Foundations — Fluid definition — shear stress, no fixed shape

2.2.1 · D1 · Physics › Fluid Mechanics › Fluid definition — shear stress, no fixed shape

Yeh page yeh assume karta hai ki tumne kuch bhi nahi dekha. Isse pehle ki tum parent note Fluid definition padh sako, tumhare paas har woh symbol hona chahiye jo woh tumpe throw karta hai. Hum unhe ek-ek karke build karte hain, har ek ko uss picture se jisme woh rahta hai.

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1. Force $\vec{F}$ — ek direction ke saath push

Yeh topic ise kyun chahta hai. Ek fluid ko define kiya jata hai ki woh push pe kaise react karta hai. Lekin har push ek jaisi nahi hoti: ek surface ko seedha push karna aur use sideways scrape karna bahut alag hai. Toh pehli cheez jo hume chahiye woh ek arrow hai jiska direction hum discuss kar sakein.

Figure s01 dekho: wahi arrow seedha wall mein point kar sakta hai, ya uss par slide kar sakta hai, ya kuch bhi beech mein.

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2. Surface aur area $A$ — woh patch jis par force land karti hai

Yeh topic ise kyun chahta hai. Deformation intensity ki parwah karta hai, raw force ki nahi. Intensity paane ke liye hum force ko area se divide karenge, isliye hume pehle area ek clean, named quantity ke roop mein chahiye.

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3. Force ko split karna: normal part $F_n$ aur tangential part $F_t$

Yeh poore topic ki sabse important picture hai. Ek surface se takraata force arrow lo. Hum us ek arrow ko do arrows mein todenge jo right angles par hain:

• woh part jo seedha (perpendicular) surface mein point karta hai — use $F_n$ kaho ("n" normal ke liye, jo geometry mein "$90^{\circ }$ par" matlab hai);
• woh part jo surface ke saath (parallel/tangent) point karta hai — use $F_t$ kaho ("t" tangential ke liye, matlab "along slide karna").

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4. Stress $\sigma$ aur $\tau$ — force per unit area

Ab hum "force ko split karo" (step 3) ko "patch se divide karo" (step 2) ke saath combine karte hain.

Yeh topic ise kyun chahta hai. Parent note ki headline — "ek fluid rest mein shear stress resist nahi kar sakta" — $\tau$ ke baare mein ek sentence hai. Bina $\tau$ define kiye, definition sirf words hain. Symbol $\tau$ hi topic hai.

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5. Shear strain $\gamma$ — ek slab kitna tilt hua

Ek soft block ke top ko sideways push karo jabki uska base fixed rahe. Block ek slanted shape mein jhuk jaata hai. Jhukne ki matra shear strain hai.

Yeh topic ise kyun chahta hai. Ek solid ke liye, shear stress is lean ke proportional hota hai: $\tau =G\gamma$. Yeh woh law hai jisse parent note fluids ko contrast karta hai. Jab tak tum solid ke $\gamma$ ko nahi samjhoge tab tak tum appreciate nahi kar sakte ki fluid ko kya special banata hai.

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6. Rate of change aur gradient $\frac{du}{dy}$ — fluid ka twist

Yeh solids se fluids ki taraf leap hai, aur iske liye ek naya idea chahiye: rate, matlab kuch kitni tezi se change hota hai.

Ab velocity gradient. Imagine karo fluid ek moving top plate aur ek fixed bottom ke beech gap fill kar raha hai. Top ke paas layers fast move karti hain; bottom ke paas layers muskil se move karti hain. Speed $u$ height $y$ mein climb karne par change hoti hai. Speed height ke per unit kitni tezi se change hoti hai yeh likha jaata hai

$\frac{du}{dy}=\frac{\text{layer speeds mein difference}}{\text{unke beech height}}.$

Yeh topic ise kyun chahta hai. Poora payoff — Newton ka law $\tau =\mu \frac{du}{dy}$ — is gradient par built hai. Agar $du/dy$ ek mystery hai, toh woh boxed formula ek magic spell hai. Profile kahaan se aata hai iske baare mein deeper detail Velocity Profile and No-Slip Condition mein hai.

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7. Viscosity $\mu$ — "thickness" constant

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8. Alphabet ko saath mein rakhna

Symbol	Bol ke padhein	Picture	Topic mein kaam
$\vec{F}$	force arrow	arrow with length + direction	woh push jo hum apply karte hain
$A$	area	ek flat patch	woh patch jis par push spread hoti hai
$F_n,F_t$	normal / tangential parts	do arrows $90^{\circ }$ par	"into" vs "along" mein split
$\sigma ,\tau$	normal / shear stress	force-per-patch	$\tau$ hi fluid definition hai
$\gamma$	shear strain	slanted block	solid ka response
$\dot{\gamma }=\frac{du}{dy}$	rate of tilt / gradient	layers sliding	fluid ka response
$\mu$	viscosity	"thickness" slope	$\tau$ ko $du/dy$ se link karta hai

Recall Self-check: scroll karne se pehle har symbol ka naam bolo

$\tau$ ::: shear stress, sliding-along force per unit area, Pa mein. $\sigma$ ::: normal stress, straight-in force per unit area, Pa mein. $\gamma$ ::: shear strain, woh (unitless) matra jitna ek slab tilted hai. $\dot{\gamma }$ ::: rate of shear strain = tilt kitni tezi se badhti hai = $du/dy$. $\mu$ ::: dynamic viscosity, fluid ka "thickness" constant, Pa·s mein.

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Yeh foundations topic ko kaise feed karte hain

Jab tum yeh map left-to-right padh sako, toh parent note plain English ki tarah padha jaata hai. Stress and Strain in Solids mein do response laws compare karo aur Pressure in Fluids aur Hydrostatics — Fluids at Rest mein pressure story dekho.

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Equipment checklist

Recall Kya main parent note ke liye ready hoon?

Main ek force ko arrow ki tarah draw kar sakta hoon aur keh sakta hoon ki uski direction ka matlab kya hai ::: Haan — ek force ek push/pull hai jisme size (arrow length) aur direction hoti hai. Main ek surface par force ko ek perpendicular part aur ek parallel part mein split kar sakta hoon ::: Haan — $F_n$ surface mein point karta hai, $F_t$ uss ke saath slide karta hai, $90^{\circ }$ par. Main jaanta hoon ki hum force ko area se kyun divide karte hain ::: Intensity (fierceness per patch) paane ke liye, jo actually matter ko deform karti hai. Main $\sigma$ aur $\tau$ ko unke formulas aur units ke saath state kar sakta hoon ::: $\sigma =F_n/A$, $\tau =F_t/A$, dono pascals mein (${\text{N/m}}^2$). Main jaanta hoon ki shear strain $\gamma$ kya hai aur yeh ratio kyun hai ::: Tilt $\Delta x/y$; ratio kyunki tilt slab ki height ke relative hoti hai. Main "rate" samajhta hoon aur $du/dy$ padh sakta hoon ::: Rate tiny-change ÷ tiny-time hai; $du/dy$ yeh hai ki layer speed height ke saath kitni tezi se change hoti hai, units ${\text{s}}^{-1}$. Main jaanta hoon ki fluids $\gamma$ ki jagah $\dot{\gamma }$ kyun use karte hain ::: Kyunki ek fluid kabhi tilting band nahi karta, isliye koi final $\gamma$ nahi hoti — sirf ek rate hoti hai. Main jaanta hoon ki viscosity $\mu$ kya hai aur iske units kya hain ::: "Thickness" slope jo $\tau$ ko $du/dy$ se link karta hai; units $\text{Pa⋅s}$.