Fluid Properties and Units

Fluid Properties and Units

CVEN 311CVEN 311

ContinuumContinuum

All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion.

However, in dealing with fluid-flow relations on a mathematical basis, it is necessary to replace the actual molecular structure by a hypothetical continuous medium, called the continuum.

All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion.

However, in dealing with fluid-flow relations on a mathematical basis, it is necessary to replace the actual molecular structure by a hypothetical continuous medium, called the continuum.

ContinuumContinuum

In a continuum, the physical variable at a point in space is the averaged value of the variable in a small sphere.

How good is the assumption?

In a continuum, the physical variable at a point in space is the averaged value of the variable in a small sphere.

How good is the assumption?

10-3cm

3x1010 molecules of air

Dimensions and UnitsDimensions and Units

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

Dimensions of mechanics are length time mass force temperature

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

MMLT-2

Dimensions and UnitsDimensions 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

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 UnitsDimensions 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!fluid

How many independent properties? _____4

Definition of a FluidDefinition of a Fluid

“a fluid, such as water or air, deforms continuously when acted on by shearing stresses of any magnitude.” - Munson, Young, Okiishi

“a fluid, such as water or air, deforms continuously when acted on by shearing stresses of any magnitude.” - Munson, Young, Okiishi

WaterOilAirWhy isn’t steel a fluid?

WaterOilAirWhy isn’t steel a fluid?

Fluid Deformation between Parallel Plates

Fluid Deformation between Parallel Plates

Side viewSide view

Force F causes the top plate to have velocity U.Force F causes the top plate to have velocity U.What other parameters control how much force is What other parameters control how much force is required to get a desired velocity?required to get a desired velocity?

Distance between plates (b)Distance between plates (b)

Area of plates (A)Area of plates (A)

F

b

U

Viscosity!Viscosity!

Shear StressShear Stress

change in velocity with respect to distancechange in velocity with respect to distance

AFAF

2m

N

2m

N

b

U b

U b

Ub

U

dydu dydu

b

AUF

b

AUF AU

FtAUFt

2m

sN

2m

sNdimension of

s

1

s

1

Tangential force per unit area

Rate of angular deformation

rate of shear

Fluid classification by response to shear stress

Fluid classification by response to shear stress

Newtonian Ideal Fluid Ideal plastic

Newtonian Ideal Fluid Ideal plastic

NewtonianIdeal Fluid

Ideal plastic

Shear stress Shear stress

Rat

e of

def

orm

atio

nR

ate

of d

efor

mat

ion

dydu

dydu dydu

1

Fluid ViscosityFluid Viscosity

Examples of highly viscous fluids ______________________

Fundamental mechanisms Gases - transfer of molecular momentum

Viscosity __________ as temperature increases. Viscosity __________ as pressure increases.

Liquids - cohesion and momentum transfer Viscosity decreases as temperature increases. Relatively independent of pressure (incompressible)

Examples of highly viscous fluids ______________________

Fundamental mechanisms Gases - transfer of molecular momentum

Viscosity __________ as temperature increases. Viscosity __________ as pressure increases.

Liquids - cohesion and momentum transfer Viscosity decreases as temperature increases. Relatively independent of pressure (incompressible)

molasses, tar, 20w-50 oil

increases

_______

increases

Example: Measure the viscosity of water

Example: Measure the viscosity of water

The inner cylinder is 10 cm in diameter and rotates at 10 rpm. The fluid layer is 2 mm thick and 10 cm high. The power required to turn the inner cylinder is 50x10-6 watts. What is the dynamic viscosity of the fluid?

The inner cylinder is 10 cm in diameter and rotates at 10 rpm. The fluid layer is 2 mm thick and 10 cm high. The power required to turn the inner cylinder is 50x10-6 watts. What is the dynamic viscosity of the fluid?

Outer Outer cylindercylinder

Thin layer of waterThin layer of water

Inner Inner cylindercylinder

Solution SchemeSolution Scheme

Restate the goal Identify the given parameters and represent the

parameters using symbols Outline your solution including the equations describing

the physical constraints and any simplifying assumptions

Solve for the unknown symbolically Substitute numerical values with units and do the

arithmetic Check your units! Check the reasonableness of your answer

Restate the goal Identify the given parameters and represent the

parameters using symbols Outline your solution including the equations describing

the physical constraints and any simplifying assumptions

Solve for the unknown symbolically Substitute numerical values with units and do the

arithmetic Check your units! Check the reasonableness of your answer

Solution

Role of ViscosityRole of Viscosity

Statics Fluids at rest have no relative motion between

layers of fluid and thus du/dy = 0 Therefore the shear stress is _____ and is

independent of the fluid viscosity Flows

Fluid viscosity is very important when the fluid is moving

Statics Fluids at rest have no relative motion between

layers of fluid and thus du/dy = 0 Therefore the shear stress is _____ and is

independent of the fluid viscosity Flows

Fluid viscosity is very important when the fluid is moving

zerozero

Dynamic and Kinematic Viscosity

Dynamic and Kinematic Viscosity

Kinematic viscosity (__) is a fluid property obtained by dividing the dynamic viscosity (__) by the fluid density

