×
I'm working hard to be someone I'll be proud of.
--Your friends at LectureNotes
Close

Note for Fluid Mechanics - FM by VIVEK KUMAR

  • Fluid Mechanics - FM
  • Note
  • NIT Silchar - NITS
  • Civil Engineering
  • B.Tech
  • 9 Topics
  • 793 Views
  • 6 Offline Downloads
  • Uploaded 5 months ago
Vivek Kumar
Vivek Kumar
0 User(s)
Download PDFOrder Printed Copy

Share it with your friends

Leave your Comments

Text from page-1

. Properties of Fluids………………….………………………………………….………………..…………….S. K. Mondal.. Properties of Fluids Skip to Questions (IAS, IES, GATE) Highlights Definition of fluid A fluid is a substance which deforms continuously when subjected to external shearing forces. Characteristics of fluid 1. It has no definite shape of its own, but conforms to the shape of the containing vessel. 2. Even a small amount of shear force exerted on a fluid will cause it to undergo a deformation which continues as long as the force continues to be applied. 3. It is interesting to note that a solid suffers strain when subjected to shear forces whereas a fluid suffers Rate of Strain i.e. it flows under similar circumstances. Ideal and Real Fluids 1. Ideal Fluid An ideal fluid is one which has no viscosity no surface tension and incompressible 2. Real Fluid An Real fluid is one which has viscosity surface tension and compressible Naturally available all fluids are real fluid. Viscosity Definition: Viscosity is the property of a fluid which determines its resistance to shearing stresses. Cause of Viscosity: It is due to cohesion and molecular momentum exchange between fluid layers. Newton’s Law of Viscosity: It states that the shear stress (τ) on a fluid element layer is directly proportional to the rate of shear strain. The constant of proportionality is called the co-efficient of viscosity. When two layers of fluid, at a distance ‘dy’ apart, move one over the other at different velocities, say u and u+du Velocity gradient = du dy According to Newton’s law τ∞ du dy or τ=μ du dy Velocity Variation near a solid boundary Contact: swapan_mondal_01@yahoo.co.in............................................................................................................. 1

Text from page-2

. Properties of Fluids………………….………………………………………….………………..…………….S. K. Mondal.. Where = constant of proportionality and is known as co-efficient of Dynamic viscosity or only Viscosity As μ= τ ⎡ du ⎤ ⎢ dy ⎥ ⎣ ⎦ Thus viscosity may also be defined as the shear stress required producing unit rate of shear strain Units of Viscosity S.I. Units: Pa.s or N.s/m2 C.G.S Unit of viscosity is Poise= dune-sec/cm2 One Poise= 0.1 Pa.s 1/100 Poise is called centipoises. Dynamic viscosity of water at 200C is approx= 1 cP Kinematic Viscosity It is the ratio between the dynamic viscosity and density of fluid and denoted by Mathematically ν = dynamic viscosity μ = ρ density Units of Kinematic Viscosity S.I units: m2/s C.G.S units: stoke = cm2/sec One stoke = 10-4 m2/s Thermal diffusivity and molecular diffusivity have same dimension, therefore, by analogy, the kinematic viscosity is also referred to as the momentum diffusivity of the fluid, i.e. the ability of the fluid to transport momentum. Effect of Temperature on Viscosity With increase in temperature Viscosity of liquids decrease Viscosity of gasses increase Note: 1. Temperature response are neglected in case of Mercury 2. The lowest viscosity is reached at the critical temperature. Effect of Pressure on Viscosity Pressure has very little effect on viscosity. But if pressure increases intermolecular gap decreases then cohesion increases so viscosity would be increase. Classification of fluids 1. Newtonian Fluids These fluids follow Newton’s viscosity equation. For such fluids viscosity does not change with rate of deformation 2. Non- Newtonian fluids This fluid does not follow Newton’s viscosity equation. Such fluids are relatively uncommon e.g. Printer ink, blood, mud, slurries, polymer solutions. Contact: swapan_mondal_01@yahoo.co.in............................................................................................................. 2

