Foundations — Pressure-fed cycle — simplest, used in upper stages

3.3.25 · D1 · Physics › Rocket Propulsion › Pressure-fed cycle — simplest, used in upper stages

Is page par koi assumption nahi hai. Har letter, symbol, aur word jo parent note mein aata hai, yahan ground up se build kiya gaya hai — ek aisi order mein jahan har idea pehle wale par lean karta hai.

1. Pressure — poore show ka star

Is topic ke har symbol ka kisi na kisi tarah se pressure se connection hai, isliye pehle yeh nail down karna zaroori hai ki pressure actually kya hota hai.

Topic ko yeh kyun chahiye? Kyunki fluid tabhi move karta hai jab pressure uneven ho: liquid hamesha wahan se flow karta hai jahan zyada squeeze ho rahi ho, wahan ki taraf jahan kam. Yeh ek rule — high pressure → low pressure — yahan sab kuch drive karta hai.

Figure dekho: chhoti area par same force $F$ bada pressure deta hai (sharp push), aur badi area par chhota pressure (soft push). Drawing pin isliye kaam karta hai kyunki thumb ki force ek tiny point par land karti hai.

Reveal check:

2. Named pressures: $p_c$, $p_{\text{tank}}$, aur drops $\Delta p$

Ab "pressure" ka matlab samajh aa gaya, toh yeh specific pressures hain jo topic label karta hai.

Topic ko $\Delta p$ kyun chahiye: tank aur chamber ke beech har obstacle kuch pressure kha jaata hai. Tank ko itna extra pressure se start karna chahiye ki in sabhi tolls ke baad bhi $p_c$ se upar pahunche. Socho jaise ek marble downhill roll kar raha ho aur har bump par thodi height kho raha ho.

Figure ek pressure "staircase" hai: left mein tank par high se start karo, har loss par step down karo, aur liquid andar flow karne ke liye right par chamber line ke upar land karna zaroori hai.

3. Density $\rho$ aur liquid ka weight ($\rho gh$)

Parent note ki Bernoulli line mein $\rho$, $g$, $h$, aur $v$ use hote hain. Har ek earn karte hain.

Inhe saath mein rakh do toh $\rho gh$ ek pressure hai — liquid column ke bottom par extra squeeze jo upar ke liquid ke weight se aata hai. Isliye deep swimming pool mein bottom par kaanon par zyada pressure lagta hai.

Topic ko yeh kyun chahiye: pressure budget mein, propellant column ka weight liquid ko neeche push karne mein madad kar sakta hai (pressure add karke) ya acceleration ke under hindrance ban sakta hai. Yeh usually $p_c$ ke compare mein small hota hai, lekin honest accounting mein yeh belong karta hai.

Static pressure aur motion ke beech yeh trade exactly wahi hai jo Bernoulli's equation describe karta hai, jise parent apna pressure budget build karne ke liye use karta hai.

4. Material strength: $\sigma$, $t$, $r$ — tanks heavy kyun hote hain

Mass-penalty section mein hoop stress use hota hai. Yeh teen symbols use karte hain.

Figure ek spherical tank ko aadha kaat ke dikhata hai. Andar ka gas $\pi r^2$ area wale circle ke across dono halves ko alag push karta hai; wall ki thin ring (area $2\pi rt$) unhe saath hold karti hai. "Push apart = wall holds" balance karne se hoop-stress relation milta hai: $\sigma =\frac{pr}{2t}$

Topic ko yeh kyun chahiye: yahi woh reason hai ki pressure-fed engines low chamber pressure par chalte hain. Zyada pressure $p$ matlab thicker walls $t$, matlab zyada metal, matlab heavier tank. Yeh penalty inhi teen letters mein baked hai.

5. Ideal gas law: $pV=nRT$

Pressurant-sizing example mein yeh use hota hai. Har symbol:

Topic ko yeh kyun chahiye: Ideal gas law batata hai ki khali hote tank mein sahi pressure maintain karne ke liye kitna helium mass carry karna padega. Ek space mein zyada gas squeeze karo (bada $n$) aur pressure badhta hai; yahi ek pressurant bottle ki poori logic hai.

6. Sab kuch kaise fit hota hai — prerequisite map

Upar se neeche padho: pressure woh seed hai jisse sab kuch grow karta hai. Yeh pressure budget mein branch karta hai (Bernoulli, density, speed ki madad se) aur hoop stress mein (material strength ki madad se), aur dono branches "why low chamber pressure" par milte hain — jo ki pressure-fed cycle ke upper stages par hone ka dil hai.

7. Ek chhota numerical sanity check

Equipment checklist

Daayni side cover karo aur aage badhne se pehle khud test karo: