Foundations — Effective exhaust velocity c = v_e + (P_e − P_a)A_e - ṁ

3.3.8 · D1 · Physics › Rocket Propulsion › Effective exhaust velocity c = v_e + (P_e − P_a)A_e - ṁ

Yeh page hai "pehle padhna seekho, phir kitaab padho" waali cheez. Parent note tumhare samne paanch symbols phenkta hai — $v_e$, $P_e$, $P_a$, $A_e$, $\dot{m}$ — aur assume karta hai ki tum inhe pehle se picture kar sakte ho. Yahan hum har ek ko ek picture se build karte hain, usi order mein jisme woh ek doosre par depend karte hain. Neeche koi bhi aisa symbol use nahi hoga jo pehle draw na kiya gaya ho.

0 — Nozzle: woh stage jahan sab kuch hota hai

Kisi bhi symbol se pehle, us object ko dekho jis par yeh sab rehte hain.

Hum sirf exit plane ki kyun parwah karte hain? Kyunki yahi woh boundary hai "rocket ki gas" aur "bahari duniya" ke beech. Jo kuch bhi rocket ko aage push karta hai woh usi circle par decide hota hai. Yeh picture dimag mein rakho: ek bell ke peeche ek red circle.

1 — Velocity $v_e$: gas kitni tezi se nikalti hai

Sabse basic idea: jo cheezein chalti hain unki ek speed hoti hai.

"Rocket ke relative" kyun? Kyunki rocket khud bhi chal rahi hai. Jo cheez rocket ko push karti hai woh yeh hai ki gas rocket ki comparison mein kitni tezi se nikalti hai, ground ki comparison mein nahi — bilkul aise jaise ek skateboard ka kick-back depend karta hai ki tum ball kitni tezi se phenko, naki ball ki street ke upar speed se.

2 — Mass flow rate $\dot{m}$: har second kitni gas nikalti hai

Speed akeli kaafi nahi hai. Ek akela tez atom kuch nahi karta; tumhe gas ka ek firehose chahiye.

3 — Force as "momentum per second": kyun $\dot{m}$ aur $v_e$ multiply hote hain

Ab dono ko combine karte hain. Yeh hai woh key mental move jis par poora topic tika hua hai.

Units check karo taaki symbol apni jagah earn kare: $\underset{\dot{m}}{\underbrace{\frac{\text{kg}}{\text{s}}}}\times \underset{v_e}{\underbrace{\frac{\text{m}}{\text{s}}}}=\frac{\text{kg}\cdot \text{m}}{{\text{s}}^2}=\text{N (newton)}✓$

Isliye parent ka Step 1 kaam karta hai. Deeper law ke liye Conservation of Momentum dekho aur yeh kahan fit hota hai uske liye Thrust Equation dekho.

4 — Pressure $P$: woh andekhni squeeze

Gas sirf chalti nahi; woh sideways aur outward bhi push karti hai kyunki woh squeeze hui hoti hai. Woh squeeze hi pressure hai.

Hum DO pressures se milte hain, kyunki exit circle par do "sides" hain:

Dono ki zaroorat kyun hai? Kyunki bacha-khucha gas-squeeze help karta hai ya hurt, yeh depend karta hai ki bahar se kya push back kar raha hai. Atmospheric Pressure vs Altitude dekho — $P_a$ sea level par $101300\text{Pa}$ hai aur space mein $0$ ho jaata hai.

5 — Area $A_e$: ek squeeze ko ek shove mein badalna

Pressure force per area hai. Ek actual force pane ke liye, humein jaanna hoga ki woh surface kitni badi hai jis par pressure act karta hai.

$(P_e-P_a)$ positive hai, zero hai, ya negative, yeh sab decide karta hai — woh sign hi Nozzle Expansion (Under/Over/Optimal) ka subject hai:

• $P_e>P_a$: bacha-khucha squeeze bahar push karta hai → extra thrust (underexpanded).
• $P_e=P_a$: perfectly balanced → no pressure term (optimal).
• $P_e<P_a$: bahar ki hawa jeet jaati hai → thrust penalty (overexpanded).

6 — Alphabet ko saath laana

Ab har symbol ek aisi picture hai jo tumhari apni hai. Parent ka formula bas yeh sentence hai:

Pressure term ko $\dot{m}$ se kyun divide karte hain? Kyunki hum chahte hain ki answer ek velocity jaisa dikhe ($F=\dot{m}c$). Ek force ko mass-flow ($\dot{m}$) se divide karne par velocity ke units milte hain: $\frac{\text{N}}{\text{kg/s}}=\frac{\text{kg}\cdot {\text{m/s}}^2}{\text{kg/s}}=\frac{\text{m}}{\text{s}}✓$ Toh $c$ genuinely ek speed hai — ek pretend exit speed jo sirf momentum se same total push deta. Wohi cheez phir Specific Impulse aur Tsiolkovsky Rocket Equation feed on karte hain.

Prerequisite map

Equipment checklist

Right side chhupaao aur check karo ki parent note kholne se pehle har ek ka jawab de sako.