Mechanics of Fluids

I.GNANASEELANlecturer,

department of mechanical Engineering, Parisutham institute of technology and science

Mechanics of Fluids

SEQUENCE OF CHAPTER 1 IntroductionObjectiveHistoryDefinition of a fluidDimension and unitsFluid propertiesContinuum Concept of system and control

volume

Introduction• Defined: the science that deals with the forces on fluids and

their actions.• Fluids: a substance consisting of particles that change their

position relative to each other.• A substance that will continuously deform when shear stress

is applied to it.• Solids resist stress, do not easily deform.

Objectives

Identify the units for the basic quantities of time, length, force and mass.

Properly set up equations to ensure consistency of units.

Define the basic fluid properties.

Identify the relationships between specific weight, specific gravity and density, and solve problems using their relationships.

History

Fluid Mechanics 5

Faces of Fluid Mechanics

Archimedes(C. 287-212

BC)

Newton(1642-1727)

Leibniz(1646-1716)

Euler(1707-1783)

Navier(1785-1836)

Stokes(1819-1903)

Reynolds(1842-1912)

Prandtl(1875-1953)

Bernoulli(1667-1748)

Taylor(1886-1975)

Fluid Mechanics

• Definition– The study of liquids and gases at rest (statics) and in

motion (dynamics)

• Engineering applications– Blood in capillaries– Oil in pipelines– Groundwater movement– Runoff in parking lots– Pumps, filters, rivers, etc.

States of Matter

• Fluids (gasses and liquids) and solids• What’s the difference?– Fluid particles are free to move among themselves

and give way (flow) under the slightest tangential (shear) force

FluidSolid

Shear Stress

Classes of Fluids

– Liquids: Close packed, strong cohesive forces, retains volume, has free surface

• Liquids and gasses – What’s the difference?

Liquid

Free Surface

Gas

Expands

– Gasses: Widely spaced, weak cohesive forces, free to expand

Common Fluids

• Liquids:– water, oil, mercury, gasoline, alcohol

• Gasses: – air, helium, hydrogen, steam

• Borderline: – jelly, asphalt, lead, toothpaste, paint, pitch

Dimensions and Units

• The dimensions have to be the same for each term in an equation

• Dimensions of mechanics are– length– time– mass– force– temperature

aF m aF m

L

T

M

MLT-2

Dimensions and Units

Quantity SymbolDimensionsVelocity V LT-1

Acceleration a LT-2

Area A L2

Volume L3

Discharge Q L3T-1

Pressure p ML-1T-2

Gravity g LT-2

Temperature T’ Mass concentration C ML-3

Dimensions and Units

Quantity Symbol DimensionsDensity ML-3

Specific Weight ML-2T-2

Dynamic viscosity ML-1T-1

Kinematic viscosity L2T-1

Surface tension MT-2

Bulk mod of elasticity E ML-1T-2

These are _______ properties!fluidHow many independent properties? _____ 4

Fluid Properties

• Density: Mass per unit volume– How large is the volume?• Too small: # molecules changes continuously• Large: # molecules remains almost constant

– At these scales, fluid properties (e.g., density) can be thought of as varying continuously in space.

V

m

VV

*lim

Density

• Mass per unit volume (e.g., @ 20 oC, 1 atm)– Water water = 1000 kg/m3

– Mercury Hg = 13,500 kg/m3

– Air air = 1.22 kg/m3

• Densities of gasses increase with pressure• Densities of liquids are nearly constant

(incompressible) for constant temperature• Specific volume = 1/density

Specific Weight

• Weight per unit volume (e.g., @ 20 oC, 1 atm)

water = (998 kg/m3)(9.807 m2/s)

= 9790 N/m3

[= 62.4 lbf/ft3]air = (1.205 kg/m3)(9.807 m2/s)

= 11.8 N/m3

[= 0.0752 lbf/ft3]

]/[]/[ 33 ftlbformNg

Specific Gravity

• Ratio of fluid density to density at STP(e.g., @ 20 oC, 1 atm)

3/9790 mkgSG

liquid

water

liquidliquid

– Water SGwater = 1– Mercury SGHg = 13.6– Air SGair = 1

3/205.1 mkgSG

gas

air

gasgas

Ideal Gas Law

• Equation of state

TnRpV n MRRRTp n /,

Rn = universal gas constant

M = molecular weight of the gas