Lecture1b

Fluid Mechanics-I 1

FLUID MECHANICS-I

INTRODUCTION (Contd…)Lecture # 01 (b)

CONTENTS OF TODAY’S LECTURE:• Physical properties of Fluids Density Specific Weight Specific Volume Specific gravity Surface tensionEngr. Tahir Rafique

Engr. Tahir Rafique

Fluid Mechanics-I 2

Distinction between a Solid & Fluid

• Molecules of solid are usually closer together than those of a fluid.

• The attractive forces between the molecules of a solid are so large that a solid tends to retain its shape.

• In case of fluids, the attractive forces between the molecules are smaller.

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Fluid Mechanics-I 3


• An ideal elastic solid will deform under load and once load is removed will return to it’s original state. Plastic solids deform under action of applied loads and deformation continues as long as load is applied, providing the material does not rupture.

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The intermolecular cohesive forces in a fluid are not great enough to hold various elements of fluid together. Hence a fluid will flow under the action of slightest stress and flow will continue as the stress is present.

Fluid Mechanics-I 4

Distinction between a Gas and a Liquid

• A fluid may be either gas or a liquid. Gas molecules are much farther than those of a liquid. Hence a gas is very compressible. On removal of external pressure, it expands indefinitely.

• A liquid is relatively incompressible. If all pressure (except that of it’s vapor pressure) is removed, it does not expand but the cohesion holds the molecules together.

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Therefore a liquid may have FREE SURFACE i.e. a surface from which all pressure is removed, except that of it’s own vapor.

Fluid Mechanics-I 5


• A vapor is a gas whose temperature and pressure are such that it is very near the liquid phase.

• Thus, steam is considered as a vapor because it’s state is not normally far from water.

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A Gas may be defined as:“A highly super-heated vapor, that is, it’s state is far removed from a liquid phase.”Thus, air is a gas.

Fluid Mechanics-I 6


• The volume of gas or liquid is greatly affected by changes in pressure or temperature or both.

• Whenever significant temperature or phase changes are involved in dealing with vapors and gases, the subject is largely dependent on heat phenomenon (Thermodynamics).

• Thus Fluid mechanics & Thermodynamics are inter related.

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Figure 1.1 Comparison Between Solids, Liquids and Gases

• For solid, imagine that the molecules can be fictitiously linked to each other with springs.

(a) Solid (b) Liquid (c) Gas

k

k k

k

Free surface

Engr. Tahir Rafique Fluid Mechanics-I


Fluid Mechanics-I 8

Density and Specific weight• The density ƿ (rho) or mass density of a fluid is mass per unit

volume while the specific weight ɣ (gamma)is it’s weight per unit volume. Specific wt. is the force exerted by gravity on unit weight of fluid.

• Units of Density: Slugs/ft3 (B.G system) and kg/m3 (S.I system). Also, can be expressed as lb.sec2/ft4 or N.s2/m4

• Units of Specific weight: lb/ft3 (B.G system) and N/m3 (S.I system).

• Slightly affected by changes in temperature and pressure.

Typical values: Water = 1000 kg/m3; Air = 1.23 kg/m3

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Fluid Mechanics-I 9

Density and Specific weight

• Density ƿ is absolute, since it depends on mass, which is independent of location.

• Specific weight ɣ, on the other hand is not absolute, since it depends on the value of g, which varies with location (primarily latitude & elevation above mean sea level).

• Densities & specific weights of fluids vary with temperature.

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Fluid Mechanics-I 10

Density and Specific weight

• Density and specific weight of a fluid are related as:

• Ƿ = ( ɣ / g ) or ɣ = ƿ.g• Physical quantities are dimensionally

homogeneous, the dimensions of density are:• In B.G System: Ƿ = ɣ/g = (lb/ft3)/(ft/s2) =

lb.sec2/ft4 = mass/Vol. = slugs/cubic feet• In S.I System: Ƿ = ɣ/g = (N/m3)/(m/s2) = N.s2/m4

= mass/Vol. = kg/cubic meterEngr. Tahir Rafique


Specific weights of Liquids

• The specific weight of liquid depends on:– Temperature (Inversely related) – Pressure (Directly related)– g value– Presence of dissolved air, salts in solutions and

suspended matter. (Increase ɣ to slight amounts)

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Unless otherwise specified or implied by a given temperature, the value to use for water is 62.4 lb/ft3 or 9.81 kN/m3. Under extreme conditions the specific weight of water is quite different. e.g. at 260 degree celsius and 6000 psi, the ɣ of water is 51 lb/ft3.


Specific Volume

• The volume occupied by a unit mass of fluid. We commonly apply it to gases.

• ν = 1/ƿ = 1/Density• Units: In B.G: ft3/slug In S.I: m3/kg• It is reciprocal of density.

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Specific Gravity

• Denoted by “s”, the specific gravity of a liquid is the dimensionless ratio.

• Sliquid = ƿliquid / ƿwater at standard temperature

• Physiscts use 4 °C (39.2 °F) as the standard but engineers often use 15.56 °C (60 °F).

• In metric system, the density of water at 4 °C is 1.00 g/cm3 (or 1.00 g/mL3), equivalent to 1000 kg/m3.

• Density of fluid varies with temperature.Engr. Tahir Rafique

14

The specific gravity (or relative density) can be defined in two ways:

Definition 1: A ratio of the density of a liquid to the density of water at standard

temperature and pressure (STP) (20C, 1 atm), or

Definition 2: A ratio of the specific weight of a liquid to the specific weight of water

at standard temperature and pressure (STP) (20C, 1 atm),

Unit: dimensionless.

