2.2.3 · D5 · HinglishFluid Mechanics
Question bank — Viscosity — dynamic μ, kinematic ν = μ - ρ; Newtonian vs non-Newtonian
2.2.3 · D5· Physics › Fluid Mechanics › Viscosity — dynamic μ, kinematic ν = μ - ρ; Newtonian vs non
Shuru karne se pehle, ek reminder taaki har symbol earned lage:
- (Greek "tau") = shear stress, wo sideways force per unit area jo ek fluid layer apne neighbour se feel karta hai. Units pascals (Pa).
- ("mu") = dynamic viscosity, fluid ka internal-friction constant. Units Pa·s.
- ("nu") = kinematic viscosity , jahan ("rho") density hai. Units m²/s.
- = shear rate, flow speed kitni tezi se change hoti hai jab tum flow ke across (direction mein) move karte ho. Units s⁻¹.
True or false — justify
True or false: Ek river jo solid block ki tarah 10 m/s se move kar rahi hai, uske andar bahut bada viscous stress hoga.
False. Viscous stress velocity ke gradient par depend karta hai, speed par nahi. Agar har layer ek hi 10 m/s se move kar rahi hai, toh , isliye har jagah andar.
True or false: Rest mein rakhe fluid ki viscosity zero hoti hai.
False. Viscosity ek fixed material property hai jo chahe fluid move kare ya na kare, exist karti hai. Jo rest mein zero hota hai wo viscous stress hai, kyunki shear rate zero hai — lekin khud unchanged rehta hai.
True or false: Agar hai toh fluid A hamesha B se zyada slowly push spread karega.
False. Ek push (momentum) kitni tezi se spread hoti hai wo se decide hota hai, na ki sirf se. Air ka water se chhota hai phir bhi air ka bada hai (kyunki air ki ~800× chhoti hai), toh air momentum faster spread karta hai per unit mass.
True or false: Non-Newtonian ka matlab hai "bahut zyada viscous."
False. Non-Newtonian ka matlab hai ki constant nahi rehta jab shear rate change hoti hai. Water (bahut kam ) aur honey (bahut zyada ) dono Newtonian hain kyunki unka fixed rehta hai; ketchup non-Newtonian hai chahe wo itna thick nahi bhi ho.
True or false: Couette flow mein plate speed double karne se viscous stress bhi double ho jaata hai.
Newtonian fluid ke liye True. Profile linear rehta hai toh double ho jaata hai, aur linear hai, toh bhi double ho jaata hai. Non-Newtonian power-law fluid () ke liye yeh fail hota hai — stress scale karta hai, nahi.
True or false: Kinematic viscosity aur ek diffusion coefficient ke units same hote hain.
True. Dono m²/s hain. Isliye ko diffusivity of momentum kehte hain: time mein, momentum order ki distance spread karta hai, bilkul waise jaise heat ya dye spread hoti hai.
True or false: Oobleck (cornstarch + water) ki ek well-defined single viscosity number hoti hai.
False. Yeh shear-thickening hai: iska apparent viscosity tezi se shear karne par badhta hai (isliye tum us par daud sakte ho lekin khade raho toh doob jaate ho). Isko koi single describe nahi kar sakta — tumhe shear rate bhi batani hogi.
Spot the error
Error dhundho: "Parent note likhta hai , toh kinematic viscosity ek subtraction hai."
Heading mein typo hai; asli definition hai (ek division). Units confirm karte hain: , jabki incompatible units mix karta hai aur meaningless hai.
Error dhundho: "Kyunki hai, ek fast car bada viscous drag experience karti hai kyunki uski speed large hai."
Drag gradient se aata hai surface ke paas, speed se nahi. Door ki air bhi tezi se move karti hai, lekin stress is baat se decide hota hai ki speed car ki skin par zero tak kitni sharply girती hai — boundary-layer gradient. Dekho Boundary Layer.
Error dhundho: "Ketchup non-Newtonian hai, toh bottle ko zyada force se squeeze karne par uska apparent viscosity badhega."
Ketchup shear-thinning hai: zyada squeeze karna matlab zyada shear rate, toh girta hai aur woh aasani se flow karta hai. Student ne direction ulat di — woh reversal shear-thickening describe karta hai.
Error dhundho: "Toothpaste jaise Bingham plastic ke liye hai, toh zero applied stress par bhi thodi flow hogi."
Nahi — yield stress se neeche material bilkul flow nahi karta (). Formula sirf tab apply hota hai jab , se zyada ho jaaye; ek genuine threshold hai, isliye toothpaste apni shape pakde rehti hai.
