Applied Fluid Mechanics (Unit 2) Viscosity of Fluids PDF

APPLIED FLUID MECHANICS (UNIT 2) Viscosity of Fluids ▪ Viscosity ▪ Newton’s Law of Viscosity ▪ Dynamic viscosity ▪ Kinematic Viscosity ▪ Newtonian fluids & non-Newtonian fluids ▪ Viscosity with temperature ▪ Viscosity measurement ▪ SAE viscosity grades / ISO...

APPLIED FLUID MECHANICS (UNIT 2) Viscosity of Fluids ▪ Viscosity ▪ Newton’s Law of Viscosity ▪ Dynamic viscosity ▪ Kinematic Viscosity ▪ Newtonian fluids & non-Newtonian fluids ▪ Viscosity with temperature ▪ Viscosity measurement ▪ SAE viscosity grades / ISO viscosity grades VISCOSITY OF FLUIDS 1 Learning Outcomes https://www.google.com/url?sa=i&url=http%3A%2F%2Ftqfstrategies.blogspot.com%2F2012%2F06%2Fon-learning- outcome.html&psig=AOvVaw2vW7m0kSCnVOhm_93cvywu&ust=1638632020894000&source=images&cd=vfe&ved=2ahUKEwjshbqN-sf0AhUS3RoKHY5uCGoQr4kDegUIARDcAQ At the end of this section, students will be able to:- Explain the concept of Newton’s Law of Viscosity with the aid of governing equations. Compare the differences between dynamic and kinematic viscosity. Solve the problems with the aid of governing equations. Apply the concept of viscosity in process engineering. 10/9/2024 2 Basics of Fluid Properties  OBJECTIVES Define dynamic and kinematic viscosity. Identify the units of viscosity in SI system. Illustrate the difference between a Newtonian fluid and a non-Newtonian fluid. Describe the methods of viscosity measurement Describe the viscosity of lubricants using SAE viscosity grades and the ISO viscosity grades VISCOSITY OF FLUIDS 3  Viscosity Viscosity is a measure of the resistance of a fluid to flow (or) fluid's internal resistance to flow. It is a property of fluids, which resists the movement of one layer of fluid over another layer of fluid. All fluids have some resistance to flow. Hence, all the fluids have some viscosity. VISCOSITY OF FLUIDS 4  EXAMPLES OF VISCOUS FLUIDS Glycerine, castor oil, tar have high viscosity Water, kerosene, petrol have low viscosity VISCOSITY OF FLUIDS 5  NEWTON’S LAW OF VISCOSITY NEWTON’S LAW OF VISCOSITY Consider two layers of fluid of area A, at a distance of y. Force F acts on upper fluid to move over the lower fluid, with a velocity U. It states that the shear stress on a fluid element layer is directly proportional to the rate of shear strain or velocity gradient.   (du/dy) To remove the above proportionality, a constant is included, which is called as constant of proportionality or the coefficient of viscosity or dynamic viscosity (μ).  = μ (du/dy) Where,  = shear stress = FORCE / AREA, (N/m2) du = change in velocity, (m/s) dy = change in the distance, (m) du/dy = Velocity Gradient or shear strain, (1/s) or (s-1) μ = coefficient of viscosity or dynamic viscosity (kg/ms) or (Ns/m2) (Rajput, 2011) du VISCOSITY OF FLUIDS 6  APPLICATIONS OF VISCOSITY APPLICATION OF VISCOSITY 1. Transparent and storing facilities for fluids i.e., pipes, tanks 2. Bitumen used for road construction. 3. Designing of the sewer line or any other pipe flow, viscosity play an important role in finding out its flow behavior. 4. Drilling for oil and gas requires sensitive viscosity. 5. To maintain the performance of machine and automobiles by determining thickness of lubricating oil or motor oil. Types of viscosity Dynamic viscosity (µ) Kinematic viscosity () VISCOSITY OF FLUIDS 7  Dynamic Viscosity Unit of Dynamic Viscosity (µ) are Pa.s (Pascal.second) or Ns/m2 or kg/ms or poise.  = μ (du/dy) μ =  / (du/dy) 1 Pa.s = 10 Poise 1 Ns/m2 = 10 poise 1 poise = (1/10) Ns/m2 VISCOSITY OF FLUIDS 8  Kinematic Viscosity Kinematic Viscosity (ν ) It is defined as the ratio between the dynamic viscosity and density of the fluid. 𝜇 2 𝜐 = (𝑚 /𝑠) 𝜌 Kinematic viscosity (ν) has SI unit m²/s. Its CGS unit is stoke (S) or centistoke (cSt). 