liye ye maximum thrust deta hai — nozzle ambient ke saath perfectly matched hai.
Sea level par over-expanded nozzle ke liye, kya apne momentum term se neeche ja sakta hai?
Haan. pressure term ko negative banata hai, toh .
Jab expansion infinity tak jaaye () vacuum mein, ki limiting value kya hai?
Ye ke paas jaata hai, ek hard ceiling jo sirf se fix hoti hai.
Agar pressure ratio (essentially koi expansion nahi), toh momentum term kya karta hai?
Bracket ho jaata hai, toh — koi expansion nahi toh gas koi directed speed gain nahi karti aur nozzle koi momentum thrust produce nahi karta.
Kya physically possible hai ki total negative ho jaaye?
Sirf extreme over-expansion mein jahan bada negative pressure term ek chote momentum term ko overwhelm kare (flow separation — neeche definition dekho — aksar pehle intervene karti hai), toh practice mein positive rehta hai.
Throat par flow Mach 1 hai; kya iska matlab hai ki thrust throat par generate hoti hai?
Nahi. Throat set karta hai; high speed tak acceleration (aur isliye zyaatar thrust) downstream diverging section mein hota hai jahan gas expand karti hai. Dekho Specific Impulse Isp ki overall efficiency se kaise back-connect karta hai.
Recall Har trap ka one-line summary
sirf , , , par depend karta hai — ya par kabhi nahi; pressure term ek sign carry karta hai aur subtract kar sakta hai; aur coefficient ek nozzle grade hai, jabki thrust magnitude phir bhi ke saath scale karti hai.