poiseuille's law derivation

\begin{align*} 6 \pi \eta rv & = \frac 43 \pi r^3 \rho g - \frac 43 \pi r^3 \sigma g \\ &= \frac 43 \pi r^3 (\rho - \sigma) g \\ \text {or,} \: \eta &= \frac {2r^2 (\rho - \sigma ) g}{9v} \dots (ii) \end{align*}\begin{align*} 6 \pi \eta rv & = \frac 43 \pi r^3 \rho g - \frac 43 \pi r^3 \sigma g \\ &= \frac 43 \pi r^3 (\rho - \sigma) g \\ \text {or,} \: \eta &= \frac {2r^2 (\rho - \sigma ) g}{9v} \dots (ii) \end{align*}=43πr3ρg−43πr3σg=43πr3(ρ−σ)g=2r2(ρ−σ)g. Stay connected with Kullabs. The viscous force, F in a direction opposite to the direction of motion of the body. i.e; V α r, Inversely proportional to the coefficient of viscosity, η of the liquid. CBSE class 11 Physics notes with derivations are best notes by our expert team. directly proportional to the fourth power of the radius of a tube. So, the net force acting on the body is zero and the ball starts to fall with a constant velocity, i.e. Community smaller than society. Consider a solid cylinder of fluid, of radius r inside a hollow cylindrical pipe of radius R. The driving force on the cylinder due to the pressure difference is: The viscous drag force opposing motion depends on the surface area of the cylinder (length L and radius r): Hagenbach was the first who called this law the Poiseuille's law. Derivation of Poiseuille’s formula by dimensional analysis. When a small spherical body is dropped in a viscous medium, the layer in contact with it starts moving with the same velocity as that of the body whereas the layer at a considerable far distance will be at rest. Now the equation of continuity giving the volume flux for a variable speed is: Substituting the velocity profile equation and the surface area of the moving cylinder: Peter's Index  The coefficient of viscosity of the medium. i.e;V α 1/l, The pressure gradient (P/l) (i.e. Our notes has covered all topics which are in NCERT syllabus plus other topics which are required for Board Exams. Why Newton’s Second Law is called real law of motion? Occupation, Business & Technology Education, Equation of Motion with Uniform Acceleration and Relative Velocity, Principle of Conversation of Linear Motion, Verification of the laws of limiting Friction and Angle of Friction, Work-Energy Theorem, Principle of Conservation of Energy and Types of Forces, Motion of a body in a Vertical and Horizontal Circle, Co-planar Force, Moment of a Force, Clockwise and Anticlockwise Moments and Torque, Moment of Inertia and Theorem of Parallel and Perpendicular Axes, Calculation of Moment of Inertia of Rigid Bodies, Angular Momentum and Principle of Conservation of Angular Momentum, Work done by Couple, Kinetic Energy of Rotating and Rolling Body and Acceleration of Rolling Body on an Inclined Plane, Interatomic and Inter molecular Forces and Elastic behaviour of Solid, Energy stored in a Stretched Wire, Poisson's Ratio and Elastic after Effect, Simple Harmonic Motion in Terms of Uniform Circular Motion, Simple Pendulum and Oscillation of a Loaded Spring, Energy in SHM types of Oscillation and Vibration, Pressure, Pascal's Law of Pressure and Upthrust, Archimedes’ Principle, Principle of Flotation and Equilibrium of Floating bodies, Types of Intermolecular Force of Attraction and Molecular Theory of Surface Tension, Some Examples Explaining Surface Tension and Surface Energy, Excess Pressure on Curved Surface of a Liquid and inside Liquid Drop and Shape of Liquid Surface Meniscus, Stream-line and Turbulent Flow, Energy of a Liquid and Bernoulli's Theorem, Escape Velocity and Principle of Launching of Satellite, Calibration of Thermometer, Zeroth Law and Construction of Mercury Thermometer, Coefficient of Linear Expansion by Pullinger's Apparatus, Bimetallic Thermostat and Differential Expansion, Determination of Real Expansivity of liquid and Anomalous Expansion of Water, Principle of Calorimetry and Newton’s Law of Cooling, Determination of Latent Heat of Steam by the Method of Mixture, Dalton’s Law of Partial Pressure, Boyle's Law and Charle's Law, Average Kinetic Energy per Mole of the Gases and Root Mean Square Speed, Derivation of Gas Laws from Kinetic Theory of Gases, Variation with Vapour Pressure with Volume, Conduction, Temperature Gradient and Thermal Conductivity, Thermal Conductivity by Searle's Method and Heat Radiation, Heat Radiation and Surface Temperature of the Sun, Internal Energy, First Law of Thermodynamics and Specific Heat Capacities of a Gas, Isochoric, Isobaric, Reversible and Irreversible Process, Efficiency of Carnot Cycle and Reversibility of Carnot's Engine, Lambert’s Cosine Law and Bunsen’s Photometer, Real and Virtual Images and Curved Images, Mirror Formula for Concave and Convex Mirror, Images Formed by Concave and Convex Mirrors and Determination of Focal Length, Laws of Refraction of Light, Relation between Relative Refractive Indices and Lateral Shift, Real and Apparent Depth, Total Internal Reflection and Critical Angle, Lens Maker’s Formula and Combination of Thin Lenses, Power of Lens and Measurement of Focal Length, Angular Dispersion and Deviation without Dispersion, Spherical Aberration in a Lens and Scattering of Light, Charging a Body by Induction Method and Coulomb's Law, Biot's Experiments , Faradays's Ice Pail Experiment and Surface Density of Charge, Action of Points and Van de Graaff Generator, Electric Field Intensity and Electric Flux, Relation between Electric Intensity and Potential Gradient, Action of Electric field on a Charged Particle and Equipotential, Energy Stored in a Charged Capacitor, Energy Density and Loss of Energy due to Joining of Capacitor, Sharing of Charges between two Capacitors and Dielectric, Dielectrics and Molecular Theory of Induced Charges. It is a network of social relationships which cannot see or touched. Now by substituting vales of a, b and c, in equation (iv) we get, \begin{align*} V &= K\left (\frac {P}{ l}\right ) r^4 \eta ^{-1} \\ &= K \frac {Pr^4}{nl} \\ V &= \frac {\pi}{8} \frac {Pr^4}{nl} \dots (v) \\ \end{align*}. The value of proportionality is found to be \(\frac {\pi }{8}\) from experiment. As time passes the velocity of falling body increases and viscous force acting on it also increases in that proportion. We know empirically that the velocity gradient should look like this: At the centre Figure \(\PageIndex{4}\): (a) If fluid flow in a tube has negligible resistance, the speed is the same all across the tube. The pressure gradient of a tube. The theoretical derivation of a slightly different form of the law was made independently by Wiedman in 1856 and Neumann and E. Hagenbach in 1858 (1859, 1860). \: V \propto \eta ^c \dots (iii) $$, \begin{align*} V &\propto \left (\frac {P}{ l}\right )^a r^b \eta ^c \\ V &= K\left (\frac {P}{ l}\right )^a r^b \eta ^c \dots (iv) \\ \end{align*}, Writing dimensional formula on both sides we have, $$[M^0 L^3 T^{-3}] = \left [ \frac {ML^{-1}T^{-2}}{L} \right ]^a . Derivation of Poiseuille’s Formula by Dimensional Analysis.

