Drag — pressure (form) drag, skin friction drag

2.2.24 · Physics › Fluid Mechanics

Drag exist kyun karta hai?

WHY: Ek fluid molecule jo moving body se takraata hai, uska momentum change ho jaata hai. Newton ke third law se, body pe equal-and-opposite force lagti hai. Fluid surface ko sirf do tarike se touch kar sakta hai:

• Yeh seedha push kar sakta hai (normal stress = pressure $p$).
• Yeh surface ke saath sideways drag kar sakta hai (viscosity se shear stress $\tau$).

Toh outward normal $\hat{n}$ wale surface element $dA$ pe total force hai:

$d\vec{F}=\underset{\text{pressure}}{\underbrace{-p\hat{n}dA}}+\underset{\text{shear}}{\underbrace{\vec{\tau }dA}}$

Iska component flow direction $\hat{x}$ ke saath drag hai.

Part 1 — Skin Friction Drag (viscous rub)

HOW (first principles se): Wall pe viscous shear stress hai

${\tau }_w=\mu {\frac{du}{dy}|}_{y=0}$

jahan $u$ flow speed hai, $y$ wall se distance hai, aur $\mu$ dynamic viscosity hai. WHY yeh form? Newton's law of viscosity: stress, rate of shear ke proportional hota hai, yaani velocity kitni steeply gap ke across change hoti hai. Steeper profile → zyada rubbing → zyada drag.

Wetted surface pe sum karte hue: $D_{\text{friction}}=\oint {\tau }_{w}dA$

Key dependences:

• Zyada viscous fluid → bada ${\tau }_w$.
• Bada wetted area → zyada drag (flow ke saath aligned flat plate almost saara skin friction hai).
• Thinner boundary layer (faster, chhoti body) → steeper gradient → zyada shear.

Part 2 — Pressure (Form) Drag (the wake)

HOW: Ideal (frictionless) fluid ke liye, pressure front-to-back perfectly symmetric hogi → koi net drag nahi (d'Alembert's paradox). Real viscosity separation cause karti hai → asymmetric pressure → net drag:

$D_{\text{form}}=\oint (p_{\text{front}}-p_{\text{back}})d{A}_{\perp }$

• Bluff body (flat plate facing flow, ek brick) → jaldi separation → bada wake → form drag dominate karta hai.
• Streamlined body (teardrop) → flow attached rehti hai → tiny wake → form drag tiny, skin friction dominate karta hai.

Sab milake: drag coefficient

WHY ek coefficient? Drag messily $\rho ,v,A$, shape pe depend karta hai. Hum predictable part ko dynamic pressure $\frac{1}{2}\rho v^2$ mein package karte hain aur saari "shape mystery" ek dimensionless number $C_D$ mein daal dete hain.

Worked Examples

Common Mistakes (Steel-manned)

Active-Recall Flashcards

#flashcards/physics

Connections

• Boundary Layer & No-Slip Condition — ${\tau }_w$ ka origin aur jahan separation shuru hoti hai.
• Reynolds Number — decide karta hai flow laminar/turbulent hai aur $C_D$ kaise behave karta hai.
• Viscosity & Newton's Law of Viscosity — skin friction ke neeche hai.
• Flow Separation & Wakes — form drag ka mechanism.
• Terminal Velocity — drag weight ko balance karta hai ($D=mg$).
• Bernoulli's Principle — form-drag pressure differences ke peeche pressure–velocity link.
• Dimensional Analysis & Drag Coefficient — $C_D$ kahan se aata hai.

Concept Map