Ye ek question bank hai parent topic ke liye. Neeche har line ek answer chhupati hai — right side cover karo, pehle apna guess lagao, phir reveal karo. Har answer tumhe reasoning deta hai, sirf verdict nahi.
Pehle traps mein jaane se pehle, hum har symbol scratch se build karte hain aur har picture draw karte hain jinpar answers rely karte hain. Kuch bhi skip mat karo — neeche ke reveals yahi assume karte hain.
Throat aur exit kahan hote hain, aur ϵ geometrically kya mean karta hai:
Ek nozzle teen states mein ho sakta hai — yeh single figure neeche ke aadhe reveals ka source hai. Exhaust plume ki shape aur wall-pressure trace dekho:
Ek rocket ki thrust hai
F=m˙ve+(pe−pa)Ae.
Pehla piece obvious momentum hai: m˙ kg/s ko peeche ve speed par phenkte ho. Lekin doosra piece kahan se aata hai? Control volume dekho — engine ke aas-paas bana box — aur har face par pressure ka hisaab lagao:
Hum kehte rehte hain "ϵMe set karta hai." Yahan actual law hai, isentropic flow mein mass conservation se:
AtAe=Me1[γ+12(1+2γ−1Me2)]2(γ−1)γ+1.
Ise ek machine ki tarah padho: geometry ϵ=Ae/At feed karo, aur yeh supersonic Me wapas deta hai. Yeh non-linear kyun hai — kyun ϵ ko chaar guna karne se Me muskil se hilta hai — woh neeche ki picture mein hai: bahut fast supersonic flow ke liye area, Mach number ke climb se kahin zyada tezi se balloon karta hai.
Ek baar jab Me (aur isliye pe) pata ho, to ideal exhaust speed energy conservation se milti hai: chamber mein hot pressurised gas apni thermal/pressure energy ko kinetic energy mein trade karti hai jab woh expand hoti hai.
ve=γ−12γRT0[1−(p0pe)(γ−1)/γ]
Chamber energy T0 (heat) aur R,γ (kaun sa gas) se set hoti hai; bracket woh fraction hai jo cash in hua, yeh govern karta hai ki pressure p0 se pe tak kitna gira. Jab pe→0 to bracket →1 aur vesaturate ho jaata hai — yeh neeche ke har "diminishing returns" answer ki root hai.
False. Over-expanded ka matlab hai gas bahut zyada expand ho gayi aur uska exit pressure ambient se neeche chala gaya, to pe<pa aur bahar ki hawa flow par peeche dhakelta hai.
Sea level par perfectly expanded nozzle poore space tak perfectly expanded rehta hai.
False. Ascent ke dauran ambient pa∼101 kPa se ∼0 tak gir jaata hai jabki ek fixed nozzle wahi pe rakhta hai; ek altitude match karna baaki sab par mismatch guarantee karta hai.
Extendable nozzle ek upper-stage engine ko sea level par bhi acchi thrust produce karne deta hai.
False. Stowed aur deployed dono states mein bahut zyada ϵ hota hai (≳100); aisa nozzle sea level par badly over-expanded hoga aur separate ho jaayega. Yeh kabhi bhi sirf near-vacuum mein fire hota hai.
Zyada expansion ratio exhaust velocity ko hamesha useful amount se badhata hai.
False.vep0,pe,T0,γ par depend karta hai aur pe→0 par saturate ho jaata hai: bracket [1−(pe/p0)(γ−1)/γ]→1, to extra ϵ se chhote aur chhote gains milte hain.
Extendable nozzle ki stowed (retracted) state sea-level performance dene ke liye exist karti hai.
False. Yeh launch ke dauran fairing/interstage ke andar length bachane ke liye exist karti hai. Engine dono states mein near-vacuum mein ignite hota hai.
Aerospike exhaust boundary ko poore ascent mein ambient pressure ke hisaab se khud adjust karne deta hai.
True. Exhaust plume jo open (spike) side par hota hai woh bahar ki hawa se bounded hota hai, to jab pa garta hai to woh apni shape khud-ba-khud adjust karta hai — ek fixed bell ke unlike continuous compensation deta hai.
Vacuum mein (pa=0) pressure-thrust term (pe−pa)Ae hamesha negative hota hai.
False.pa=0 ke saath yeh peAe≥0 ke barabar hai, to yeh non-negative hai aur thrust mein add karta hai; vacuum mein yeh kabhi negative nahi ho sakta.
Expansion ratio double karne se exit-Mach number double ho jaata hai.
False. Area–Mach relation strongly non-linear hai (dekho ϵ–Me curve); jaise ϵ21 se 84 (×4) jump karne par Me sirf ≈3.8 se ≈4.75 jaata hai.
Specific impulse Isp aur exhaust velocity same information carry karte hain (ek constant tak).
True.Isp=ve/g0, to Isp bas ve divided by fixed constant g0 hai; zyada ϵ jo ve badhata hai woh Isp ko identically badhata hai.
"ϵ=100 karo taaki nozzle vacuum mein perfect ho, aur bas kamzor sea-level thrust accept karo."
Error hai flow separation ko ignore karna: sea level par itna over-expansion bell ke andar shocks drive karta hai (three-state figure ka right panel), exhaust asymmetrically wall se detach ho jaata hai, aur side loads nozzle ko faad sakte hain — sirf "weak" thrust nahi.
"Kyunki ve∝ϵ, ϵ chaar guna karne se exhaust velocity double ho jaati hai."
