3.1.14 · D1Shock wave angle, deflection angle
Jab hawa sound se tez chalti hai aur kisi wedge se takrati hai, toh use aage warn nahi kiya ja sakta, isliye wo ek pal mein ek patli tirchi line ke across mod leti hai jise shock kehte hain. Is topic ki saari baatein bas us mod ke do angles measure karne ki hain — line kitni jhuki hai (β muda (θ M 1
Parent note padhne se pehle, tumhe har wo symbol khud se samajhna hai jo wahan milta hai. Neeche har idea ko zero se build kiya gaya hai: seedhe words → ek picture → kyun is topic ko yeh chahiye. Upar se neeche padho; har rung pichle pe khada hai.
Definition Speed of sounda Speed of sound a sabse tez possible warning ki speed samjho: hawa aage sirf tab jaanti hai koi aa raha hai jab ek sound signal wahan pahunchti hai.
Intuition Yeh ratio kyun, sirf "speed" kyun nahi?Physics ko metres-per-second se matlab nahi apne aap mein; use matlab hai ki hawa us signal se tez hai ya dheere jo use warn kar sakta. Ek pure number M M 1 pehle ) aur M 2 downstream , shock ke baad) mein likha hai — raw speeds mein nahi.
Subscripts jo tumhe har jagah milenge:
1 pehle (upstream).2 baad (downstream).
Toh M 1 V 1 ρ 1 ρ 2
Intuition Shock ek patli "squash ki deewar" haiFigure dekho. Supersonic hawa (left) wedge ke against pile ho jaati hai aur apni warning upstream nahi faila sakti. Iske badle wo ek razor-thin line ke saath slam ho jaati hai — shock . Us line ke across, ek baal se bhi patli distance mein, pressure aur density jump up ho jaate hain aur speed drop ho jaati hai. Yeh ek step hai, slope nahi.
Parent note mein do types milte hain:
Normal shock — shock line flow ke seedha across hoti hai (perpendicular). Dekho Normal Shock Waves .Oblique shock — shock line flow ke angle pe hoti hai. Pura yeh topic isi ke baare mein hai.
Parent note ka magic sentence hai: "ek oblique shock sirf us velocity ke part ke liye normal shock hai jo seedha iske andar point kar rahi hai." Yeh samajhne ke liye, hume velocity split karna seekhna hoga — Section 4.
ρ Density ρ crowded hain.
Intuition "Compression" kaisa dikhta haiEk box mein dots imagine karo. Upstream (ρ 1 ρ 2 ρ 2 > ρ 1 compression hai — yeh hawa ko hamesha crowd karta hai. Parent note ka density ratio ρ 2 / ρ 1
Topic ko ρ mass kabhi destroy nahi hota : jo bhi mass shock ke andar flow karta hai woh bahar bhi flow karna chahiye. Yeh bookkeeping rule (jise continuity kehte hain) derivation ke Step 2 mein density ko velocity se jodhta hai.
Yeh page pe sabse important tool hai. Velocity ek arrow hai: iska ek size aur ek direction hota hai. Koi bhi tilted arrow do right-angle arrows se rebuild ho sakta hai — jaise directions dena "3 blocks east aur 4 blocks north" ek diagonal walk ke bajaaye.
Definition Normal aur tangential componentsShock line ke relative:
Normal component u seedha shock line mein jaata hai (perpendicular).Tangential component w shock line ke along hai (parallel).
is tarah kyun split karte hain (along/into the shock)?
Ek shock sirf ek direction mein push karta hai — seedha apne face se bahar (pressure ek surface ke perpendicular kaam karta hai). Toh wo sirf us motion ke part ko fight kar sakta hai jo iske andar point kar raha hai (normal part u along slide karta hai (w
u w V β
Is topic ka har angular cheez ek right triangle (ek triangle jisme ek 9 0 ∘
Intuition Yeh velocity split karne mein kyun aate hainFull velocity arrow V hypotenuse banao aur β β V sin β β V cos β u 1 = V 1 sin β , w 1 = V 1 cos β . "Sine for the Shock-normal Speed." Cosine sliding part pakadta hai.
Intuition Final formula meintan V u / w = tan β tan velocity ratio ko pure angle mein badalne ka natural tarika hai. Isliye θ β M tan θ cot β
cot Cotangent cot β cot β = sin β cos β = tan β 1 cos β / sin β
Ab jab hum arrows split kar sakte hain, do headline angles sirf ek picture pe labels hain.
β θ
Wave angle β incoming flow direction se shock line tak ka angle. Shock kitna jhukta hai yeh hai.Deflection (turn) angle θ hawa ka khud ka path shock cross karte waqt kitna muda. Ek wedge ke liye, θ
β θ Kyun galat lagta hai: dono ek hi corner pe draw hote hain aur dono "shock scene ke angles" hain.
Fix: β θ θ < β β = 9 0 ∘ θ = 0
μ Mach angle μ vanishingly weak disturbance ka lean angle — ek whisper jaisi shock jo kuch bend nahi karti:
μ = sin − 1 ( M 1 1 ) Mach Angle and Mach Waves .
sin − 1 sin − 1 "konsa angle is sine value ka hai?" Yahan sabse weak shock woh hai jiska normal Mach number barely 1 M 1 sin μ = 1 sin μ = 1/ M 1 μ sin − 1
μ sabse chhota β sabse bada 9 0 ∘ θ = 0
Definition Ratio of specific heatsγ γ γ = 1.4 θ β M Rankine-Hugoniot Relations ).
Supersonic means M above 1
Shock forms as thin squash line
Density rho and mass bookkeeping
Split velocity into normal u and tangential w
Right triangle sin cos tan
Wave angle beta and turn angle theta
Mach angle mu from arcsine
Ek saanp mein bottom-up padho: sound M M > 1 β θ γ parent topic ke θ β M
Right side chhupao aur khud test karo — jab har cheez instant ho tab tum parent note ke liye taiyaar ho.
Mach number M Flow speed V a M = V / a
M > 1 Hawa apne warning signals se tez chalti hai, toh obstacles bina warning ke aate hain aur abrupt shocks force karte hain.
Subscripts 1 2 State 1 2
Shock kya hai, ek line mein? Ek baal-thin line jiske across pressure aur density jump up karte hain aur speed drop ho jaati hai.
Density ρ Mass per unit volume packed — molecules kitne crowded hain; shock hamesha ρ 2 > ρ 1
Velocity ko normal aur tangential parts mein kyun split karte hain? Shock sirf apne face ke perpendicular push karta hai, toh sirf normal part squash hota hai; tangential part bina change ke nikal jaata hai.
u 1 w 1 V 1 β u 1 = V 1 sin β w 1 = V 1 cos β
Final relation mein tan Normal ko tangential se divide karna (u / w = tan β
β θ β θ θ < β
Mach angle μ Sabse weak possible shock ka lean, μ = sin − 1 ( 1/ M 1 ) β
sin − 1 Sine undo karta hai — jawab deta hai "konse angle ka yeh sine value hai?"
γ Ratio of specific heats, gas ki springiness; air ke liye γ = 1.4
Recall Ek-sentence summarySound warnings ke liye ek speed limit set karta hai; use beat karo aur hawa ko ek tilted shock ke across abruptly muda padta hai, jiska lean (β θ
