Drag — pressure (form) drag, skin friction drag: Question bank

2.2.24 · D5 · Physics › Fluid Mechanics › Drag — pressure (form) drag, skin friction drag

Shuru karne se pehle, kuch symbols aur words hain jo tumhe confuse nahi karne chahiye — inhe ek baar anchor kar lo, taaki neeche ka har reveal saaf pade bina doosre pages khoje:

Definition Is page par use hone wale symbols aur words

$D$ = drag force: fluid ka total peeche ki taraf push (newtons, N mein measured) jo body par lagta hai, relative motion ke opposite direction mein. Yeh form drag plus skin friction drag ka sum hai.
$ρ$ = fluid ki density (mass per unit volume, kg/m³). $v$ = body aur fluid ke beech ki relative speed (m/s). $A$ = ek chosen reference area (m², usually bluff bodies ke liye frontal/projected area).
$C_{D}$ = drag coefficient: ek dimensionless number jo saare messy shape/geometry effects ko ek experimentally-measured value mein lump karta hai. Milke ye dete hain $D = \frac{1}{2} ρ v^{2} A C_{D}$ .
$μ$ (Greek "mu") = dynamic viscosity: ek fluid kitni strongly resist karta hai apni layers ko ek doosre ke upar slide karne se (units Pa·s). Yeh Newton's law of viscosity mein proportionality constant hai, $τ = μ d u / d y$ . Bada $μ$ → stickier fluid → zyada rubbing.
Normal force = surface ke andar seedha push (perpendicular). Yeh pressure $p$ hai.
Tangential force = surface ke saath drag (parallel). Yeh shear stress $τ$ (Greek "tau", units Pa) hai.
Wake = ek churning, low-pressure pocket jo body ke peeche rah jaati hai jab flow uske shape ko follow nahi kar pata aur separate ho jaata hai.

Is bank ko self-contained rakhne ke liye, ek picture poori us distinction ko pin karti hai jo questions test karti hai. Shuru karne se pehle ise dekho: wahi arrows baar baar reveals mein aate hain.

Figure — Drag — pressure (form) drag, skin friction drag

Yahan ka har question aslmein yeh pooch raha hai: "Kya yeh drag perpendicular push (form) se aa rahi hai, parallel rub (skin friction) se, ya dono thodi thodi — aur kya viscosity ne secretly ise cause kiya?"

True or false — justify

A perfectly inviscid (zero-viscosity) fluid in steady flow exerts zero drag on a sphere.

True — yeh d'Alembert's paradox hai; viscosity na hone par pressure perfectly symmetric hoti hai front-to-back, isliye pushes cancel ho jaate hain, aur koi bhi shear nahi hoti. Us symmetry ko todne ke liye tumhe viscosity chahiye.

Skin friction drag tab bhi exist kar sakti hai jab body ka koi wake hi nahi hota.

True — ek flat plate ko flow ke edge-on rakhne par flow attached rehti hai (essentially koi wake nahi) phir bhi fluid dono faces par rubbing karta hai, isliye skin friction wahan poori drag hai.

Form drag ek real fluid mein exist kar sakti hai jahan body par har jagah shear stress exactly zero ho.

False — ek real fluid mein form drag separation se aati hai, aur separation sirf isliye hoti hai kyunki viscosity hoti hai, jo necessarily shear bhi produce karti hai. Toh "zero shear everywhere" quietly inviscid matlab hai, aur inviscid fluid zero form drag deta hai. Separation bina shear ke nahi ho sakti.

Parachute ki drag mostly skin friction hai kyunki itna zyada fabric air ko touch karta hai.

False — parachute ek bluff body hai jisme enormous wake hoti hai, isliye yeh ~100% form (pressure) drag hai; fabric par rubbing front–back pressure difference ke aage negligible hai.

Body ko streamline karna hamesha uska total surface area reduce karta hai.

False — ek teardrop usually sphere se zyada surface rakhta hai; tum extra skin friction accept karte ho wake ko khatam karne ke liye, aur phir bhi net total drag kam ho jaata hai.

Speed double karne par drag double ho jaati hai.

False — high Reynolds number par

C_{D}

roughly constant hota hai, isliye

D = \frac{1}{2} ρ v^{2} A C_{D}

se drag

v^{2}

ke saath scale hoti hai;

v

double karne par

D

chaar guna ho jaati hai.

