fluid properties

MZA@UTPChemEFluidMech

Do you still remember?

Fluid Mechanics Fluid dynamics Fluid statics Stress, Normal stress, Pressure Shear force, shear strain Newtons law of viscosity If YES lets move on.


Viscosity

Newtons law of viscosity Shear stress is linearly proportional to the velocity gradient

dydV =

=

dydV

= f (types of fluid, time and T)


Types of fluids

Newtonian fluids Fluids that obey Newtons law of viscosity A fluid whose viscosity doesn't depend on gradients in flow speed. Gases and low-molecular weight liquids are usually Newtonian fluids. Non-Newtonian fluids Fluids that do not obey Newtons law of viscosity A fluid whose viscosity changes when the gradient in flow speed changes. Colloidal suspensions and polymer solutions like ketchup and starch/water paste are non-Newtonian fluids.


varies with types of fluid Newtonian fluids is proportional to dV/dy All gases All liquids having simple

chemical formula E.g: H2O, CH3OH, C6H6

Most dilute solution of simple molecules in water or organic solvents Metal ion solution, sugar

in water


Newtonian fluids Straight line through origin


Non-Newtonian fluids Shear stress is a

function of the velocity gradient.

(viscosity is not a constant)

varies with types of fluid


Bingham fluids Resist small shear stress. Flow easily under larger

shear stress (Force must be given in

order to move the fluid)



Pseudoplastic fluids

Shear thinning fluids as dV/dy


A shear thinning fluid decreases in viscosity with increasing shear rate

High stress, Low Viscosity


Dilatant fluids Shear thickening fluids as dV/dy


High stress, High Viscosity


varies with time

Viscosity is time independent

All Newtonian fluids are time independent

Most of non-Newtonian fluids are time dependent


Rheopectic Viscosity increases with time

varies with time

A rheopectic fluid increases in viscosity over time at a constant shear rate.


Thixotropic Viscosity decreases with time

varies with time

A thixotropic fluid decreases in viscosity over time at a constant shear rate.

Non-newtonian fluid classification

Time-dependent viscosity

Rheopectic Viscosity increases with duration of stress Lubricants

Thixotropic Viscosity decreases with duration of stress Clays, honey

Shear-stress-dependent viscosity

Dilatant (Shear thickening)

Viscosity increases with increased stress

Corn starch, printing inks

Pseudoplastic (Shear thinning)

Viscosity decreases with increased (stress Blood, ketchup

Does not exhibit any shear rate (no flow) until a certain stress is achieved

Bingham Viscosity constant Toothpaste, jellies


Unit Pas / N/m2s / kg/m-s(SI) Ibm/ft-s (BG) Poise centipoise (cP)

For water, = 1 cP (at 20oC)

Unit of


Tb A ln ln

equation) (Andrade Ae Tb

+=

=

equation) sd'(Sutherlan T

law)(power

o23

STS

TT

TT

oo

n

oo

++

=

=

varies with T


Kinematic Viscosity

Unit m2/s (SI) ft2/s (BG)

Common unit: centistoke (cSt)

=

sft1008.1

sm10

cmg 1

cP 1 cSt 12

52

6-

3

===


Density

Units : kg/m3 (SI) or Ibm/ft3 (BG) Density of liquids are slightly affected by pressure and

temperature Density of gases are strongly influenced by pressure

and temperature

Vm

volumemass ==


Density

Density of water at different temperatures:

Temperature (oC) (kg/m3) 0 999.0 4 1000.0 10 999.7 20 998.2 30 995.7


Density Density of gases can be calculated through ideal gas

equation: PV = nRT PV = (m/M)RT m/V = PM/RT

where R = gas constant = 8.314 m3 Pa/mol K

PM/RT =


Specific volume

Specific volume,

Unit: m3/kg (SI) or ft3/Ibm (BG)

mV1 ==


Specific weight

Specific weight,

Unit: N/m3 (SI) or Ibf/ft3 (BG)

