2.2.1
Fluid woh substance hai jo rest mein shear stress resist nahi kar sakta — jab tak shear lagta hai, tab tak continuously deform hota rehta (flow karta) hai . Ek solid fight back karta hai aur fixed deformation pe ruk jaata hai; fluid kabhi nahi rukta, bas chalte rehta hai.
Fluid ek aisi substance hai jo kisi bhi shear stress ke action mein continuously deform hoti rehti hai, chahe woh stress kitna bhi chhota kyun na ho. Fluids mein liquids aur gases dono aate hain.
Ek solid finite amount deform hota hai aur phir ruk jaata hai (woh stress ko spring ki tarah store kar leta hai).
Ek fluid kabhi nahi rukta deform hona jab tak shear act karta rahe — iska koi fixed shape nahi hota aur yeh apne container ka shape le leta hai.
Intuition "No fixed shape" kyon "can't resist shear" se aata haiGravity ke against shape hold karne ke liye, ek object ko slanted surfaces ke saath shear forces support karni hoti hain. Kyunki fluid kisi bhi shear ke liye rasta de deta hai, woh apni khud ki shape maintain nahi kar sakta — isliye flow karta hai aur container ko bottom-up bharta hai.
Jab koi force F A
Surface ke perpendicular part → normal force F n
Surface ke parallel (tangential) part → shear force F t
Definition Normal & Shear Stressσ = A F n ( normal stress, pressure-like ) τ = A F t ( shear stress ) pascal hoti hain: 1 Pa = 1 N/m 2
Area se kyun divide karte hain? Kyunki deformation ke liye push ki intensity matter karti hai, total force nahi. Usi force ko ek tiny patch pe lagao toh huge stress hoga; badi area pe spread karo toh gentle rahega.
Intuition Solid vs Fluid response (Feynman-style)Jelly (solid) ke block ko shear τ γ ∝ angle (strain): τ = G γ τ kitni tez angle grow ho raha hai (rate of strain) pe, angle pe nahi.
Newtonian fluid (paani, hawa, oil) ke liye, shear stress velocity gradient ke proportional hoti hai:
Solid: τ = G γ Fluid: τ = μ γ ˙ γ ˙ = 0 zero shear stress sustain karta hai — yahi defining property hai.
Worked example Example 1 — Plates ke beech oil mein shear stressTop plate speed u = 0.3 y = 2 mm = 0.002 μ = 0.1 τ Step 1: Velocity gradient d y d u = 0.002 0.3 = 150 s − 1 Yeh step kyun? Linear profile ⇒ gradient = (speed difference)/(gap).
Step 2: τ = μ d y d u = 0.1 × 150 = 15 Pa Yeh step kyun? Newton's law of viscosity ka direct use.
Worked example Example 2 — Plate drag karne ke liye forcePlate area A = 0.5 m 2 Step 1: τ = 15 Step 2: F t = τ A = 15 × 0.5 = 7.5 N Yeh step kyun? Shear stress force per unit area hoti hai, toh force wapas pane ke liye area se multiply karo.
Worked example Example 3 — "Kya woh shape hold kar sakta hai?" reasoningPaani ka ek blob aur steel ka ek blob dono table pe rakhe hain. Tiny sideways shear (halki breeze) act karti hai.
Reasoning: Steel τ = G γ shape maintain karta hai . Paani ka static shear ke liye G = 0 γ ˙ > 0 Kyun? Kyunki fluid rest mein koi bhi shear balance nahi kar sakta, shape ki equilibrium impossible hai.
Common mistake "Gases fluids nahi hote — sirf liquids hote hain."Kyun sahi lagta hai: Gases invisible hoti hain aur "pour" nahi hoti. Fix: Fluid define hota hai shear resist karne ki inability se, jo gases bhi satisfy karti hain — woh flow karti hain aur container ka shape le leti hain. Liquids aur gases dono fluids hain.
Common mistake "Fluids mein shear stress kabhi nahi hoti."Kyun sahi lagta hai: Hum kehte hain "fluid rest mein shear resist nahi kar sakta." Fix: Moving fluid bilkul shear stress carry karta hai τ = μ d u / d y static equilibrium pe zero shear , har waqt zero shear nahi.
Common mistake "Viscosity matlab shear ∝ kitna deform hua."Kyun sahi lagta hai: Yeh solids ke liye sach hai (τ = G γ Fix: Fluids ke liye, shear ∝ rate d u / d y
Fluid ko kya define karta hai? Ek aisi substance jo kisi bhi shear stress ke under continuously deform hoti hai, chahe kitni bhi chhoti kyun na ho.
Fluid ka koi fixed shape kyun nahi hota? Yeh rest mein shear sustain nahi kar sakta, isliye gravity ke against apni surfaces hold nahi kar sakta — container fill karne ke liye flow karta hai.
Normal stress formula aur meaning? σ = F n / A
Shear stress formula? τ = F t / A
Newton's law of viscosity? τ = μ d y d u
Solid vs fluid stress law? Solid τ = G γ τ = μ γ ˙
Dynamic viscosity μ Pa·s (pascal-second).
Kya gas ek fluid hai? Haan — liquids aur gases dono fluids hain.
Static rest mein fluid mein shear stress kitni hoti hai? Zero — yahi defining property hai.
d u / d y Velocity gradient = rate of shear strain, units s − 1
Recall Feynman: 12-saal ke bachche ko explain karoSocho paper ki stack ke top ko sideways push kar rahe ho. Paper (ek solid-jaisi cheez) thodi tilt hoti hai aur ruk jaati hai. Ab socho stack slippery paani ki layers se bani hai: top push karo aur layers ek doosre ke upar hamesha ke liye slide karti rehti hain — kabhi nahi ruktein. Yahi "sideways push karne pe kabhi nahi rukna" exactly woh cheez hai jo kuch cheez ko fluid banati hai. Aur kyunki yeh sideways push ke against khud ko hold nahi kar sakta, woh bas girat ho jaata hai aur jis bhi cup mein daalo use fill kar leta hai. Thicker fluids (honey) slowly slide karti hain, thin wale (paani) fast — yahi "slowness" viscosity hai.
"Fluids FLEE Forever From Force" — woh Flee (flow) karte hain Forever (continuously) kisi bhi Force (shear) se. Aur law ke liye: "Tau = Mu times the Gradient grew" → τ = μ d u / d y
Pressure in Fluids — normal stress σ p Viscosity and Newtonian vs Non-Newtonian Fluids — μ Hydrostatics — Fluids at Rest — kyun static fluids mein sirf normal forces hoti hain.Stress and Strain in Solids — contrast law τ = G γ Velocity Profile and No-Slip Condition — d u / d y
stress prop rate of strain