Text from page-3

. Properties of Fluids………………….………………………………………….………………..…………….S. K. Mondal.. Non-Newtonian Fluids (τ ≠ μ du ) dy Purely Viscous Fluids Time - Independent Time - Dependent 1. Pseudo plastic Fluids 1.Thixotropic Fluids ⎛ du ⎞ n ⎛ du ⎞ τ = μ ⎜⎜ ⎟⎟ ; n < 1 ⎝ dy ⎠ n τ = μ ⎜⎜ ⎟⎟ + f (t ) ⎝ dy ⎠ Example: Blood, milk f(t)is decreasing 2. Dilatant Fluids ⎛ du ⎞ Example: Printer ink; crude oil Visco-elastic Fluids Visco- elastic Fluids du τ =μ + αE dy Example: Liquid-solid combinations in pipe flow. 2. Rheopectic Fluids n τ = μ ⎜⎜ ⎟⎟ ; n > 1 ⎝ dy ⎠ n ⎛ du ⎞ τ = μ ⎜⎜ ⎟⎟ + f (t ) Example: Butter ⎝ dy ⎠ 3. Bingham or Ideal Plastic f(t)is increasing Fluid Example: Rare liquid solid suspension ⎛ du ⎞ τ = τ o + μ ⎜⎜ ⎟⎟ ⎝ dy ⎠ n Example: Water suspensions of clay and flyash Surface tension Surface tension is due to cohesion between particles at the surface. Capillarity action is due to both cohesion and adhesion. Surface tension The tensile force acting on the surface of a liquid in contact with a gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension. Pressure inside a curved surface ⎛1 1⎞ + ⎟ r ⎝ 1 r2 ⎠ For a general curved surface with radii of curvature r1 and r2 at a point of interest Δp = σ ⎜ a. Pressure inside a water droplet, Δp = b. Pressure inside a soap bubble, c. Liquid jet. Δp = 2σ d Δp = 4σ d 8σ d Capillarity A general term for phenomena observed in liquids due to inter-molecular attraction at the liquid boundary, e.g. the rise or depression of liquids in narrow tubes. We use this term for capillary action. Capillarity rise and depression phenomena depends upon the surface tension of the liquid as well as the material of the tube. Contact: swapan_mondal_01@yahoo.co.in............................................................................................................. 3

Text from page-4

. Properties of Fluids………………….………………………………………….………………..…………….S. K. Mondal.. 1. General formula, h= 4σ cos θ ρ gd 2. For water and glass θ = 0o, h= 4σ ρ gd 3. For mercury and glass θ = 138o , h=− 4σ cos 42 ρ gd (h is negative indicates capillary depression) Note: If adhesion is more than cohesion, the wetting tendency is more and the angle of contact is smaller. Questions (IAS, IES, GATE) Fluid 1. The drag force exerted by a fluid on a body immersed in the fluid is due to (a) pressure and viscous forces (b) pressure and gravity forces (c) pressure and surface tension (d) viscous and gravity forces Forces [IES-2002] 2. Which one of the following sets of conditions clearly apply to an ideal fluid? (a) Viscous and compressible (b) Nonviscous and incompressible (c) Nonviscous and compressible (d) Viscous and incompressible [IAS-1994] Viscosity 3. Newton’s law of viscosity depends upon the (a) stress and strain in a fluid (c) shear stress and rate of strain [IES-1998] (b) shear stress, pressure and velocity (d) viscosity and shear stress 4. The shear stress developed in lubricating oil, of viscosity 9.81 poise, filled between two parallel plates 1 cm apart and moving with relative velocity of 2 m/s is [IES-2001] (a) 20 N/m2 (b) 19.62 N/m2 (c) 29.62 N/m2 (d) 40 N/m2 5. The SI unit of kinematic viscosity ( υ ) is (a) m2/s (b) kg/m-s (c) m/s2 6. What are the dimensions of kinematic viscosity of a fluid? (a) LT-2 (b) L2T-1 (c) ML-1T-1 (d) m3/s2 (d)ML-2T-2 [GATE-2001] [IES-2007] 7. An oil of specific gravity 0.9 has viscosity of 0.28 Strokes at 380C. What will be its viscosity in Ns/m2 ? (a) 0.2520 (b) 0.0311 (c) 0.0252 (d) 0.0206 [IES-2005] 8. Kinematic viscosity of air at 200C is given to be 1.6 × 10-5m2/s. Its kinematic viscosity at 700C will be vary approximately [GATE-1999] (a) 2.2 × 10-5m2/s (b) 1.6 × 10-5m2/s (c) 1.2 × 10-5m2/s (d) 3.2 × 10-5m2/s Contact: swapan_mondal_01@yahoo.co.in............................................................................................................. 4

Lecture Notes