1 stoke = 10-4 m2 /s or 0.0001 m2 /s or 1 cm2/s 1 cSt = 10-6 m2 /s or 0.000001 m2 /s VISCOSITY OF FLUIDS 9  VARIATION OF VISCOSITY WITH TEMPERATURE Due to effects of cohesive forces and molecular momentum transfer, the variation in viscosity varies with temperature. For liquids, cohesive forces are dominant, so viscosity decreases on heating. For gases, molecular momentum dominates and hence viscosity increases Viscosity (poise) Temperature (⁰C) Viscosity (poise) Temperature (⁰C) VISCOSITY OF FLUIDS 10 Due to effects of cohesive forces and molecular momentum transfer, the variation in viscosity varies with temperature. For liquids, cohesive forces are dominant, so viscosity decreases on heating. For gases, molecular momentum dominates and hence viscosity increases Viscosity (poise) Temperature (⁰C) Viscosity (poise) Temperature (⁰C) VISCOSITY OF FLUIDS 11 VARIATION OF VISCOSITY WITH TEMPERATURE (MOTT, 2015) VISCOSITY OF FLUIDS 12  FLUIDS CLASSIFICATION IDEAL FLUID or IMAGINARY FLUID (ZERO viscosity, surface tension & incompressible) REAL FLUID or PRACTICAL FLUID (all fluids) NEWTONIAN FLUID (water, kerosene) NON-NEWTONIAN FLUID (alcohol, honey) IDEAL PLASTIC FLUID (e.g. drilling fluid)  (N /m2) (1 /s) (MOTT, 2015) VISCOSITY OF FLUIDS 13  Newtonian & Non-Newtonian Fluids Fluids which obeys Newton law of viscosity, are known as Newtonian fluids. (Eg. Air, water etc.) Fluids which does not obey Newton law of viscosity, are known as Non-Newtonian fluids. (Honey, Paints etc.) VISCOSITY OF FLUIDS 14  Viscosity index (VI) ▪Viscosity index is a aspect which shows how the viscosity of fluid changes with temperature. ▪This is especially important for lubricating oils and Hydraulic fluids used in equipments that must operate at extreme temperatures VISCOSITY OF FLUIDS 15  VISCOSITY MEASUREMENT VISCOMETERS or RHEOMETERS are used to measure viscosity of fluids. Various types are: 1. Rotating drum Viscometer 2. Capillary tube Viscometer 3. Falling –ball Viscometer 4. Saybolt Universal Viscometer VISCOSITY OF FLUIDS 16  Viscosity Measurement Saybolt Universal Viscometer Saybolt Equations: (Rajput, 2015) (cS) = 0.226t - 195/t, t< 100 SUS (cS) = 0.220t – 135/t, t> 100 SUS Where t, amount of time (seconds, SUS, Saybolt Universal Seconds) it takes for 60 cm3 to flow through orifice (Saybolt viscometer) VISCOSITY OF FLUIDS 17  SAE VISCOSITY GRADES for engine oils & for automobile lubricants The actual viscosity grade of a lubricant is determined by the Society of Automotive Engineers (SAE) (Mott, 2015) For example SAE-15W for a monograde oil SAE-15W40 for a multi-grade oil, and SAE-40 for a monograde oil. The first number (15W) refers to the viscosity grade at low temperatures, whereas the second number (40) refers to the viscosity grade at high temperature. REFER THE TABLE IN THE BOOK (MOTT, 2015) Steve Streater. Technical Advisor – Fluids and Lubricants, TransDiesel Ltd VISCOSITY OF FLUIDS 18  ISO VISCOSITY GRADES ▪There are 20 ISO Viscosity grades for oils used in industries ▪The Standard designation is ISO VG followed by a number representing the nominal kinematic viscosity in cSt (mm2 /s). eg : ISO VG 22 ▪This refers to a viscosity grade of 22 cSt ± 10% at 40°C. REFER THE TABLE IN THE BOOK VISCOSITY OF FLUIDS 19  Characteristics of Hydraulic Fluids Adequate viscosity Lubricating capability Cleanliness Chemical stability Non-corrosiveness Ability to resist growth of bacteria Ecologically acceptable Low compressibility VISCOSITY OF FLUIDS 20  SAE VISCOSITY GRADES MEANING The scale ranges from 0 to 60. The numbers from 0 to 25 have the letter W added. This means that they are "winter" viscosity, for use at lower temperatures. A single grade oil like 15W or SAE 40 oil has a high viscosity when cold and a lower viscosity when hot. The first number 15W is the viscosity of the oil at cold temperature, and the second number 40 is the viscosity at 100 °C. The viscosity of a liquid is its resistance to flow. High intermolecular forces between the molecules cause a high viscosity. As the liquid warms up, the added kinetic energy overcomes some of the attractive forces. The viscosity decreases. VISCOSITY OF FLUIDS 21 PROBLEMS RELATED TO SHAFT AND BEARING π𝑑𝑁 𝑚 1. VELOCITY (u) = ( ) WHERE, ‘N’ is the speed of the shaft (RPM) 60 𝑠 𝑆𝐻𝐸𝐴𝑅 𝐹𝑂𝑅𝐶𝐸 𝑁 2. SHEAR STRESS = ( ) 𝐴𝑅𝐸𝐴 𝑚2 3. Area of the shaft = π * d * L (𝑚2) WHERE, ‘d’ & ‘L’ is the diameter and length of the shaft (m) 4. Torque (T) = radius of the shaft * Shear force (N.m) 2π𝑁𝑇 5. Power of the shaft (P) = (W) 60 VISCOSITY OF FLUIDS 22 References Rajput, R.K. (2011). Fluid Mechanics & Hydraulic Machines, New Delhi: S Chand Publications. Robert L. Mott (2015). Applied Fluid Mechanics, London: Pearson Global Edition. VISCOSITY OF FLUIDS 23