Related to density through:

where g = local gravitational acceleration

VW

volumeweight ==

= g


Specific gravity

Specific gravity, SG of liquid and solid

Throughout the course, specific gravity referred to water at 4oC is used

Unit: Dimensionless

SG P and T specifiedat water

substance

=


Specific gravity

Specific gravity, SG of gas

For ideal gas;

Where: M = molar mass of the gas

MM

SG air

gasidealgas,

=

P and T same atair

gasgas SG

=


Class Example 1

A reservoir of carbon tetrachloride (CCl4) has a mass of 500 kg and a volume of 0.315 m3. Determine the CCl4: a) Weight b) Density c) Specific weight d) Specific volume e) Specific gravity

Take gravitational acceleration, g = 9.81 m/s2


Solution

a) Weight, W= mg = (500)(9.81) = 4905 N = 4.905 kN

b) Density, =

c) Specific weight, =

3mkg1587

0.315500

Vm

==

3mkN15.57

0.3154905

VW

==


d) Specific volume,

e) Specific gravity, SG

kgm106.301

158711

34-===

59110001587

OH

CCl

2

4 .===


Class Example 2

The volume of a rock is found to be 0.00015 m3. If the specific gravity of the rock is 2.60, determine its mass and weight.


Solution

S.G rock = 2600 kg/m3 Mass, m = V = (2600)(0.00015) = 0.39 kg Weight, W = mg = (0.39)(9.81) = 3.826 N

6021000

rock

OH

rock

2

.===


Class Example 3

Nitrogen gas occupies a volume of 100 L at 120 kPa and 100oC. Determine its specific volume and specific weight.


Solution

V = 100 L = 100 10-3 m3

( )

33 mkg1.08

K 273100

kmolkg28

KkmolmkPa 8.314

kPa 120RTP

RT P

=

+

==

=


Specific volume,

Specific weight, = g = (1.08)(9.81) = 10.6 N/m3

kgm9230

1.0811

3

.===

Fluid Properties

Week 2

Viscosity & kinematic viscosity Density, Specific volume, Specific weight, Specific gravity

Surface tension, Pressure

Non-newtonian fluid classification

Time-dependent viscosity

Rheopectic Viscosity increases with duration of stress Lubricants

Thixotropic Viscosity decreases with duration of stress Clays, honey

Shear-stress-dependent viscosity

Dilatant (Shear thickening)

Viscosity increases with increased stress

Corn starch, printing inks

Pseudoplastic (Shear thinning)

Viscosity decreases with increased (stress Blood, ketchup

Does not exhibit any shear rate (no flow) until a certain stress is achieved

Bingham Viscosity constant Toothpaste, jellies

Unit m2/s (SI), ft2/s (BG)

Common unit: centistoke (cSt)

=

Units : kg/m3 (SI) or Ibm/ft3 (BG) Vm

volumemass ==

dydV =

PM/RT =

Unit: m3/kg (SI) or ft3/Ibm (BG)

mV1 ==

Unit: N/m3 (SI) or Ibf/ft3 (BG)

VW

volumeweight == = g

SG P and T specifiedat water

substance

=

MM

SG air

gasidealgas,

=

P and T same atair

gasgas SG

=


Surface tension

An effect within the surface layer of a liquid that causes that layer to behave as elastic sheet.

What is surface tension?

What causes surface tension?

The intermolecular forces between the liquid molecules


liquid

A

B

Surface Tension In the bulk of liquid, A is pulled equally in all directions by neighboring liquid molecules, resulting in a net force of zero At the surface of the liquid, B is pulled inwards by other molecules deeper inside the liquid which can be balanced only by the resistance of the liquid to compression. This inward pull tends to diminish the surface area, and in this respect a liquid surface resembles a stretched elastic membrane.


Effects in everyday life

Water beading on flowers Insects walking on water


Capillarity

Capillary attraction, or capillarity, is the ability of a liquid to flow in narrow spaces without the assistance of, and in opposition to external forces like gravity

Depends on

the relative magnitudes of the cohesion of the liquid and the adhesion of the liquid to the walls of the containing vessel


Application: Capillarity

Liquids rise in tubes if they wet (adhesion > cohesion)

Liquids fall in tubes if they do not wet

(cohesion > adhesion).