Drag coefficient

C_{D}

ki units newtons hoti hain.

False —

C_{D}

deliberately dimensionless hai; saari units

\frac{1}{2} ρ v^{2} A

mein hain (jo already newtons mein aata hai), aur

C_{D}

sirf "shape mystery" carry karta hai.

No-slip condition ka matlab hai ki wall ke paas har jagah fluid speed zero hoti hai.

False — no-slip condition kehti hai ki speed exactly wall par zero hai; just upar se speed teezi se badhti hai, aur wahi teez climb exactly wall shear create karti hai.

Ek bahut zyada streamlined body ke liye, skin friction total drag ka dominant part ho sakti hai.

True — jab wake chhoti hoti hai, form drag kam hoti hai, isliye bachi hui skin friction (badi wetted area par) bada share ban jaati hai.

Turbulent boundary layer ka matlab hamesha laminar se zyada total drag hoti hai.

False — turbulent boundary layer mein zyada skin friction hoti hai, lekin yeh surface se zyada der tak chipki rehti hai, separation delay karti hai aur wake shrink karti hai. Ek bluff body par (jaise golf ball) yeh form drag itni zyada cut kar sakti hai ki total drag drop ho jaaye — exactly isliye golf balls mein dimples hote hain.

Spot the error

"Drag sirf body aur fluid ke beech friction hai, jaise floor par box slide karna."

Error yeh hai ki drag ko ek mechanism treat kiya ja raha hai. Do hain: perpendicular pressure push (form) aur parallel viscous rub (skin friction). Zyaatar bluff bodies ke liye pressure push dominate karta hai, rubbing nahi.

"Kyunki form drag pressure se aati hai, aur pressure ko viscosity ki zaroorat nahi, isliye form drag ideal fluid mein bhi exist karti hai."

Hidden step galat hai: form drag ko asymmetric pressure chahiye, aur woh asymmetry separation se produce hoti hai, jise viscosity chahiye. Ek ideal (inviscid) fluid mein pressure symmetric rehti hai, front aur back pushes exactly cancel ho jaate hain, aur net drag zero hoti hai (d'Alembert's paradox). Toh conclusion ulta hai.

"Ek flat plate face-on aur edge-on ki drag same hoti hai kyunki yeh same plate hai same area ke saath."

Orientation change karti hai ki kaun sa source dominate karta hai. Face-on badi wake deta hai (form drag,

C_{D} \approx 1.2

); edge-on almost pure skin friction deta hai (

C_{D} \approx 0.005

) — sau guna se bhi kam.

"Wall shear stress poore velocity profile par depend karti hai, isliye ise compute karne ke liye tumhe poori boundary layer chahiye."

Sirf wall par velocity ka slope matter karta hai:

τ_{w} = μ (d u / d y) ∣_{y = 0}

. Skin friction sirf us gradient ko "dekhti" hai

y = 0

par, kuch aur nahi.

D = \frac{1}{2} ρ v^{2} A C_{D}

mein reference area

A

hamesha woh surface area hoti hai jise fluid touch karta hai."

Bluff bodies ke liye

A

frontal (projected) area hai, wetted area nahi. Wetted area skin friction ke liye matter karti hai, lekin drag formula ka

A

ek chosen reference hai, usually frontal.

"Bernoulli kehta hai pressure girti hai jahan speed badhti hai, isliye car ke peeche fast wake ko high pressure hona chahiye aur car ko aage push karna chahiye."

Wake slow aur swirly hai, fast nahi, aur Bernoulli separated, turbulent region ke across apply nahi hota. Wake low-pressure hoti hai, isliye yeh back ko aage push karne mein fail ho jaati hai — exactly yahi form drag hai.

Why questions

Teardrop shape total drag kyun reduce karta hai jab ki iske paas rub karne ke liye zyada surface hai?

Gentle tail pressure ko slowly recover karne deta hai isliye flow attached rehti hai, wake shrink hoti hai aur form drag drastically kam ho jaati hai. Extra skin friction par thoda lose karte ho lekin wake khatam karke bahut zyada win karte ho.

\frac{1}{2} ρ v^{2}

(dynamic pressure) natural combination kyun hai,

ρ v

ρ v^{3}

ki jagah?

