JJ309 Chapter 1

JJ 309 FLUID MECHANICS

CHAPTER 1 FLUID & PROPERTIES

SUB TOPIC

1. Explain fluid characteristicsDefine fluidDescribe fluid termsCompare the characteristics between liquid,

gas and solid

2. Ilustrate types of pressure gaugeDefine: Atmospheric pressure, absolute

pressure, gauge pressure, vacuum pressure

Solve problem related to pressure gauge

CONT…..

3. Apply physical properties of fluidDefine: i. Viscosity

ii. fluid compressibilityiii.mass density and relative

density iv.specific weight and specific volume

solve problem related to physical properties of fluid

  [C2;CLO 1, C3;CLO 2 & A4;CLO 3]

1. WHAT IS A FLUID?????

A substance in the liquid or gas phase is referred to as a Fluid

Fluid as a substance that can flow. It is no particular form. It changes shape, as the container contains. if a lower shear force values acting on the

fluid it will deform. therefore, the fluid at rest can not bear the shear stress.

(In any fluid, the molecules themselves are in constant, random motion, colliding with each other and with the walls of any container )

PHASES OF MATTER

Droplet of liquid water

SOLID, LIQUID & GAS

Liquid or gas as a fluid because they can be made to flow, or move

Solid & fluid is made on the basis of the substance’s ability to resist an applied shear (or tangential) stress that tend to change its shape.

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress, no matter how small

SOLIDS AND FLUIDS

A solid can resist a shear force with only a finite deformation. If force is maintained, the deformation is unchanged

A fluid will undergo a continuous deformation due to a shear force

GAS AND LIQUIDS

Liquids are more dense

Gases are more compressible

CONT…

In a liquid, molecules are in their equilibrium distance with respect to intermolecular forces and the motion due to thermal vibration of the molecules is quite small: about equal to the distance between molecules. Thus there is some order in the molecular structure.

In gases the spacing is large enough so that intermolecular forces are very small; molecules are basically oscillating with large amplitudes and collisions are common.

SHEAR STRESS

FLUID DISTRIBUTION

SOLID VS FLUIDS

EXAMPLE

Another great example of a solid, liquid and gas is coke with ice. Coke is carbonated, which means it has gas in it, the actual coke is a liquid, and the ice/cup is a solid!

A good example of a solid, liquid and gas is hot coffee in a cup. The steam coming out of the coffee is a gas, the coffee is a liquid and the cup is a solid!

ASSESTMENT……

What is a fluid?How does a fluid differ from solid?

How does a gas differ from a liquid?

Can you make a difference of liquids, gases and solids?

2. PRESSURE GAUGES

Pressure normal force exerted by a fluid per unit area (gas or liquid)

1 Pa = 1 N/m2 1 kPa = 103 Pa1 Mpa = 106 Pa1 Bar = 105 Pa1 atm = 101.325 kPa = 1.01325 bars

PRESSURE

In mathematically pressure may be expressed as:

where:

is the pressure is the perpendicular force is the area. The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N·m-2 or kg·m-1·s-2). It was given that SI name in 1971. Before that, pressure in SI was expressed simply as N/m2.

Pressure in head gives

Where:

is the pressure is the perpendicular force is the area.

ABSOLUTE PRESSURE Absolute Pressure, PAbs : any system is the gauge

pressure of the system plus the local atmospheric or ambient pressure

Gauge Pressure, Pgauge : The difference between the absolute and the local atmospheric pressure

Vacuum Pressures, PVac : Pressures below atmospheric pressure

Atmospheric pressure, PAtm : as a result of heavy pressure from the air or atmosphere on the surface of the earth used as a reference pressure or the pressure datum

Patm , PAbs , Pgauge & PVac

THE RELATIONSHIP OF PRESSURES

EXAMPLE

An example of the difference is between gauge and absolute pressure is the air pressure in a vehicle tire. A tire pressure gauge might read 220 kPa as the gauge pressure, but that means the pressure is 220 kPa above atmospheric pressure.

Since atmospheric pressure at sea level is about 101 kPa, the absolute pressure in the tire is therefore about 321 kPa.

EXERCISE

1. If the absolute pressure in a gas is 40.0 psia and the atmospheric pressure is 846 mbar abs, find the gauge pressure in kPa and bar.

Solution:

EXERCISE

2. If the atmospheric pressure is 0.900 bar abs and gauge attached to tank reads 390 mmHg vacuum. What is the absolute pressure within the tank?

Solution:

3. PHYSICAL PROPERTIES OF FLUID

Viscosity dynamic, & kinematic, v fluid compressibility mass density, ρ relative density/specific gravity, s specific weight, specific volume, ν

µ

ω

VISCOSITY

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity)

CONT.

Dynamic viscosity dynamic viscosity is the pascal-second

(Pa·s), (equivalent to N·s/m2, or kg/(m·s)). Kinematic viscosity with the ratio of the inertial force to the

viscous force (i.e. the Reynolds number, Re = VD / ν) , the former characterized by the fluid density ρ. This ratio is characterized by the kinematic viscosity (Greek letter nu, ν), defined as follows:

The SI unit of ν is m2/s. The SI unit of ρ is kg/m3.

CONT.

FLUID COMPRESSIBILITY

In thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.

,pa(T = constant)where V is volume and p is pressureNote: most textbooks use the notation κ for this quantity

EXAMPLE A rigid steel container is partially filled with a liquid

at 15 atm. The volume of the liquid is 1.23200 L . At a pressure of 30 atm, the volume of the �liquid is 1.23100 L . Find the average bulk modulus of elasticity of the liquid over the given range of pressure if the temperature after compression is allowed to return to its initial value. What is the coefficient of compressibility (ß)? Solution:

EXERCISE

A liquid compressed in a cylinder has a volume of 1000 cm3 at 1 MN/m2 and a volume of 995 cm3 at 2 MN/m2. What is its bulk modulus of elasticity (κ)? Ans: 200MPa

Solution:

CONT….

