1, intro fluids

8/10/2019 1, Intro Fluids

1/26

Fluid Mechanics

Introduction to fluid properties


2/26

Fluid MechanicsStudy of the behaviour of fluids when subject to applied forces

Two subcategories Fluid statics Behaviour of fluids at rest

Fluid dynamics Behaviour of fluids in motionFluids are everywhere

Everyday phenomenon

Environmental flowsBiological flowsMedical devices

Aerodynamics


3/26

A fluid is a substance which continuously deforms (i.e. it isstrained) when subjected to a shear (tangential) stressFluids generally consist of liquids and gasesSolids, although deforming initially, do not deform

continuously F

What is a fluid?


4/26

Mixing of a biological fluid


5/26

Different fluids flow differently This is because different fluids have different

characteristics (cp. water, oil, honey, air, tar) Quantification of these fluids therefore

requires the definition of fluid propertiesDensity, specific volume, specific gravity

ViscosityVapour pressure

Fluid Properties

Superfluids:Liquid helium can climb walls


6/26

Fluid as a ContinuumAll fluids (gases & liquids) are made up of molecules

But generally we do not analyze fluids at the molecular level i.e.the interaction of individual molecules

Instead we look at very tiny volumes containing large numbers ofmolecules

Number of molecules per mm 3 is order 10 18 for gasses, 10 21 for liquids

Assume that using averaged values of important properties(pressure, velocity, temp) over very small volumes isreasonable

That is

We treat the fluid as a continuum

Describe these small volumes as fluid particles or fluid elements


7/26

Density, specific volume, specific gravity (Munson, 1.4)A measure of a fluids mass/weight

Viscosity (Munson, 1.6)A measure of how easily a fluid flows

Vapour pressure (Munson, 1.8)A measure of when a liquid evaporates (becomes a gas)

Fluid Properties


8/26

Density = Mass m per unit volume V :SI Units, kg/m 3

Dependent on temperature and pressureCan be measured using a hydrometer

Position of device sinks to equilibrium positionwhere weight balances buoyancy force (upthrust)Archimedes principle: buoyancy force = V g Knowing V (volume of fluid displaced) then allows to be calculated

Density

V

m


9/26

Specific volume (units: m3

/kg)Volume V per unit mass mReciprocal of density:

Specific gravity or relative density (dimensionless)Density relative to density of water at 4 oC (1000 kg/m 3):

Specific weight (units: kg/m2

s2

)Weight per unit volume :

Specific Volume & Specific Gravity

1

mV

v

OH 2

SG

g


10/26

Recall definition of a fluid: Substance which continuously

deforms when subjected to ashear (tangential) stress

Introduce concept of viscosityto describe fluidity of a fluid,i.e. how easily it flows

Viscosity


11/26

Shear stress is a force per unit area, i.e. F / AShear stress means the force F is applied tangential to area A

Compare this with normal stress (pressure) where force F is applied normal to area A

How much shearing stress (i.e force) must be applied to get a fluid to

deform/move?Note when you deform a fluid you change its velocityi.e. you set up a velocity gradient

Viscosity


12/26

Consider fluid trapped between two plates:Continuity of velocity boundary conditionFluid directly adjacent to moving upper platemoves at velocity U , i.e.

Fluid directly adjacent to stationary lower plate

is stagnant (no slip condition), i.e.

Thus, velocity u is a function of yAssume linear dependence:

Velocity gradient is then

Viscosity

00 yu

U h yu u( y)

U

y = 0

y = h F

u = 0

u = U

hU

y yu

hU

dydu

Note: parabolic velocity profile heredue to absence of upper boundary


13/26

Define constant of proportionality, which weshall call the dynamic (or absolute) viscosity

Units for dynamic viscositykg/ms, Ns/m 2 or Pa.sCommon to use Poise (P): 1 P = 0.1 Pa.s

Viscosity of water at room temperature is 1 cP = 0.001 Pa.s

Also define kinematic viscosity, (incorporates fluids density)

Viscosity (dynamic & kinematic)

u( y)

U

y = 0

y = h F

u = 0

u = U dy

du

A

F

Units: m 2/s or Stoke (St) where 1 St = 1 cm 2/s = 0.0001 m 2/s

dydu

A F


14/26

Viscosity

u( y)

U

y = 0

y = h F

u = 0

u = U

Note: parabolic velocity profile heredue to absence of upper boundary

Assuming a linear velocity profile is

not always appropriate

See velocity profile (below) for flow overa wall


15/26

Measure of a fluid

s resistance to deformation and hence flowActs like friction between layers of fluid when they move relative to each other

