Chapter 1 - Properties of Fluids

Fluid Mechanics

a physical science dealing with the action of fluids at rest or in motion, and with applications and devices in engineering using fluids

• Fluid Statics

• Fluid Dynamics

Two major areas of fluid mechanics:

Fluid Statics

deals with fluids at rest

Fluid Dynamics

concerned with fluids in motion

Hydrodynamics

applied to the flow of liquids or to low-velocity gas flows where the gas can be considered as being essentially incompressible

Hydraulics

deals with the application of fluid mechanics to engineering devices involving liquids, usually water or oil

Hydraulics

deals with such problems as the flow of fluids through pipes or in open channels, the design of storage dams, pumps, and water turbines, and with other devices for the control or use of liquids, such as nozzles, valves, jets, and flowmeters

• Ideal Fluids

• Real Fluids

Two categories of fluids:

Ideal Fluids

assumed to have no viscosity (and hence, no resistance to shear)

Ideal Fluids

incompressible

Ideal Fluids

have uniform velocity when flowing

Ideal Fluids

no friction between moving layers of fluid

Ideal Fluids

no eddy currents or turbulence

Real Fluids

exhibit infinite viscosities

Real Fluids

non-uniform velocity distribution when flowing

Real Fluids

compressible

Real Fluids

experience friction and turbulence in flow

• Newtonian Fluids

• Non-Newtonian Fluids

Real fluids are further divided into:

• Pseudoplastic Fluids

• Delatant Fluids

• Bingham Fluids

What is under non-Newtonian fluids?

Mass Density

mass per unit volume

• English: slugs/ft³

• Metric: gram/cm³

• SI: kg/m³

Units of Mass Density (ρ):

Density in pound-mass divided by g, which represents the acceleration due to gravity (ρ_lbm/g)

Density expressed in slugs (ρ_slugs) is equal to what?

• ρ - absolute pressure of gas in Pa

• R - gas constant Joule/kg-°K

• T - absolute temperature in °Kelvin

Formula of density for an ideal gas:

• 287 J/kg-°K

• 1716 lb-ft/slug-°R

What is the gas constant of air?

°K = °C + 273

Temperature conversion from °C to °K:

°R = °F + 460

Temperature conversion from °F to °R:

• 1.29

• 1.20

• 790

• 602

• 720

• 1260

• 13600

• 1000

What are the approximate room temperature densities of common fluids?

• Air (STP)

• Air (21 °F, 1 atm)

• Alcohol

• Ammonia

• Gasoline

• Glycerine

• Mercury

• Water

Specific Volume (V_s)

the volume occupied by a unit mass of fluid

What is the formula for specific volume?

Specific Weight/Unit Weight (γ)

the weight of a unit volume of a fluid

• γ = ρg

What are the formulas for specific weight/unit weight (γ)?

• English: lb/ft³

• Metric: dyne/cm³

• SI: N/m³ or kN/m³

Units of Specific Weight/Unit Weight (γ):

Specific Gravity (sg)

a dimensionless ratio of a fluid’s density to some standard reference density

Water at 4 °C

For liquids and solids, what is the reference density?

What is the formula of specific gravity (sg)?

Density of air

In gases, what is the standard reference to calculate the specific gravity?

• γ = 62.4 lb/ft³ = 9.81 kN/m³

• ρ = 1.94 slugs/ft³ = 1000 kg/m³

• sg = 1.0

For water 4 °C, what are the values for:

• γ

• ρ

• sg?

Viscosity (µ)

determines the amount of its resistance to shearing forces

no viscosity

A perfect fluid would have _____.

Constant of Proportionality

What is the k?

Dynamic of Absolute Viscosity

What is the constant of proportionality k called?

μ

What is the dynamic of absolute viscosity denoted by?

• τ = shear stress in lb/ft² or Pa

• μ = absolute viscosity in lb-sec/ft² (poises) or Pa-sec

• y = distance between the plates in ft or m

• U = velocity in ft/s or m/s

What is the formula for viscosity (μ)?

Kinematic Viscosity (v)

the ratio of dynamic viscosity of the fluid, μ, to its mass density, ρ

• μ = absolute viscosity in Pa-sec

• ρ = density in kg/m³

What is the formula for kinematic viscosity (v)?

• English = lb-sec/ft² (slug/ft-sec)

• Metric = dyne-s/cm² (poise)

• SI = Pa-s (N-s/m²)

What are the common units of viscosity for (absolute, μ):

• English

• Metric

• SI?

• English = ft²/sec

• Metric = cm²/s (stoke)

• SI = m²/s

What are the common units of viscosity for (kinematic, v):

• English

• Metric

• SI?