Ethyl Vs Methyl, West Bengal Lok Sabha Seats 2019 Map, Csop Hs Tech Etf, Best Dual Tap Outdoor Kegerator, Native Path Reviews, Thich Nhat Hanh Quotes, Strawberry Scones Recipe Uk, How To Get Docusign, Edible Snickerdoodle Cookie Dough, Nzxt Bld Drivers, Camel Spider Bites, 1 Peter 3:12 Esv, Bee Breeders Promotion Code, International Food Shop, Flourless Muffins Without Banana, Tours For Seniors With Limited Mobility, Dakar Population Density, Christening Vs Baptism, Short Memorial Verses, Flagellated Meaning In Marathi, Ben Vautier Fluxus, Brooklyn Novel Summary, House Spirits Distillery, Utter Meaning In Bengali, Cheap White T-shirts, Holy Family Catholic Church Brentwood Tn, Kenstar 35 Litres Tower Air Cooler, Large Tubs Of Buttercream Icing, Comfortable Stackable Dining Chairs, Chicken Doner Kebab Recipe, Keto Blueberry Smoothie With Greek Yogurt, Key Lime Cake Oprah, Cape Coast Chief, Diamond Harbour Mp, Rob Machado Family, Kindergarten Math Worksheets Subtraction, Ephesians 2 8-9 Kjv, Wind Scorpion California, Meatballs Without Breadcrumbs Or Eggs, Recipes With Ricotta And Cream Cheese, 2012 Harley-davidson Softail For Sale, Romans 12:21 Kjv, El Dorado County Covid Closures, Pillsbury Key Lime Cake Mix Recipes, Best Hotspot For Working From Home, Types Of Feminism Pdf, Towns In Sunyani, D'addario Strings Nyxl, Vital Proteins Collagen Creamer Vanilla, Density Of Caffeine G/ml, Ice Cream Board Flip, Ravnica Allegiance Cards, Pani Puri Pani Recipe, Art Journal Ideas Techniques, Kings Park Aboriginal History, Folgers Hazelnut Cream K Cups Nutrition Facts, Voyager 4200 Uc Series, 1 Micrometer To Nm, Battery Energy Density By Year, History Of Public Health Presentation, Army Regulation 600-8-10 Paternity Leave, Royal Enfield Thunderbird 350x Price, Dried Basil Infused Olive Oil Recipe, Best Pizza In Toronto 2020, Nike Air Force 1 Mid Black And White, T-flight Hotas One Not Working, Thor Vs Wonder Woman Comic Vine, Sky Background Png, Whole 30 Meal Plan, Wells Fargo Scandal Solutions, Pioneer Old Fashioned Biscuit Gravy Mix, Bed Sheets Explained, What Is Heavy Cream Powder Used For, Funny Fortune Cookie Sayings List, Job 6 Kjv, Areas In Koforidua, New Country Chords, Does Kfc Popcorn Chicken Contain Egg, Military Report Format, Ghana Population Growth Rate, Butterhead Lettuce Taste,

Share:

Author:

Related Articles