Step by step build karo. Ek second mein body length

v

aur cross-section

A

ka ek fluid tube sweep karti hai, isliye har second

ρ (v A)

mass pass hota hai (yeh mass flux hai). Us mass ka har bit speed

v

lekar aata hai, isliye momentum jo woh per second laata hai woh hai (mass per second)

\times v = ρ v A \cdot v = ρ v^{2} A

— ek force. Yeh

v^{2}

aur

ρ A

fix karta hai. Extra

\frac{1}{2}

ek convention hai jo group ko dynamic pressure

\frac{1}{2} ρ v^{2}

ke barabar banata hai, isliye

C_{D}

ek clean dimensionless corrector ban jaata hai.

Tez ya chhoti body ki wall par skin friction stress zyada kyun hoti hai?

Patli boundary layer same speed change ko chhote gap mein squeeze karti hai, isliye

d u / d y

steeper hoti hai, aur

τ_{w} = μ d u / d y

badhta hai.

Hum pure physics ki formula ki jagah sab kuch

C_{D}

mein package karne ki kyun bother karte hain?

Form drag separation par depend karti hai, jo real shapes ke liye exactly solve karna bahut messy hai. Hum clean part (

ρ, v, A

) predict karte hain aur saari geometric mystery ko experimentally-measured $C_D$ mein stuff karte hain.

Viscosity ko "dono drag types ka hidden source" kyun kaha jaata hai?

Skin friction directly viscous shear hai; form drag sirf isliye exist karti hai kyunki viscosity separation cause karti hai. Viscosity remove karo aur dono vanish ho jaate hain (d'Alembert). Toh ek property secretly dono ko drive karti hai.

Boundary layer laminar hai ya turbulent, yeh form aur skin friction ke beech split kyun change karta hai?

Laminar layer smooth aur thin hoti hai (low skin friction) lekin jaldi separate hoti hai, wide wake aur large form drag deti hai. Turbulent layer fast fluid ko wall tak mix karti hai (zyada skin friction) lekin zyada der attached rehti hai, wake shrink karti hai aur form drag cut karti hai. Toh flow regime shift karta hai ki dono sources mein se kaun dominate karta hai.

Terminal velocity usi

C_{D}

par kyun depend karti hai jo yahan drag govern karta hai?

Terminal velocity par gravity drag

\frac{1}{2} ρ v^{2} A C_{D}

ko balance karti hai, isliye wahi coefficient jo set karta hai ki fluid kitna hard push back karta hai, wahi us speed ko bhi set karta hai jis par push weight ke barabar hoti hai.

Edge cases

Jis exact instant par body ke relative fluid speed zero ho, drag kya hogi?

Zero —

v = 0

ke saath dynamic pressure

\frac{1}{2} ρ v^{2}

vanish ho jaati hai, isliye form aur skin friction drag dono vanish ho jaate hain. Koi relative motion nahi, koi rub nahi, koi front–back pressure difference nahi.

Zero viscosity (

μ \to 0

) ki limit mein skin friction drag ka kya hoga?

Yeh zero ho jaayegi, kyunki

τ_{w} = μ d u / d y

mein

μ

direct factor hai — koi viscosity nahi matlab koi shear rub hi nahi.

Ek body jo flow ke perfectly aligned hai (jaise razor-thin plate edge-on), drag ka kaun sa fraction form drag hai?

Almost kuch nahi — koi frontal projected area nahi wake banane ke liye, flow attached rehti hai, isliye drag essentially saari skin friction hai.

Ek ideal flat plate jo exactly face-on (perpendicular) ek real fluid mein rakhi ho, usmein kaun si drag dominate karti hai aur kyun?

Form drag, overwhelmingly — flow sharp edges par right separate ho jaati hai ek badi low-pressure wake chhod ke, isliye front–back pressure difference tiny edge shear ko dwarf karta hai.

Perfectly symmetric pressure distribution ki limit mein (koi separation nahi), net form drag kya hai?

Zero — front par forward push exactly barabar push se cancel hota hai back par, isliye body ke around pressure integral koi net rearward force nahi deta.

Laminar aur turbulent flow ke beech boundary par ("drag crisis"), ek sphere ka

C_{D}

speed ke critical Reynolds number se guzarne par kya hota hai?

Yeh suddenly drop karta hai, badhta nahi — boundary layer turbulent ho jaati hai, surface se zyada der chipki rehti hai, wake narrow hoti hai, aur form drag sharply girta hai. Yeh counter-intuitive dip drag crisis hai.