3.1.9 · D1Converging nozzle — subsonic flow, Mach 1 at exit
Ek converging nozzle ek aisi pipe hai jo narrow hoti jaati hai, aur gas usme se squeeze hokar speed pakadti hai — lekin ek hard ceiling hai, yaani speed of sound , jise exit pe gas kabhi exceed nahi kar sakti. Yeh samajhne ke liye ki kyun aisa hota hai, hume sirf yeh track karna hai ki jaise gas accelerate hoti hai, chaar properties (pressure, temperature, density, aur speed) aapas me kaise trade off karti hain, aur yeh jaanna hai ki "top speed" is baat se set hoti hai ki pressure change gas me kitni tez travel kar sakti hai.
Yeh page kuch bhi assume nahi karta . Parent derivation touch karne se pehle, uske har letter ka matlab kuch aisa hona chahiye jo aap picture kar sako. Hum unhe ek ek karke banate hain, har ek pichle ke upar. Jahan aap koi link dekhein jaise Isentropic Flow Relations , woh baad ke liye ek deeper vault note hai — is page ko padhne ke liye aapko uski zaroorat nahi.
Is topic ki har cheez ek hi picture ke andar hoti hai: ek bada tank jisme still gas bhari hai aur woh ek narrowing pipe ke through khule hawa me khali ho rahi hai.
Yeh picture apne dimaag me rakho. Neeche diya har symbol iske kisi na kisi hisse ka label hai.
==Pressure p push per unit area hai jo gas apne touch karne wali kisi bhi surface par lagaati hai. Socho ki gas ke countless tiny molecules ek wall par drum ki tarah baar baar marte hain; jitna zyada aur jitni baar woh hit karein, utna zyada pressure.
Picture: arrows jo ek wall ke andar ki taraf point kar rahe hain, tight pack hue = high p p Topic ko kyun chahiye: poori kahaani ek pressure difference se drive hoti hai. Tank me high pressure, bahar low pressure — gas high se low ki taraf flow karti hai, aur yeh kitna accelerate hota hai yeh poori tarah is difference par depend karta hai.Units: pascals (Pa) ya kilopascals (kPa). 1 kPa = 1000 Pa
Definition Temperature aur density
==Temperature T T Kelvin (K) me measure hota hai, jo absolute zero (bilkul bhi jiggle nahi) se shuru hota hai, isliye T
==Density ρ har cubic metre me pack ki hui mass . Molecules paas paas cramped = high ρ ρ kg/m 3
Intuition Teen dials kyun, ek kyun nahiEk gas parcel ke paas teen cheezein hain jo flow karte waqt change ho sakti hain: kitna zyada push karta hai (p T ρ independent nahi hain — gas ko squeeze karo (raise ρ
==V gas ki khud ki speed hai — poori stream pipe ke neeche kitni tez ja rahi hai, metres per second me. Still tank me V = 0 V
Hum yeh Greek symbols bhi milenge, isliye abhi unhe bolna seekho:
Symbol
Bolo
Matlab
ρ "roe"
density
γ "gamma"
heat-capacity ratio (§7)
m ˙ "m-dot"
mass flow rate (§8)
m ˙ rate .
Yeh poore show ka star hai, isliye isse ek figure milti hai.
Definition Speed of sound==a a = γ R T
Picture: taali bajao; "kisine hawa ko dhakka diya" ka message speed a a T Topic ko kyun chahiye — is page par sabse gehra reason: pressure change hi woh tarika hai jisse downstream duniya upstream gas ko "room hai, zyada tez aao" bataati hai. Woh message sirf speed a a
a = γ R T Speed of Sound dekhein.
M = 1 Kyun sahi lagta hai: humne school me "sound 340 m/s hai" yaad kiya tha.
Fix: a = γ R T local temperature par depend karta hai. Exit gas jo thandi hai (T ∗ = 250 K 300 K M = 1 317 m/s M local sound speed se compare kiya jaata hai, kisi ek fixed number se nahi.
Definition Heat-capacity ratio==γ γ = 1.4
Picture: gas ko ek spring ki tarah socho. γ Topic ko kyun chahiye: γ har formula me appear karta hai — a = γ R T 0.528
Definition Stagnation conditions==Stagnation properties p 0 , T 0 , ρ 0 rest me , flow shuru karne se pehle hoti hain — bade tank ke andar deep, jahan V = 0 0
Picture: reservoir tank ka shant interior, pipe se door, jahan kuch bhi move nahi kar raha.Topic ko kyun chahiye: yeh known, fixed starting numbers hain. Har result inke ratio ke roop me express hota hai — p / p 0 T / T 0
Yeh samajhne ke liye ki ek moving parcel ke stagnation values kaise define hote hain, Stagnation Properties dekhein.
Definition Back pressure aur starred (critical) values
==Back pressure p b
==Starred values p ∗ , T ∗ , ρ ∗ jab exactly M = 1 exit par ho. Star hamesha sonic (choked) condition tag karta hai.
Topic ko kyun chahiye: poora behaviour p b p ∗ p b p ∗
Definition Mass flow rate==m ˙ har second ek cross-section se guzarne wale gas ke kilograms hain:
m ˙ = ρ A V A
Picture: pipe me ek imaginary hoop se har second phisalti hui mass gino. Denser gas (ρ A V Topic ko kyun chahiye: "choking" define hoti hai jab m ˙ M = 1 Mass Flow Rate & Choking dekhein.
Definition Isentropic flowIsentropic = adiabatic (pipe walls ke paas se koi heat cross nahi karti) aur reversible (koi friction nahi, koi shock losses nahi). Yeh "idealised, lossless" flow hai.
Picture: gas ek perfectly smooth, perfectly insulated pipe me glide kar rahi hai — kuch bhi waste nahi, kuch bhi leak nahi.Topic ko kyun chahiye: sirf is assumption ke under hi p T ρ shock aaye, toh isentropy toot jaaye — Normal Shock Waves dekhein.
perfect gas law p = rho R T
critical star values at M = 1
choking and mass flow ceiling
Ise upar se neeche padho: teen dials gas law ko feed karte hain; temperature aur γ M M = 1
Right side cover karo aur out loud jawab do. Agar koi bhi jawab fuzzy lage, toh parent derivation se pehle woh section dobara padho.
Pressure p Molecules ke kisi surface se takrane se aane wali push (force) per unit area.
Density ρ Mass per cubic metre; bolo "roe".
Perfect-gas law batao aur R p = ρR T R
Speed of sound a Choking ke liye speed of sound kyun matter karta hai? Pressure "messages" a M = 1
Mach number M M = V / a
Kya M = 1 Nahi — a M = 1 T
γ Heat-capacity ratio (gas ki "stiffness"); air ke liye γ = 1.4
Subscript 0 Stagnation / reservoir value — jab gas rest par ho (V = 0
Ek starred quantity jaise p ∗ Jab exactly M = 1
p b Back pressure — us environment ka pressure jisme nozzle exhaust karta hai.
Mass flow rate ko ρ , A , V m ˙ = ρ A V
"Isentropic" ka kya matlab hai? Adiabatic (koi heat exchange nahi) aur reversible (koi friction/shock nahi) — lossless flow.