LiquidsViscosity due to cohesive intermolecular forces between liquid moleculesAt higher temperatures, molecules have higher energy and are able to overcome thesecohesive forces, thus being able to move more freely T

GasesGas molecules more widely spaced cohesive forces relatively smallResistance to flow arises from random molecular collisionsAt higher temperatures, gas molecules experience increased collisions with increasedtransfer of momentum btw molecules, decreasing coherent flow motion T

Viscosity (temperature dependence)

T

Oil

Water

Air


16/26

Viscosity can be determined from slope of shear stress vs strain rate (deformation rate orvelocity gradient du/dy) graphSlope (viscosity)

Linear for most common fluids (Newtonian)

Some fluids have nonlinear curves (Non-Newtonian):

Viscosity

Shear/Deformation rate ( du/dy )

Shearstress

Newtonian

Dilatant

PseudoplasticBingham plastic

dydu

A F


17/26

Viscosity can be measured using a viscometerConsists of two 400 mm long concentric cylinders

Inner radius 60 mm rotating at 300 rpm by applying a torque of 1.8NmFluid flowing in the 1.5 mm annular gap is oil whose viscosity is to bedetermined

Linear velocity on surface of rotating cylinder

Assuming a linear velocity profile, the velocity gradient is

This assumption only valid if curvature effects negligible, which,in turn, is true only if l


18/26

Shear stress defined as

Thus, shear force is

Since applied torque is

Solve for :

Example: Determination of Viscosity

l u

dr du

L D A F i 1257

= 1.81257 120 10 3( ) 400 10 3( ) 60 10 3( )

= 0.158 kg/ms

Nm8.1i FRT


19/26

Exam Question S2 2006

Answers / Hintsa) Use 3 boundary conditions + linearvelocity profileb) Top plate & 0.6 up from bottom platec) Shear force from above & below total force 1.62 N


20/26

Consider evaporation from a liquid container left open to the atmosphereLiquid molecules near the surface with sufficient momentum to overcomeintermolecular cohesive forces will escapeIf space around container closed, then the liquid molecules that escape toform the vapour will exert a pressure on the liquid surface

At equilibrium, no. of molecules leaving surface (evaporation) equals no. ofmolecules arriving at surface (condensation), this pressure is known as thevapour pressureSince temperature governs the energetics of the molecules, vapour pressure isa function of temperature

Vapour Pressure


21/26

Boiling is the formation of vapour bubbles inthe liquidOccurs when pressure of the liquid equalsthe vapour pressure above itExplains why water at atmospheric pressureboils at 100 oC but at lower temperatures athigher elevations when the atmosphericpressure is lowerThus, can force a liquid to boil not only byraising the temperature at constant pressurebut also by lowering the vapour pressure at agiven temperature

Vapour Pressure


22/26

There are certain instances in flowing liquids where regions of low pressure areencounteredFor example, at the neck of a converging-diverging nozzle

Fluid velocity is high at the neck to maintain mass flow conservationThus pressure is low in this regionIf this pressure decreases below the vapour pressure of the liquid, boiling

occurs, i.e. vapour bubbles form in the neck regionBubbles swept into other regions by flowIf they enter high pressure regions, they will be forced to collapseThis sudden bubble collapse is known as cavitation

Vapour Pressure (Boiling & Cavitation)

High velocity, low pressure regionVapour bubble formation


23/26

Should avoid cavitation especially in pumps since bubblecollapse can occur with such intensities that it can causestructural damage

Vapour Pressure


24/26

Pressure (Munson 1.5)Pressure in a fluid at rest is:The normal force per unit area exerted on a plane surface (real or imaginary)immersed in a fluid

Units: N/m 2 or Pa

If the pressure on every surface is equal

the net force generated by the pressure iszero irrespective of the pressuremagnitude i.e. relative pressure is veryimportant


25/26

Pressure is measured with respect to a reference levelIf reference level is a vacuum, the pressure is known as absolute pressure p

absMore convenient to measure pressure relative to atmospheric pressure ( p0 =1.0125 x 105 Pa); this is known as the gauge pressure p gauge :

Note in the ideal gas eqn you must use absolute pressure.

Pressure

0 p p p abs gauge


26/26

pabs = p0 p gauge = 0

When measuring tyre pressures, the reading shows the gauge pressure (amount bywhich the pressure exceeds the atmospheric pressure)

At liquid surfaces, the gauge pressure is zero the absolute pressure is equal to theatmospheric pressure

Pressure

1, intro fluids

Documents