3.3.38 · D1Solid rocket Isp — grain properties se derivation
Ek solid rocket ek shaped fuel ka block hota hai jo layer by layer jalta hai, solid ko hot gas mein convert karta hai jo nozzle se bahar jaati hai. Har second kitni gas banti hai (thrust) — yeh fuel surface ki shape se decide hota hai, lekin woh gas kitni fast bahar jaati hai (efficiency, jise I s p chemistry aur nozzle se decide hota hai. Yeh dono ideas alag-alag boxes mein rehte hain, aur inhe alag samajhna hi is poore subject ka point hai.
Parent derivation padhne se pehle, har letter ke peeche ek picture honi chahiye. Yeh page unhe ek-ek karke banata hai, har ek pichle pe tikaa hua. Yahaan kuch bhi assumed nahi hai — hum "rate kya hota hai" se shuru karte hain.
Definition Rate (kuch cheez har second)Rate matlab hai "koi cheez har second kitni hoti hai." Agar ek tap 2 2 L/s m ˙
Dot notation pe thoda rukna zaroori hai, kyunki parent ise baar baar use karta hai.
Definition Dot ka matlab hai "per second"m ˙ rate , kilograms per second mein (kg/s m ˙ nahi hai — yeh mass-per-time hai.
ρ p Density matlab hai kisi material ke har cubic metre mein kitna mass packed hai. Symbol ρ p kg/m 3 ρ p = 1800 kg/m 3 1800
A Area matlab kisi cheez ki kitni surface hai, square metres mein (m 2
A b burning surface area (fuel ki exposed face jo jal rahi hai).A t throat area (sabse chhota hole jisme se gas squeeze hoti hai).A e exit area (bilkul end mein chauda muh).
Figure mein red surface dekho: woh A b andar hoti hai. Jo gas banti hai woh chhote A t A e
Grain solid propellant ka moulded block hota hai. Yeh loose powder nahi hota — yeh ek solid shaped piece hota hai, aksar beech mein ek khokha channel hota hai taaki andar ki surface bhi jal sake.
Intuition Jalna ek onion chhilne jaisa haiSolid grain ek saath nahi jalta. Sirf exposed surface hi aag mein hoti hai, aur woh aag andar ki taraf, ek patli layer ek time pe, surface ke seedhi andar (perpendicular) khaati jaati hai. Socho jaise har second ke ek hisse mein onion se ek kaagaz jaisi patli layer uthaa lete ho.
r Burn rate r m/s nahi batata ki gas nozzle se kitni fast nikli; yeh batata hai ki aag ki surface fuel mein kitni fast khaati hai. Typical value: r ≈ 0.008 m/s 8
Red arrows recession ki direction dikhate hain: har jagah surface ke perpendicular , andar ki taraf. Ek chhote time d t r d t
p Pressure woh force hai jo area ke har square metre pe push karta hai, pascals (Pa 1 MPa = 1 0 6 Pa chamber pressure p c
p c p e exit pe gas ka pressure.p a ambient pressure — bahar ki hawa jo peeche dhakelta hai (sea level pe lagbhag 1 0 5 Pa 0
Intuition Pressure kyun control karta hai ki kitni fast jalta haiHot gas ko burning surface pe zyada zor se dabaao toh woh solid mein heat zyada fast vapas bhejti hai, isliye aag andar zyada fast khaati hai. Zyada p c r Saint-Robert Burn Rate Law :
Recall n < 1 n ≥ 1 ( ⋅ ) 1/ ( 1 − n ) n → 1
Nozzle peeche ka shaped funnel hota hai. Chamber ki gas chhote throat (A t exit (A e
Definition Exhaust velocityv e v e m/s quality hai — bada v e v e 2500 m/s r 0.008 m/s Nozzle Isentropic Expansion .
Figure dono speeds ko contrast karti hai taaki tum inhe kabhi mix na karo: slow andar ki r v e
Ab woh Greek letters jo v e
γ R M T c
γ γ = c p / c v 1.2 1.4 R = 8.314 J/(mol⋅K) universal gas constant , har gas ke liye same.M molar mass , kg/mol H 2 v e T c chamber temperature , kelvin (K
F Thrust F N F = m ˙ v e + ( p e − p a ) A e p e = p a
Definition Effective exhaust velocityc c ∗
c = F / m ˙ effective exhaust velocity — thrust divided by mass flow, F c ∗ characteristic velocity — sirf chemistry ka number jo batata hai ki chamber kitni efficiently pressure banata hai. Yeh c alag quantity hai; dekho Characteristic Velocity c-star .
g 0 g 0 = 9.81 m/s 2 fixed conversion constant hai jo velocity ko "seconds" number mein convert karne ke liye use hota hai. Yeh gravity jaisa likha hai lekin space mein ya Moon pe nahi badalta — yeh hamesha exactly 9.81 I s p
Definition Specific impulseI s p I s p = g 0 ∫ m ˙ d t ∫ F d t = g 0 c weight per total push. Yeh quality / efficiency number hai — "kick per kilogram." Zyada I s p Tsiolkovsky Rocket Equation se link hota hai, jahaan I s p c
A b F m ˙ A b I s p = F / ( m ˙ g 0 ) A b same I s p
rate and the dot notation
Saint-Robert law r = a p^n
grain cancels chemistry wins
Har line tab reveal karo jab tum ise zor se bol ke answer kar sako.
m ˙ "per second" — m ˙
ρ p Propellant density, mass per cubic metre, kg/m 3
Kaun si area jal rahi hai — A b A t A e A b
Burn rate r Surface ke perpendicular, andar ki taraf khaate hue, layer by layer.
Mass generation law likho. m ˙ = ρ p A b r
Saint-Robert burn-rate law aur stability condition batao. r = a p c n n < 1
Kya v e r Nahi — v e r
v e Sirf chemistry/nozzle wali: γ R T c M p e / p c
Pressure term ke saath thrust likho. F = m ˙ v e + ( p e − p a ) A e
Kya g 0 Nahi — yeh ek fixed conversion constant 9.81 m/s 2 I s p
I s p Propellant ki unit weight per total impulse, I s p = c / g 0
Bada A b I s p A b F m ˙ I s p = F / ( m ˙ g 0 )