Kinematic viscosity (__) is a fluid property obtained by dividing the dynamic viscosity (__) by the fluid density

3mkg

smkg

3mkg

smkg

2m

sN

2m

sN

2s

mkgN

2s

mkgN

[m2/s]

Connection to Reynolds number!

mm

nn

ReVDrm

=ReVDrm

=

Density and Specific WeightDensity and Specific Weight

Density (mass/unit volume) density of water: density of air at

atmospheric pressure and 15 C:

Specific Weight (weight per unit volume) __________________

Density (mass/unit volume) density of water: density of air at

atmospheric pressure and 15 C:

Specific Weight (weight per unit volume) __________________

950960970980990

1000

0 50 100Temperature (C)

Den

sity

(kg

/m3 )

997

998

999

1000

0 10 20

Temperature (C)

Den

sity

(kg

/m3 )

1000 kg/m3

1.22 kg/m3

= g = 9806 N/m3

Specific mass

Perfect Gas LawPerfect Gas Law

PV = nRT R is the universal gas constant T is in Kelvin

PV = nRT R is the universal gas constant T is in Kelvin

Note deviation from the text!Note deviation from the text!

R

8 314.N m

mol K

Use absolute pressure for P and absolute temperature for T

Bulk Modulus of ElasticityBulk Modulus of Elasticity

Relates the change in volume to a change in pressure changes in density at

high pressure pressure waves

_________ ______ __________

Relates the change in volume to a change in pressure changes in density at

high pressure pressure waves

_________ ______ __________ 2.00

2.05

2.10

2.15

2.20

2.25

2.30

2.35

0 20 40 60 80 100

Temperature (C)

Bul

k M

odul

us o

f el

asti

city

(G

Pa)

soundsoundwater hammerwater hammer

Edp

dv /

Edp

dV Vv /

Water

-

vE

a

vEa speed of soundspeed of sound

Vapor PressureVapor Pressure

0

1000

2000

3000

4000

5000

6000

7000

8000

0 10 20 30 40

Temperature (C)

Vap

or p

ress

ure

(Pa)

liquid

What is vapor pressure of water at 100°C?101 kPa

Connection forward to cavitation!

CavitationCavitation

Cavitation DamageCavitation Damage

pR2 = 2R

Surface TensionSurface Tension

Pressure increase in a spherical droplet

Pressure increase in a spherical droplet

Rp

2R

p2

pR2

2R

Surface moleculesSurface molecules

0.0500.0550.0600.0650.0700.0750.080

0 20 40 60 80 100

Temperature (C)

Sur

face

tens

ion

(N/m

)

Example: Surface TensionExample: Surface Tension

Estimate the difference in pressure (in Pa) between the inside and outside of a bubble of air in 20ºC water. The air bubble is 0.3 mm in diameter.

Estimate the difference in pressure (in Pa) between the inside and outside of a bubble of air in 20ºC water. The air bubble is 0.3 mm in diameter.

Rp

2R

p2

R = 0.15 x 10-3 mR = 0.15 x 10-3 m

= 0.073 N/m = 0.073 N/m

m1015.0

N/m 073.023

p

m1015.0

N/m 073.023

p

970 Pap =970 Pap =

What is the difference between pressure in a water droplet and in an air bubble?

hp hp waterm 1.0/9806

9743

mN

Paph

waterm 1.0

/9806

9743

mN

Paph

Statics!

Outline the solutionOutline the solution

Restate the goal Identify the given parameters and represent

the parameters using symbols Outline your solution including the

equations describing the physical constraints and any simplifying assumptions

Restate the goal Identify the given parameters and represent

the parameters using symbols Outline your solution including the

equations describing the physical constraints and any simplifying assumptions

23- s/mN 1.16x10

Viscosity Measurement: SolutionViscosity Measurement: Solution

hr

Pt322

hr

Pt322

23-32

6-

s/mN 1.16x10m) (0.1m) (0.05(1.047/s)2

m) (0.002 W)10(50

x 23-32

6-

s/mN 1.16x10m) (0.1m) (0.05(1.047/s)2

m) (0.002 W)10(50

x

tAU

F t

AUF U U A A

thr

F22

thr

F22

P P

thr

P322

thr

P322

Outer Outer cylindercylinder

Thin layer of waterThin layer of water

Inner Inner cylindercylinder

r = 5 cmt = 2 mmh = 10 cmP = 50 x 10-6 W10 rpm

r 2rh

Fr