Koi clean ϵ law nahi hai. Sahi ve=γ−12γRT0[1−(pe/p0)(γ−1)/γ] saturate hota hai; ϵ sirf indirectly enter karta hai pe set karke.
"Sea level par ek over-expanded nozzle thrust sirf isliye khota hai kyunki (pe−pa)Ae term negative hai."
Incomplete — negative pressure term ke aage, internal shocks flow separation aur unsteady vibration/structural loads cause karte hain, jo alag loss aur failure mechanisms hain.
"Extension structural mass proportional add karta hai kitna thrust woh recover karta hai, to yeh muskil se help karta hai."
Extension large radius par hota hai jahan pressure low hai, isliye yeh thin-walled aur light ho sakta hai; mass penalty, Isp gain ke relative chhota hai, isliye upper stages iska use karte hain.
"Aerospike efficient hai kyunki iska koi throat nahi hai, to koi shock losses kabhi nahi bante."
Aerospike mein bilkul throat hota hai (gas ko kahin supersonic hona hi padega). Iska advantage spike side par free boundary hai (bell-vs-spike figure dekho), throat ki absence nahi.
"Under-expanded matlab nozzle altitude ke liye bahut bada hai."
Ulta hai. Under-expanded (pe>pa) matlab nozzle bahut chhota hai / ϵ bahut kam hai — usne expand karna band kar diya jab pressure energy abhi baaki thi.
Atmospheric pressure over-expanded nozzle mein "exhaust ko andar crush" kyun karta hai?
Kyunki pe<pa, bahar ki hawa ka pressure flow ke pressure se zyada hai, boundary ko andar push karta hai aur oblique shocks banata hai jo flow ko wall se separate kar sakte hain.
Ek single fixed bell nozzle launch se orbit tak optimal kyun nahi ho sakta?
Kyunki matching condition pe=pa chahti hai ki pe girte hue pa ko track kare, lekin fixed geometry pe ko ek value par lock kar deti hai — yeh sirf ek altitude par sahi ho sakta hai.
Hum pe=pa kyun chahte hain na ki sabse bada possible pe?
Jab pe=pa ho to saari available pressure energy exhaust velocity mein convert ho chuki hoti hai; koi bhi bacha hua pe>pa woh momentum hai jo tumne extract nahi kiya, aur pe<pa back-pressure aur shocks ke zariye cost karta hai.
ϵ badhane se pressure-thrust term kyun shrink hota hai jabki momentum term badhta hai?
Zyada expansion pe gira deta hai (chhota (pe−pa)Ae) lekin us pressure ko zyada ve mein convert kar deta hai, to momentum thrust m˙ve badhta hai jab pressure term fade hota hai.
Aerospike ko "compensating" nozzle kyun kehte hain jabki extendable ko nahi (ascent ke across)?
Aerospike ka plume boundary poore climb ke dauran continuously pa ka response karta hai (bell-vs-spike figure); extendable nozzle sirf ek discrete change karta hai aur hamesha near-vacuum mein operate karta hai.
ϵ bada hone par exit-Mach number itna slowly kyun badhta hai?
Area roughly highly supersonic, nearly parallel flow ke geometric spread ke saath badhta hai, to har additional bit of Mach number squeeze karne ke liye enormous extra area chahiye — isliye ϵ–Me curve flat hoti jaati hai.
Thrust equation term (pe−pa)Ae exactly perfect expansion par kya hota hai?
Yeh zero ho jaata hai, to thrust purely m˙ve hoti hai — "cleanest" case jahan saari pressure energy already velocity mein ja chuki hai.
pa=0 (deep vacuum) par, ek longer nozzle kitna thrust add kar sakta hai yeh kya limit karta hai?
ve ka saturation jab pe→0: bracket [1−(pe/p0)(γ−1)/γ]1 tak approach karta hai (ve curve ka flat right end), to momentum thrust plateau karta hai aur sirf chhota peAe term shrink karta rehta hai.
Agar pe exactly 0 tak pahunch sake, to kya woh ideal nozzle hoga?
Sirf limit mein — iske liye infinite exit area (infinite ϵ) aur infinite length/mass chahiye hogi, to real designs wahan ruk jaate hain jahan added mass vanishing ve gain se zyada ho jaata hai.
High-ϵ upper-stage nozzle ko (galti se) sea level par fire karne ka danger boundary kya hai?
Severe over-expansion flow separation aur asymmetric side loads trigger karta hai bell ke andar, structural failure ka risk hota hai — isliye precisely yeh engines sirf tab ignite hote hain jab atmosphere thin ho chuki ho.
Deep vacuum mein pahunchne par aerospike ka advantage kya hota hai?
Compensation benefit fade hoti hai kyunki pa→0 ke saath har nozzle effectively same tarah under-expanded hota hai; aerospike ka edge varying-pressure lower atmosphere mein sabse bada hota hai.
Vacuum mein ideally under-expanded nozzle ke liye, pressure term help kar raha hai ya hurt?
Help kar raha hai — pa=0 aur pe>0 ke saath term peAe positive hai, halaanki yeh woh velocity represent karta hai jo tumne gain kar sakti thi agar flow aur expand karti.
Recall Build-up symbols par quick self-test
ϵ=Ae/At kya compare karta hai? ::: Wide exit area ko narrow throat area ke against — funnel kitna phailta hai.
ve kyun grow karna band kar deta hai jab pe→0? ::: Energy-cash-in bracket [1−(pe/p0)(γ−1)/γ]1 par top out kar jaata hai.
(pe−pa)Ae thrust term physically kahan se aata hai? ::: Woh ek hi nozzle face jahan ambient pressure cancel nahi hota — exit disc.
