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3.3.6 · D5 · HinglishRocket Propulsion

Question bank — Thrust equation F = ṁv_e + (P_e − P_a)A_e — derivation

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3.3.6 · D5 · Physics › Rocket Propulsion › Thrust equation F = ṁv_e + (P_e − P_a)A_e — derivation

Yeh page ek misconception minefield hai. Neeche har line ek trap hai jo parent thrust equation invite karti hai. Prompt padho, apne dimaag mein ek jawab pakko, phir reveal karo. Agar tumhara gut aur reasoning mein disagreement ho — wahi gap exactly fix karne wali cheez hai.

Shuru karne se pehle, ek shared vocabulary reminder taaki kuch bhi unexplained na rahe:

  • (padho "m-dot") — har second mein rocket se kitne kilograms ka exhaust nikalta hai.
  • — woh exhaust rocket se measured kitni speed se nikalta hai, ground se nahi.
  • — nozzle ke munh par (the "exit plane") gas pressure.
  • — surrounding air ka pressure ("ambient").
  • — us nozzle ke munh ka area.
  • Momentum thrust ("mass phenkne" wala part). Pressure thrust ("pressure imbalance" bonus).

True or false — justify

Agar ho toh thrust zero hai
False. Sirf pressure term gayab hoti hai; momentum thrust puri tarah se maujood rehti hai. Asliyat mein (perfect expansion) us altitude ke liye best-case thrust hai, zero thrust nahi.
Ek rocket vacuum mein thrust produce nahi kar sakta kyunki push karne ke liye kuch nahi hota
False. Yeh apne exhaust ke against push karta hai, air ke nahi. Vacuum mein () pressure thrust ban jaati hai, toh wahi engine asliyat mein sea level se zyada thrust banata hai.
Overexpansion hamesha total thrust ko momentum thrust se neeche le aata hai
True. Overexpanded ka matlab hai, toh aur total , se neeche baithta hai. Atmosphere exit gas ko peeche dhakka de raha hai.
ko double karte hue ko half karne par momentum thrust unchanged rehti hai
True. ek product hai, toh . Lekin note karo ki pressure term aur required nozzle geometry change ho sakti hai — sirf momentum thrust preserve hoti hai, total thrust zaruri nahi.
Pressure thrust negative ho sakti hai
True. Jab nozzle overexpanded ho (), toh negative hota hai, isliye ambient air jo exit gas par push karti hai woh ek sachchi backward force produce karti hai jo thrust khaati hai.
Ambient pressure ek push contribute karta hai aur isliye rocket ki madad karta hai
False. Ek closed body par saare ambient pushes zero mein cancel ho jaate hain. Sirf ek unbalanced jagah hai — open exit — jahaan inward/backward push karta hai — isliye yeh mein minus ke roop mein appear hota hai.
Thrust exhaust ki ground se measured speed par depend karta hai
False. Momentum bookkeeping ke baad jo bachta hai woh hai — gas ki speed rocket ke relative. Pad par khada ek rocket () phir bhi full thrust rakhta hai — yeh proof hai ki ground speed irrelevant hai.
Ek fixed chamber ke liye, rocket jaise-jaise thinner air mein climb karta hai thrust smoothly badhti rehti hai
True (roughly). Jaise altitude badhti hai, girta hai, toh badhta hai. Thrust apni vacuum value ki taraf increase hoti hai — isliye first-stage thrust liftoff ke baad climb karti hai.

Spot the error

"Thrust ."
Sign ulta hai. Exit gas par forward push karta hai, ambient back push karta hai, toh forward-positive term hai, nahi.
"Vacuum mein, poori pressure term drop karo kyunki koi air nahi hai."
==Galat — sirf drop karo, nahi.== Vacuum mein , toh term ban jaati hai, jo positive aur sabse badi hoti hai. Exit gas ka apna pressure abhi bhi forward push kar raha hai.
"Perfect expansion maximum thrust deta hai, toh hume hamesha har altitude par ke liye design karna chahiye."
Overstated. Ek fixed nozzle ka ek exit area hota hai, toh yeh sirf ek altitude par perfectly expanded ho sakta hai. Baaki jagah yeh over- ya underexpanded hoga; "" local optimum hai, koi aisi design nahi jo poore raaste hold ho sake.
"Kyunki , effective exhaust velocity bas hai."
Incomplete. . Yeh ke barabar sirf tab hota hai jab pressure term zero ho (perfect expansion). Warna pressure contribution ko absorb karta hai.
" ke units kg·m/s hain, yani momentum, toh yeh force nahi ho sakta."
Units galat gine gaye. kg per second hai, toh hai . Yeh momentum delivery ki ek rate hai, jo ek force hai.
"Zyada exhaust pressure hamesha acha hota hai, toh hum ise jitna bada ho sake utna chahte hain."
Trap. badhane se pressure term help karta hai lekin iska matlab usually hota hai ki gas kafi expand nahi hui, toh kam hai. Real design exit pressure ko exit velocity ke against trade karta hai; sachcha optimum target altitude par hai.

