Fluid Mechanics & Fluid Machines

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  • Properties of Fluids S K Mondals Chapter 1

    1. Properties of Fluids

    Contents of this chapter 1. Definition of Fluid 2. Characteristics of Fluid 3. Ideal and Real Fluids 4. Viscosity 5. Units of Viscosity 6. Kinematic Viscosity 7. Units of Kinematic Viscosity 8. Classification of Fluids 9. Effect of Temperature on Viscosity 10. Effect of Pressure on Viscosity 11. Surface Tension 12. Pressure Inside a Curved Surface 13. Capillarity 14. Derive the Expression for Capillary Rise

    Theory at a Glance (for IES, GATE, PSU)

    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.

    Concept of Continuum

    Page 1 of 372

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    Page 2 of 372

  • Properties of Fluids S K Mondals Chapter 1

    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. Newtons Law of Viscosity: It states that the shear stress () 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 = dudy

    According to Newtons law dudy

    or = dudy

    Velocity Variation near a solid


    Where = constant of proportionality and is known as co-efficient of Dynamic viscosity or only Viscosity

    As dudy

    = 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= dyne-sec/cm2 One Poise= 0.1 Pa.s 1/100 Poise is called centipoises. Dynamic viscosity of water at 20oC is approx= 1 cP

    Page 3 of 372

  • Properties of Fluids S K Mondals Chapter 1

    Kinematic Viscosity It is the ratio between the dynamic viscosity and density of fluid and denoted by

    Mathematically dynamic viscositydensity

    = =

    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.

    Classification of Fluids 1. Newtonian Fluids These fluids follow Newtons viscosity equation.

    For such fluids viscosity does not change with rate of deformation. 2. Non- Newtonian Fluids These fluids does not follow Newtons viscosity equation.

    Such fluids are relatively uncommon e.g. Printer ink, blood, mud, slurries, polymer solutions.

    Non-Newtonian Fluid (dydu )

    Purely Viscous Fluids Visco-elastic Fluids

    Time - Independent Time - Dependent Visco-elastic Fluids

    Edydu +=

    Example: Liquid-solid combinations in pipe flow.

    1. Pseudo plastic Fluids


    = ndydu


    Example: Butter

    3. Bingham or Ideal

    1.Thixotropic Fluids





    f(t)is decreasing Example: Printer ink; crude oil

    2. Rheopectic Fluids

    Page 4 of 372

  • Properties of Fluids S K Mondals Chapter 1

    Plastic Fluid n

    o dydu


    Example: Water suspensions of clay and flash





    f(t)is increasing Example: Rare liquid solid suspension

    Fig. Shear stress and deformation rate relationship of different fluids

    Effect of Temperature on Viscosity With increase in temperature Viscosity of liquids decrease Viscosity of gasses increase Note: 1. Temperature responses 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.

    Page 5 of 372

  • Properties of Fluids S K Mondals Chapter 1

    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 For a general curved surface with radii of curvature r1 and r2 at a point of interest

    1 2

    1 1pr r

    = + a. Pressure inside a water droplet, 4p

    d =

    b. Pressure inside a soap bubble, 8pd =

    c. Liquid jet. 2pd =

    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.

    Capillary rise and depression phenomenon depends upo