Foundations — Choked flow — condition M = 1 at throat, maximum mass flow

3.1.8 · D1 · Physics › Compressible Flow & Aerodynamics › Choked flow — condition M = 1 at throat, maximum mass flow

Yeh page ek toolbox hai. Parent note Choked flow — condition M = 1 at throat, maximum mass flow ko padhne se pehle, tumhe usmein likha har letter apna banana hoga. Hum unhe ek ek karke banate hain, har ek apni jagah earn karta hai uske pehle ki agli cheez aaye. Koi bhi symbol use nahi hoga jab tak woh draw nahi hua.

1. Flow, aur "steady 1-D" ka matlab

Socho gas ek smooth pipe mein left-to-right flow kar rahi hai jiska width change hota hai. Hum do simplifying promises karte hain:

• Steady: kisi bhi fixed spot par gas har pal ek jaisi dikhti hai — picture kabhi time ke saath nahi badlti, sirf pipe ke along position ke saath badlti hai.
• 1-D (one-dimensional): har cross-section par har particle ki same speed, pressure aur density hoti hai. Hum walls ke paas ki patli slow layer ko ignore karte hain. Toh flow ki poori state numbers ka ek set hai jo sirf is baat par depend karta hai ki pipe mein kitni door tum ho.

Hume chaaron kyun chahiye: sirf speed se pata nahi chalta kitni gas move ho rahi hai — tumhe yeh bhi jaanna hai ki woh kitni densely packed hai aur kitne wide opening se guzar rahi hai. Woh combination mass flow hai, jo humaara poora target hai.

2. Area $A$ aur throat

Star superscript throat ke liye reserved hai jab woh sonic ho: $A^{\ast }$ choke par throat area hai, $p^{\ast }$ wahan ka pressure hai, aur aise hi aage. Hum §6 mein star earn karenge.

Throat special kyun hai: yeh sabse tanga squeeze hai, isliye yahan gas sabse fast force hoti hai — pehli jagah jo speed of sound reach kar sakti hai.

3. Mass flow $\dot{m}$ — woh quantity jis par humein dhyan dena hai

Yahi formula kyun koi aur nahi: yeh literally "packing density × kitna volume har second sweep hota hai" hai. Har term un pictures mein se ek hai jo humne already draw ki. Parent note ki poori derivation sirf inhi teen factors $\rho$, $A$, $V$ ko us ek master variable ke zariye rewrite karna hai jise hum aage milenge.

4. Speed of sound $a$ aur Mach number $M$

Pressure changes gas mein tiny compressions — yaani sound — ke roop mein travel karte hain. Uski speed gas aur uske temperature par depend karti hai.

Poori build ke liye Speed of Sound & Mach Number dekho. Yahan key mental image hai:

$M$ kyun aur sirf $V$ kyun nahi: flow chokes hoti hai ya nahi, yeh sirf is baat par depend karta hai ki speed sound se kaise compare hoti hai, uski raw value par nahi. $M$ exactly wahi comparison hai — ek single dimensionless dial. Sab kuch $M$ mein likhna problem ko "woh $M$ dhundo jo $\dot{m}$ maximise kare" mein badal deta hai.

5. Gas constants $\gamma$ aur $R$, aur $c_p$

Hume inki zaroorat kyun hai: $\gamma$ aur $R$ sound speed $a=\sqrt{\gamma RT}$ aur har isentropic relation ki exact shape fix karte hain. Inke bina Mach algebra mein koi numbers nahi hain.

6. Stagnation ("total") conditions aur star

Stagnation (Total) Properties dekho. Picture: $p_0,T_0$ par ek bada calm reservoir ek chhote nozzle se khali ho raha hai. Kyunki reservoir essentially still hai, uski static aur stagnation values coincide karti hain.

7. Teen notations jo beginners ko daraate hain

8. Foundations topic ko kaise feed karte hain

Ise top-down padho: plain flow picture aur geometry $\dot{m}=\rho AV$ deti hai; gas constants sound speed aur Mach number dete hain; stagnation values plus isentropic relations hume $\dot{m}$ sirf $M$ use karke rewrite karne deti hain; us single function ko maximise karna tumhe $M=1$ par land karta hai — poora parent topic.

Equipment checklist

Right side cover karo aur aloud answer do; check karne ke liye reveal karo.