II. Properties of Fluids

Contents 1. Definition of Fluids 2. Continuum Hypothesis 3. Density and Compressibility 4. Viscosity 5. Surface Tension 6. Vaporization 7. Forces Acting on Fluids

1. Definition of Fluids

Definition of Fluids A fluid is a substance that deforms continuously when subjected to a shear stress, no matter how small that the shear stress may be Flows

SolidFluid

Fixed Plate Fluid

Definition of Fluids A fluid is a substance that cannot support any shear stress in static state

Fluids Liquids (water) Gases (air) Classification of Fluids

Liquids and Gases Liquid has definite volume; gas has no definite volume.

2. Continuum Hypothesis

The Sensitive Volume The minimal volume in which the number of fluid molecule is big enough so that the average of any physical quantity over this volume is essentially independent of the volume itself

Physical quantity Sensitive volume Micro effect Macro effect

The Sensitive Volume FACT: There are 2.7  molecules in 1 mm 3 air of 0  C at 1 atm The sensitive volume is usually very small (infinitesimally small) from a macroscopic view

Fluid Particle A mass of fluid that has a spatial dimension equivalent to the sensitive volume

Mathematical point of view: Fluid particle = Moving point with no size with no orientation

Continuum Hypothesis At any point in a fluid we can find a fluid particle which occupies that point The fluid is a continuum formed by fluid particles

3. Density and Compressibility

Density

Density Density is the mass per unit volume Unit: kg / m 3

Specific Weight Unit: N / m 3

Specific Volume Specific Volume is the volume occupied by a unit mass of fluid

Compressibility of Fluid (Bulk modulus)

Compressibility of Water

Incompressible Fluid

The bulk modulus of liquid is usually very large, or the compressibility of liquid is usually very small Water can be assumed as incompressible fluid in hydraulics

Incompressible Fluid A fluid can be assumed to be incompressible if the variation of density within the flow is not large Air can be assumed as incompressible fluid when velocity is much smaller than the speed of sound

4. Viscosity

Viscosity EXPERIMENT A measurement on stickiness of fluids

Viscosity A measurement on the ability of a fluid to resist shearing

Fixed Plate Moving Plate

Measured Results  The flow is nearly parallel  The fluid near the lower plate does not move  The fluid near the upper plate moves with the plate  The velocity distribution in y direction is linear 

Viscosity Viscosity Shear stress Rate of strain

Viscosity Coefficient of Viscosity Absolute Viscosity Dynamic Viscosity Unit of  : N  s / m 2

Dynamic Viscosity of Fluids

Viscosity is a function of temperature

Newtonian and Non-Newtonian Fluid

Inviscid Fluid (   ) The viscosity of water is very small and may be omitted depends on the problem of interest Water can be assumed as inviscid fluid in many situations

Kinematic Viscosity Unit of  : m 2 / s

Kinematic Viscosity of Fluids

Problem A journal bearing consists of a shaft and a sleeve as shown in the following figure. The clearance space is filled with oil. The sleeve is fixed. The shaft turns at a known speed. Calculate the rate of heat generation at the bearing. Diameter of shaft: d (m) Diameter of sleeve: d  (m) Length of sleeve: l (m) Viscosity of oil:  (N  s/m 2 ) Speed of shaft: n (rpm) Shaft Sleeve Oil

Solution Angular velocity of the shaft: Shear stress on the surface of the shaft: Torque to keep rotation of the shaft: Heat generation rate (= Power):

5. Surface Tension

Capillary Rise

Surface Tension  = Surface tension per unit length Unit of  : N / m

6. Vaporization

ICE WATERVAPOR

Vapor Pressure p Water Vapor

Vapor Pressure

6. Forces Acting on Fluids

Two Types of Forces Body force Body force  Forces acting on fluid mass, e.g. gravity force Surface force Surface force  Contact force acting on fluid surface

Description of Body Force (Force per unit mass) In case of gravity,

Description of Surface Force (Force per unit area = Stress) Normal stress Shear Stress

END OF CHAPTER II