Error dhundho: " ki units Pa honi chahiye kyunki yeh ek tarah ka stress hai."
stress nahi hai; yeh stress aur shear rate ka ratio hai. se derive karo: , yaani kg/(m·s), na ki Pa.
Error dhundho: "Power-law mein ek shear-thickening fluid describe karta hai."
exactly Newtonian hai (constant ). Shear-thickening ke liye chahiye; shear-thinning ke liye .
Why questions
Kyun shear stress layer speeds ke difference par depend karta hai, speeds par nahi?
Viscous stress layers ke beech molecular momentum-swapping hai. Agar dono layers already same speed par move kar rahi hain, toh ek exchanged molecule same momentum dono taraf le jaata hai, toh net transfer kuch nahi — isliye stress ko speed difference (gradient) chahiye.
Jab hamare paas already hai toh define karne ki kya zaroorat hai?
Newton ka second law kehta hai acceleration = force/mass, toh motion predict karne ke liye viscous force ko inertia se compare karna hota hai. density (inertia) ko fold kar leta hai, bata ta hai ki viscosity actually kitni tezi se flow accelerate aur spread karti hai — dekho Momentum Diffusion.
Reynolds number ke andar ki jagah natural quantity kyun hai?
Reynolds number inertial aur viscous effects compare karta hai, aur yeh comparison dimensionless tabhi hota hai jab viscosity (m²/s) ke roop mein length aur speed ke saath aaye. Dekho Reynolds Number.
Honey air se bahut zyada viscous kyun lagta hai jabki air ka bada hota hai?
"Lagana" track karta hai (shear karne ka force), jahan honey bahut aage hai. Lekin mein density se divide hota hai; air ki density saikdon guna chhoti hai, toh air ke liye bada ho jaata hai chahe uska tiny ho.
Newton ka law local gradient kyun use karta hai na ki overall ratio ?
gradient ke barabar tabhi hota hai jab velocity profile straight line ho. Curved profiles mein (jaise Poiseuille Flow pipe mein) gradient position ke saath vary karta hai, toh stress har point par true local se compute karna hota hai.
Shear-thinning paint brush par aur wall par dono jagah kaise kaam aata hai?
Brush par shear rate high hoti hai, toh low hota hai aur paint thinly spread hoti hai. Wall par shear rate near zero hoti hai, toh high hota hai aur paint chipki rehti hai bina drip kiye. Ek hi material do opposite needs serve karta hai.
Edge cases
Edge case: Kisi bhi fluid ke liye — Newtonian ho ya nahi — par viscous stress kya hoga?
Zero. Newtonian ke liye ; power-law fluid ke liye (agar hai). Iska ek exception Bingham plastic hai, jahan bina flow ke nonzero yield stress present ho sakta hai.
Edge case: Shear-thinning power-law fluid () ke liye par apparent viscosity ka kya hoga?
mein hai, toh par yeh infinity tak blow up karta hai. Physically paint rest mein effectively "solid" ban jaati hai — isliye woh drip nahi karti. Real fluids isko ek finite zero-shear plateau se cap karte hain.
Edge case: Shear-thickening fluid () ke liye par ka kya hoga?
mein hai, toh yeh grow karta rehta hai, isliye fast impact ke neeche fluid increasingly solid ki tarah behave karta hai — "oobleck par daudna, khade raho toh doobna" wala effect.
Edge case: Ideal (inviscid) fluid ke liye hai. kya hoga, aur kya break hota hai?
: momentum bilkul diffuse nahi hota, toh koi boundary layer nahi banta aur layers zero drag ke saath slide karte hain. Yeh ek useful idealisation hai lekin real wall par no-slip condition satisfy nahi kar sakta — dekho Stokes Drag aur Terminal Velocity jahan finite zaroori hai.
Edge case: Ek sphere oil mein girta hai aur steady speed reach karta hai. Final velocity kaun si viscosity govern karti hai, aur speed constant kyun rehti hai?
Dynamic viscosity drag force govern karta hai (Stokes drag ). Terminal velocity par upward drag exactly gravity minus buoyancy balance karta hai, toh net force zero hai aur speed change karna band ho jaata hai. Dekho Terminal Velocity.
Edge case: Agar do fluids ka same ho lekin alag ho, toh same Couette setup mein dono ka wall shear stress same hoga kya?
Haan — wall shear stress hai aur ismein nahi hai. Density tabhi aata hai jab tum acceleration ya momentum ke diffusion ke baare mein poochho ( ke through), instant stress mein nahi.
Recall One-line survival kit
Stress ko gradient chahiye; force-strength hai; spreading-speed hai; "Newtonian" ka matlab hai constant , magnitude se koi lena-dena nahi.