• 0.1

• 0.0001

• 1 poise = _____ Pa-sec

• 1 stoke = _____ m²/s

surface tension

The membrane of “skin” that seems to form on the free surface of a fluid is due to the intermolecular cohesive forces, and is known as _____.

Surface Tension (σ)

the reason that insects are able to sit on water and a needle is able to float on it

Surface Tension (σ)

causes bubbles and droplets to take on a spherical shape, since any other shape would have more surface area per unit volume

• σ = surface tension in N/m

• diameter of the droplet in m

• p = gage pressure in Pa

What is the formula of surface tension (σ)?

Capillarity/Capillary Action

the name given to the behavior of the liquid in a thin-bore tube

surface tension, cohesion, adhesion

The rise or fall of a fluid in a capillary tube is caused by _____ and depends on the relative magnitudes of the _____ of the liquid and the _____ of the liquid to the walls of the containing vessel.

adhesion > cohesion, cohesion > adhesion

Liquids rise in tubes they wet (_____) and fall in tubes they do not wet (_____).

Capillary

important when using tubes smaller than about 3/8 inch (9.5 mm) in diameter

• h = capillary rise or depression in m

• γ = unit weight in N/m³

• d = diameter of the tube in m

• σ = surface tension in Pa

What is the formula of capillarity/capillary action?

0°

What is the angle for complete wetting, as with water on clean glass?

What will be the formula if the angle is 0° for capillarity?

• Mercury-glass = 140°

• Water-paraffin = 107°

• Water-silver = 90°

• Kerosene-glass = 26°

• Glycerin-glass = 19°

• Water-glass = 0°

• Ethyl alcohol-glass = 0°

What are the contact angles for:

• Mercury-glass

• Water-paraffin

• Water-silver

• Kerosene-glass

• Glycerin-glass

• Water-glass

• Ethyl alcohol-glass?

Compressibility/Coefficient of Compressibility (β)

the fractional change in the volume of a fluid per unit change in pressure in a constant-temperature process

• △V = change in volume

• V = original volume

• △p = change in pressure

• dV/V = change in volume (usually in percent)

What are the formulas for compressibility (β)?

Bulk Modulus of Elasticity (E_B)

expresses the compressibility of the fluid

Bulk Modulus of Elasticity (E_B)

the ratio of the change in unit pressure to the corresponding volume change per unit of volume

What are the formulas for bulk modulus of elasticity (E_B)?

Pressure Disturbances

imposed on a fluid move in waves

celerity, acoustical, sonic velocity

The velocity or _____ of pressure wave (also known as _____ or _____) is expressed as:

PROPERTY CHANGES IN IDEAL GAS

For any ideal gas experiencing any process, the equation of state is given by:

Boyle’s Law

PROPERTY CHANGES IN IDEAL GAS

When temperature is held constant, what is the original formula reduced to?

Charle’s Law

PROPERTY CHANGES IN IDEAL GAS

When temperature is held constant (isothermal condition), what is the original formula reduced to?

• p₁ = initial absolute pressure of gas

• p₂ = final absolute pressure of gas

• V₁ = initial volume of gas

• V₂ = final volume of gas

• T₁ = initial absolute temperature of gas in °K (°K = °C + 273)

• T₂ = final absolute temperature of gas in °K

• k = ratio of the specific heat at constant pressure to the specific heat at constant volume (adiabatic exponent)

For Adiabatic or Isentropic Conditions (no heat exchanged), what are the formulas?

Molecular Activity

(in a liquid) will allow some of the molecules to escape the liquid surface

condense

Molecules of the vapor also _____ back into the liquid.

equilibrium processes

The vaporization and condensation at constant temperature are _____.

Vapor Pressure/Saturation Pressure

the equilibrium pressure exerted by free molecules

volatize liquids, barometers

Liquids near their boiling point or that vaporizes easily are said to _____. Liquids with low vapor pressure are used in accurate _____.

temperature

The tendency toward vaporization is dependent on the _____ of the liquid.

Boiling

occurs when the liquid temperature is increased to the point that the vapor pressure is equal to the local ambient (surrounding) pressure

local ambient pressure, vaporize

A liquid’s boiling temperature depends on the _____, as well as the liquid’s tendency to _____.

• Mercury = 0.000173

• Turpentine = 0.0534

• Water = 2.34

• Ethyl Alcohol = 5.86

• Ether = 58.9

• Butane = 218

• Freon-12 = 584

• Propane = 855

• Ammonia = 888

What are the typical vapor pressures (in kPa, 20 °C) for:

• Mercury

• Turpentine

• Water

• Ethyl Alcohol

• Ether

• Butane

• Freon-12

• Propane

• Ammonia