Why questions

Ambient pressure equation mein sirf nozzle exit par kyun appear karta hai, aur kahin nahi?
Kyunki ek uniform pressure ko ek closed surface par integrate karne par net force zero milta hai. Rocket ki surface har jagah closed hai siwaay open nozzle mouth ke, toh sirf wahan hi ambient/exit mismatch ke roop mein bachta hai.
Hum (rocket ke relative) kyun use karte hain aur ground-frame exhaust velocity kyun nahi?
Momentum balance mein matter ke usi chunk par kiya jaata hai; jab algebra clear hoti hai, ground velocity cancel ho jaati hai aur sirf relative ejection speed thrust term mein rehti hai. Thrust is baare mein hai ki gas rocket se kitni tezi se nikl rahi hai.
Ek rocket engine vacuum mein sea level se zyada efficient (per unit fuel) kyun hota hai?
Vacuum mein , toh pressure thrust apne maximum tak pahuncha jaata hai, ambient back-pressure se reduce hone ki bajaye. Usi ke liye zyada thrust ka matlab hai zyada effective exhaust velocity → better specific impulse. Dekho Specific Impulse.
Hum rocket ke liye sirf kyun nahi use kar sakte?
Kyunki rocket ka mass fuel jaalne ke saath badalta rehta hai. fixed mass assume karta hai; hume iske badle matter ke ek fixed chunk (rocket + about-to-be-ejected gas) ka total momentum par track karna padta hai. Dekho Conservation of Momentum.
Pressure thrust ko "bonus" kyun kaha jaata hai aur main effect kyun nahi?
Zyaatar engines ke liye ek order of magnitude dominate karta hai; pressure term ek chhoti correction hai (tens of kN vs hundreds of kN). Yeh matter karta hai, lekin thrust ko drive karne ki bajaye modify karta hai.
Newton's Third Law akele tumhe complete thrust equation kyun nahi deta?
Newton's Third Law momentum thrust deliver karta hai (gas peeche dhakela gaya, rocket aage dhakela gaya), lekin yeh exit gas mein bacha hua static pressure ke baare mein kuch nahi kehta. Pressure imbalance ek alag surface-force effect hai jo Newton's Third Law akele capture nahi karta.

Edge cases

Agar ho lekin chamber pressurized ho aur valve open ho toh thrust kya hoga?
Agar koi mass actually flow nahi kar raha, toh aur sirf jo bhi static pressure imbalance exit par maujood hai, hogi. Practice mein ek pressurized open nozzle turant flow produce karta hai, toh sach mein ke saath ek fleeting/idealized instant hai.
Perfect-expansion altitude par exactly thrust kya hota hai?
Pressure term exactly zero hai, toh — pure momentum thrust. Yeh woh smooth crossover point hai jahaan thrust reduced (neeche, overexpanded) se boosted (upar, underexpanded) mein transition karta hai.
Kya total thrust kabhi negative ho sakta hai?
Principle mein tabhi agar ek severe overexpansion ko itna negative kar de ki woh se bada ho jaye — practically impossible, kyunki itni extreme overexpansion pehle flow separation cause karti hai, jo flow ko change kar deti hai aur isse rokti hai. Toh real engines net negative thrust produce nahi karte.
(ek pinhole nozzle) par equation kya predict karta hai?
Pressure term , toh thrust . Lekin ek tiny exit flow ko bhi throttle karta hai aur ko limit karta hai, toh pinhole ek buri design hai chahe iska pressure term conveniently vanish ho jaaye.
Agar ho aur rocket high speed par move kar raha ho toh kya hoga?
Thrust abhi bhi hai, unchanged. Thrust rocket ki ground velocity par depend nahi karta — identical exhaust conditions wale fast-moving aur stationary rocket identical thrust produce karte hain.
Deep vacuum mein ke saath, ko aur kam karne se pressure thrust ki koi upper bound hai kya?
Nahi — zero se neeche nahi ja sakta, toh hi limit hai. Pressure thrust par max hoti hai; "aur zyada vacuum" se kuch gain nahi hota. Dekho Tsiolkovsky Rocket Equation ki yeh long-term velocity gain mein kaise contribute karta hai.
Recall Fast self-test (cover and recall)

Pressure term tab subtract hoti hai jab ::: nozzle overexpanded ho, , toh ambient air exit gas ko backward push karta hai. Rocket ki ground speed thrust ko affect karti hai ::: kabhi nahi — sirf relative exhaust speed thrust mein enter hoti hai. sirf exit par appear karta hai kyunki ::: ek uniform pressure closed surface par integrate karke zero deta hai; sirf open nozzle closure todata hai. Wahi engine, sea level vs vacuum ::: vacuum zyada thrust deta hai, kyunki pressure term ko tak maximize kar deta hai.

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