If κ = 2.2 GPa is the bulk modulus of elasticity for water, what pressure is required to reduce a volume by 0.6 percent? Ans: 13.2 MPa

Sol:

MASS DENSITY The mass density or density of a material

is defined as its mass per unit volume. The symbol most often used for density is ρ (the Greek letter rho).

If the average density (including any air below the waterline) of an object is less than water (1000 kg/m3) it will float in water and if it is more than water's it will sink in water.

Mathematically, density is defined as mass divided by volume:

where ρ is the density, m is the mass, and V is the volume

EXAMPLE

1. An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml. (milliliter).

The density can be calculated asSolution: ρ = [(18.5 g) / (1000 g/kg)] / [(23.4 ml) /

(1000 ml/l) (1000 l/m3) ]   = (18.5 10-3 kg) / (23.4 10-6 m3) = 790 kg/m3

EXAMPLE

2. The density of titanium is 4507 kg/m3. Calculate the mass of 0.17 m3 titanium!

Solution: m = (0.17 m3) (4507 kg/m3)     = 766.2 kg

RELATIVE DENSITY/SPECIFIC GRAVITY

The terms specific gravity, and less often specific weight, are also used for relative density

Specific gravity is the ratio of the density (mass of a unit volume) of a substance to the density (mass of the same unit volume) of a reference substance.

Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance

CONT.

True specific gravity, can be expressed mathematically as:

where is the density of the sample and is the density of water.

The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air:

where represents the weight of sample and

the weight of water, both measured in air.

EXAMPLE

If the density of iron is 7850 kg/m3, 7.85 grams per cubic centimeter (cm3), 7.85 kilograms per liter, or 7.85 metric tons per cubic meter - the specific gravity of iron is:

Solution: SG = (7850 kg/m3) / (1000 kg/m3)     = 7.85 water density is 1000 kg/m3

SPECIFIC WEIGHT, The specific weight (also known as the unit

weight) is the weight per unit volume of a material

The symbol of specific weight is ω (omega) or 𝜸

(the Greek letter Gamma). specific weight represents the force exerted

by gravity on a unit volume of a fluid. For this reason, units are expressed as force per unit volume (e.g., lb/ft3 or N/m3).

whereγ is the specific weight of the material (weight per unit volume, typically N/m3 units) ρ is the density of the material (mass per unit volume, typically kg/m3) g is acceleration due to gravity (rate of change of velocity, given in m/s2)

ω or

EXAMPLE

1. Specific weight for water at 39 oF (4 oC) is 62.4 lb/ft3 (9.81 kN/m3) in imperial units. Specific weight in SI units can be calculated like

Solution: γ = (1000 kg/m3) (9.81 m/s2)     = 9810 N/m3     = 9.81 kN/m3

SPECIFIC VOLUME, V

Specific volume (ν) is the volume occupied by a unit of mass of a material

The specific volume of a substance is equal to the reciprocal of its mass density. Specific volume may be expressed in , , , or .

where, V is the volume, m is the mass and ρ is the density of the material.

EXAMPLE

Calculate the density, specific weight, and specific volume of chloride gas at 25 oC and pressure of 600 000 N/m2 abs.

Solution: ρ = P/ RT = 600 000/[(118)(25+273)] = 17.1 kg/m3ω = ρg = (17.1)(9.81) = 168 N/m3v = 1/ ρ = 1/17.1 = 0.0585 m3/kg

EXERCISE

A reservoir of glycerin (glyc) has a mass of 1200 kg and a volume of 0.952 m3. Find the glycerin’s weight (W), mass density (ρ), specific weight (γ @ ω) and specific gravity (s @ s.g) ans: (W= 11.77kN, ρ = 1261kg/m3, ω = 12.36 kN/m3)

SUMMARY: MECHANICAL PROPERTIES OF A FLUID

DENSITY OF A FLUID ρ

For small fluid volume V of mass m

ρ = Density = m/V kg/m3

SPECIFIC WEIGHT γ

γ = ρ g N m- 3

This is the weight per unit volume

SPECIFIC GRAVITY

S = Density of fluidDensity of water at 4 0C (1000 kgm-3)

CONT….

PRESSURE AND COMPRESSIBILITY

Pressure P = (normal force/area)

Pressure = F/A Nm-2 or Pascals, Pa

CONT…

The slope of these lines is an indication of the compressibility of the fluid.

Gentle slope "soft" fluid i.e. a gas⇒Steep slope "hard" fluid i.e. a liquid⇒

CONT…BULK COEFFICIENT OF ELASTICITY, К

A measure of the compressibility of a fluid is thus the slope of the lines on the P-V diagram.

where ρ = m/V = 1/ν (where υ is termed the specific volume)

Pascal

VISCOSITY

Measures the resistance to shearing motionν = kinematic viscosity = μ/ρ

ASSESSTMENT

What is specific gravity? How is it related to density?

QUIZ 1

1. Give the definition of the fluid and the difference between liquid, gas and solid.

2. How to show the relationship between atmospheric pressure, gauge pressure, absolute pressure and vacuum pressure?

3. The specific gravity of ethyl alcohol is 0.79. Calculate its specific weight and mass density.

QUIZ 1

1. Explain all the properties of liquids with an example.

2. A vacuum gage connected to a chamber reads 5.8 Pa at a location where the atmospheric pressure is 14.5 Pa. Determine the absolute pressure in the chamber.

3. Provide definitions and units used for fluid physical properties such as specific volume, density and viscosity.