Capillarity

Perfect wetting liquid spreads as a thin film over the surface of the solid

Case of no wetting Mercury on clean glass


Capillarity

Capillary rise, h can be calculated using the equation:

h = height of capillary rise = surface tension = contact angle = specific weight

area sectional Cross

perimeter Wetted cos h =


Capillarity

For circular tube:

d = diameter of the tube r = radius of the tube

r cos

d cos

dd cos h 2

2

=

=

=


Capillarity

Capillarity is important when using tubes smaller than about 3/8 inch (10 mm) in diameter.

For tube diameters larger than 1 in (12 mm), capillary effects are negligible.


Outline

Pressure and Temperature


Terminology

Gauge pressure, Pg P of a system is measured by a gauge, which excludes Patm

Its measured relative to Patm

Absolute pressure, Pabs Total P exerted on a system

Pabs = Patm + Pg Its measured relative to high vacuum (0 psia)

0 psia 14.7 psia 114.7 psia

0 psig 100 psig

1 atmosphere

vacuum range


Pressure Conversion

Atmospheric pressure, Patm P exerted on the surface of a body by a column of air in an atmosphere Standard Patm (at sea level) = 1 atm = 101.325 kPa = 760 mmHg


Relationships

Pabs = Patm + Pgage

Pabs = Patm Pvac

1 atm = 0 gage 101.3 kPa = 0 gage


Temperature

Temperature scales: Celcius (C) Kelvin (K) Fahrenheit (F) Rankine (R)

T(K) = T(C) + 273.15

T(R) = T(F) + 460


Units

SI unit (International unit) English system (foot-pound-second, BG)


Conversion

Length: 1 m = 3.281 ft 1 ft = 0.3048 m

Mass: 1 kg = 2.2046 Ibm 1 Ibm = 0.45359 kg Pressure 1 atm = 101.3 kPa = 14.696 psi


Class Example 4

A steel cylinder has a diameter of 5 cm and a length of 20 cm. It moves at a velocity of 0.5 m/s inside a tube of slightly larger diameter. Determine the clearance between the cylinder and the tube, if castor oil film of constant thickness is filled between the cylinder and the tube.

Data: at room temperature SGsteel = 7.85 castor oil = 0.287 kg/ms


Solution

Clearance, dy

dydV

AF ==

( )

( ) ( ) ( ) ( ) N 309.810.20.05410007.85 F

gVmgWF

2 =

=

===

( ) ( )( )( ) mm 15030

50200502870FdVA dy ..... ===

dy


Class Example 5

Determine the capillary rise of water at 10oC in a tube if the tube diameter is 1 mm.

What will happen if the tube diameter increases by 50%?

Data: water @ 10oC = 0.00742 N/m


Solution

( )( )( ) ( )

( )( )( ) ( ) mm 1.01.50.001 9.811000

0 cos 0.007422 h

50%by increases diameter tube if

mm 1.510.001 9.811000

0 cos 0.007422 h

=

=

==


Learning Outcome: CHAPTER 1

At the end of the chapter, you should be able to:

1. Define the term fluid 2. Determine various types of fluid 3. Determine properties of fluid 4. Solve fluid related problems using different unit

conversions


Quiz

Do you still remember?ViscosityTypes of fluids varies with types of fluidSlide Number 8 varies with types of fluid varies with types of fluid varies with types of fluid varies with types of fluid varies with time varies with time varies with timeNon-newtonian fluid classificationUnit of varies with TSlide Number 19Kinematic ViscosityDensityDensitySlide Number 23DensitySpecific volumeSpecific weightSpecific gravitySpecific gravityClass Example 1SolutionSlide Number 31Class Example 2SolutionClass Example 3SolutionSlide Number 36Fluid Properties Non-newtonian fluid classificationSlide Number 39Surface tensionSlide Number 41Slide Number 42CapillarityApplication: CapillarityCapillarityCapillarityCapillarityCapillarityOutlineTerminologyPressure ConversionRelationshipsTemperatureUnitsConversionClass Example 4SolutionClass Example 5SolutionLearning Outcome: CHAPTER 1Quiz

fluid properties

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