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CHAPTER 2

Fluid Characteristics and Behavior

ObjectivesStudent should be able to:i. Define and determine the fluid properties such as:

WeightMassDensitySpecific GravitySpecific WeightSpecific VolumeAbsolute ViscosityKinematic Viscosity

ii. Determine the liquid behavior:Surface tensionCapillary effect

General Behavior

Weight (W)The gravitational force applied to a body.

Where:m = mass of body (kg)g = gravitational acceleration

= 9.81 m/s2 or 32.174 ft/s2

Unit in kg.m/ s2 or Newton (N)

W = mg

General Behavior

Mass (m)

Amount of matter in an object.

Unit in kg

2

General Behavior

Density ()

Mass per unit volume

Unit in kg/m3

Density of gas depends on temperature and pressure.

Density of liquid depends more strongly on temperature than pressure.

3mkg

volumemass

Vm

General BehaviorDensity of ideal gases

Equation of State: equation for relationship between pressure, temperature and density.

Where:P = absolute pressure (kPa) = specific volume (m3/kg) = density (kg/m3)T = absolute temperature (K)

T(K) = T(C) + 273.15R = gas constant

RTP

P = RT or

General Behavior

The gas constant R is different for each gas and is determined from

R = Ru/M

Where, Ru = universal gas constant

= 8.314 kJ/kmol.K

= 0.287 kPam3/kg.K

M = Molecular weight

General Behavior

Specific gravity (SG) or relative density

The ratio of the density of a substance to the density of some standard substance at a specified temperature (usually water at 4°C, rH20 = 1000 kg/m3).

SG is dimensionless quantity.

OH

SG2

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General Behavior

Specific weight ()Weight per unit volume

where:

= density (kg/m3)

g = gravitational acceleration (m/s2)

Unit in N/m3.

gVmg

VolumeWeight

VW

General Behavior

Specific volume ()

Volume per unit mass

Unit in m3/kg

1

mass

volumemV

Check your understanding

Q: Determine the density, specific gravity and mass of the air in a room whose dimensions are 4m x 5m x 6m at 100 kPa and 25 C. (Rconstant = 0.287 kPa.m3/kg.K)

General BehaviorShear Stress and Fluid Motion

Fluids move under influence of applied shear

• The shear stress on the plate is:

AF

y

Stationary surface

Increasing fluid

velocityu

u + du

ux

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General BehaviorShear Stress and the concepts of Viscosity

Fluid flowing past a stationary surface consist of many layers.

Layer of liquid at the surface is static, ux = 0 and layer velocity increase with distance y above the surface.

Velocity gradients means fluid layers ‘slide’ or move relative to each other.

Molecular forces and random movement across layers will produces shear stress, between layers.

Magnitude of shear stress related to rate change of layer velocity by

dyduατ

General Behavior

Viscosity is a property that represents the internal resistance of a fluid to motion.

The force a flowing fluid exerts on a body in the flow direction is called the drag force, and the magnitude of this force depends, in part, on viscosity.

Viscosity

General Behavior

• Viscosity is caused by cohesive forces between the molecules in liquid and by the molecular collision in gases, it varies greatly with temperature.

• The viscosity of liquids decreases and the viscosity of gases increases with temperature.

General Behavior

AreaTimeForce

DistanceVelocityAreaForce

Absolute / dynamic viscosity (m)

Shear force per unit area (or shear stress ) required to drag one layer of fluid with unit velocity past another layer a unit distance away.

Units in Nsm-2 or kgm-1s-1 or Pa.s or Poise (P)

gradientvelocity stressshear

dydu

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(velocity gradient)

General BehaviorRelationship between shear stress & velocity gradient

The rate of deformation (velocity gradient) is proportional to shear stress, and the constant of proportionality is the viscosity

General BehaviorKinematic Viscosity ()

The ratio of absolute viscosity to density.

Units in Stoke (St) or m2/s

(1 stoke = 1 cm2/s) = 0.0001 m2/s)

v

Surface tensionAdhesionThe molecular attraction exerted between bodies in contact (the forces between unlike molecules, such as water and glass).

Surface tension

Cohesive force

The intermolecular attraction between like-molecules (the forces between like molecules such as water and water).

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Surface tension ()

Force per unit length at a liquid-vapor or liquid-liquid interface resulting from the imbalance in attractive forces among like liquid molecules at the interface (cohesion).

Unit in N/m

Surface tension

Surface tension

Wetting behavior

a) Liquid which wets a solid surface well, e.g. water on a very clean copper.

b) Partial wetting.

c) Liquid which does not wet a solid surface, e.g. water on teflonor mercury on clean glass.

Surface tension

Angle () shown is the angle between the edge of the liquid surface and the solid surface, measured inside the liquid.

Angle is called contact angle and is a measure of the quality of wetting.

90wets a solid surface well

= 180Zero wetting

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Capillary effect (h)

The rise or fall of a liquid in a small-diameter tube.

Caused by surface tension and depends on the relative magnitude of cohesion of the liquid and the adhesion of the liquid to the walls of the containing vessel.

Capillary effect

The curved free surface in the tube is call the meniscus.Water meniscus curves up because water is a wetting fluid.

Mercury meniscus curves down because mercury is a nonwetting fluid.

Capillary effect

• Weight of liquid in column

W = mg = Vg = g(R2h)

• Equating vertical component of surface tension to W

W = Fsurface

g(R2h) = 2R cos

Valid only for constant-diameter tubes

gRh

cos2

Capillary effect

The capillary rise is given by:

Where:

= surface tension, N/m

= contact angle

= density of a liquid, kg/m3

g = gravitational acceleration, 9.81 m/s2

R = radius of tube, m

Unit in m.

gRh

cos2

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Capillary effect

• For nonwetting liquids, the contact angle > 90 and thus cos < 0, therefore h will have negative value which correspond to a capillary drop.

• Capillary rise is inversely proportional to the radius of the tube, therefore the thinner the tube, the greater the rise (fall) of the liquid in the tube. Capillary effect is negligible in tube with diameter > 1.

• Capillary also inversely proportional to the density of the liquid, therefore lighter liquids experience greater capillary rise.

Check your understanding

Q: A 0.6 mm diameter glass tube is inserted into water at 20 C in a cup. Determine the capillary rise of water in the tube.(H2O at 20C = 0.073 N/m)