Boundary layer — Prandtl's concept, growth along flat plate: Foundations

2.2.20 · D1 · Physics › Fluid Mechanics › Boundary layer — Prandtl's concept, growth along flat plate

Yeh page ek toolbox hai. Parent topic padhne se pehle, tumhe har woh letter khud se likhna aana chahiye. Hum har ek cheez zero se build karte hain — pehle plain words, phir ek picture, phir yeh topic ko kyun chahiye. Upar se neeche padho; seedhi ka har paaydaan neeche wale par khada hai.

1. Flat plate aur stream — stage

Kisi bhi symbol se pehle, scene imagine karo: ek patla flat board moving fluid (hawa ya paani) mein edge-on karke pakda hua hai. Fluid left se ek steady speed par aa raha hai, har jagah ek jaisi.

Figure — Boundary layer — Prandtl's concept, growth along flat plate

2. Plate ke saath position — $x$ aur $y$

Humein do directions chahiye, aur woh interchangeable nahi hain.

3. Local fluid speed — $u$ , aur no-slip rule

s03 dekho: $y = 0$ par speed $0$ hai (no-slip). Upar chado aur arrows lambe hote jaate hain, jab tak upar wale poori length $U$ tak nahi pahunch jaate. Arrows ka woh stack velocity profile kehlata hai.

4. Boundary-layer thickness — $δ$

5. Viscosity — $μ$ , Newton's law, aur shear stress $τ$

Ab stickiness ki physics. Poori treatment ke liye Viscosity and Newton's law of viscosity dekho; yahan sirf utna hai jo tumhe chahiye.

6. Density $ρ$ aur kinematic viscosity $ν$

7. Reynolds number — $R e_{x}$

Aakhiri symbol, aur woh jo decide karta hai ki Prandtl ki poori picture valid hai ya nahi. Reynolds number dekho.

Foundations topic ko kaise feed karti hain

Equipment checklist

Dahini taraf cover karo; kya tum har cheez memory se likh sakte ho?

U

ka matlab kya hai, aur yeh

u

se kaise alag hai?

U

= door free-stream mein ek fixed speed;

u = u (x, y)

= local speed jo position ke saath vary karti hai.

No-slip condition kya hai?

Still wall ko touch karne wala fluid ki speed exactly

0

hoti hai; woh surface se chipak jaata hai.

x

aur

y

kya roles play karte hain, aur yeh interchangeable kyun nahi hain?

x

= downstream distance (jahan layer grow karti hai);

y

= flow ke across height (jahan speed 0 se

U

tak chadhti hai).

δ

precisely define karo.

Woh height

y

jahan

u = 0.99 U

; boundary-layer thickness (99% ek convention hai kyunki

U

asymptotically approach ki jaati hai).

Newton's law of viscosity state karo aur har symbol ka naam batao.

τ = μ \partial u / \partial y

;

τ

= shear stress,

μ

= viscosity,

\partial u / \partial y

= velocity gradient (profile ka slope).

Wall ke paas

μ

chhota hone ke bawajood hum use ignore kyun nahi kar sakte?

Kyunki

\partial u / \partial y \sim U / δ

wahan enormous hai; chhota

μ

times ek bada gradient ek significant stress deta hai.

ν

kya hai, uski units kya hain, aur yeh useful kyun hai?

ν = μ / ρ

, units

m^{2} / s

— ek diffusion coefficient ki units, isliye yeh measure karta hai ki wall ka slowing effect bahar kitni tezi se spread hota hai.

R e_{x}

likho aur batao yeh kya compare karta hai.

R e_{x} = U x / ν

; inertia aur viscosity ka ek unitless ratio.

Kya high

R e_{x}

layer ko mota banata hai ya patla?

Patla —

δ \propto 1/ R e_{x}