STPwater

liquid

STPwater

liquidSG@@

Specific Gravity

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Example 1.2

•A reservoir of oil has a mass of 825 kg. The reservoir has a volume of 0.917 m3. Compute the density, specific weight, and specific gravity of the oil.

•Solution:

•

•3/900

917.0

825mkg

m

volume

massoil

3oil m/N882981.9x900g

mg

volume

weight

9.0998

900

@

STPw

oiloilSG

• The intensity of the molecular attraction per unit length along any line in the surface is called the surface tension and is designated by the Greek symbol ‘ϭ’(sigma).

• For a given liquid the surface tension depends on

temperature as well as the other fluid it is in contact with at the interface.

• Its SI unit are N/m.

Surface Tension


Surface Tension

• Liquids have cohesion and adhesion, both of which are forms of molecular attraction.

• Cohesion enables a liquid to resist Tensile stress & adhesion enables it to adhere to another body.

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It is a liquid property by virtue of which force of attraction generates, at interface between liquid and a gas i.e. liquid surface and at the interface between two immiscible (not mixable) liquids, which exerts a tension force in the surface.

18

The pressure inside a drop of fluid can be calculated using a free-body diagram of a spherical shape of radius R cut in half, as shown in Fig. 1.7, and the force developed around the edge of the cut sphere is 2R.

This force must be balance with the difference between the internal pressure pi and the external pressure pe acting on the circular area of the cut. Thus,

2R = pR2

p = pi – pe =2R

Surface Tension


Surface Tension

• When second fluid is not specified at interface, it is understood that liquid surface is in contact with air.

• The surface tension values for liquids slightly decreases with increasing temperature.

• “Capillarity” is the property of exerting forces on fluids by fine tube or porous media; it is due to both cohesion and adhesion.

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Surface Tension

• When cohesion is less (than adhesion), the liquid will wet the solid surface in contact and rise at the point of contact.

• If cohesion is more, the liquid surface will depress at the point of contact.

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For Instance, Capillarity makes water rise in the glass tube, while mercury depresses below the true level.The curved liquid surface that develops in a tube is called Meniscus.

• Capillary effect is the rise or fall of a liquid in a small-diameter tube inserted into the liquid. Such narrow tubes or confined flow channels are called capillaries.

• The rise of kerosene through a cotton wick inserted into the reservoir of a kerosene lamp is due to this effect.

• The strength of the capillary effect is quantified by the contact (or wetting) angle f, defined as the angle that the tangent to the liquid surface makes with the solid surface at the point of contact. The surface tension force acts along this tangent line toward the solid surface. A liquid is said to wet the surface when < 90° and not to wet the surface 𝟇when > 90°.𝟇

Surface Tension

Fluid Mechanics-I 22Engr. Tahir Rafique

Capillarities are of two types

»Capillarity rise

»Capillarity fall

Fluid Mechanics-I 23Engr. Tahir Rafique

D h

A cross section in capillary rise in a tube looks like as shown in the figure. From Free body considerations, equating the lifting forces created by surface tension to gravity force.

Lifting forces = Gravity forces

2rcos = r2hɣ

h = (2cos) / (ɣ.r)

Where;s = Surface tension (sigma) in units of force / Lq = Wetting angleɣ = Specific weight of liquidr = Radius of tubeh = Capillary rise

Meniscus

Capillary Rise


Surface Tension

• The expression h = (2cos) / (ɣ.r) can be used to compute the approximate capillary rise or depression in the tube.

• If the tube is clean, = 0 degree for water and about 140 degrees for mercury.

• The equation overestimates the amount of capillary rise or depression, particularly for larger diameter tubes.

• For tube diameters larger than 0.5 inch, capillary effects are negligible.

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Surface Tension

• These effects are also important in hydraulic model studies when the model is small, in the break up of liquid jets, and in the formation of drops and bubbles.

• The formation of drops is extremely complex to analyze but is, for example, of critical concern in the design of inkjet printers, a multi-billion-dollar business.

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SURFACETENSION

SURFACETENSION

What’s going onat the surfaceof a liquid?

What’s going onat the surfaceof a liquid?

Let’s takea look!

Particles that make up a liquid are in constant random motion; they are randomly arranged.

You might expect the particles at the surface,at the micro level, to form a random surface,as shown below.

= intermolecular

attractions

But how do intermolecular forcesinfluence the surface?

Under the surface, intermolecular attractions pull onindividual molecules in all directions

= intermolecularattractions

= intermolecular

attractions

= intermolecular

attractions

At the surface, pull on the molecules is laterally and downward;there is negligible intermolecular attractionsabove the molecules (from the medium above, such as air).SO, the net force on surface molecules is downward.

Surface molecules also form a much smoother surface thanone would expect from randomlymoving molecules.

This explains the characteristic roundedshape that liquids form when droppingthrough the air: The molecules are all being pulled toward the center.

This explains the characteristic rounded shape that liquids form when dropping through the air :

The molecules are all being pulled toward the center.

Water in particular has a very high surface tension.

What property does water have that would give it such a strongsurface tension?

This is the water strider insect. Have you seen one?

How is this possible?

56

• Vapor pressure is the partial pressure produced by fluid vapor in an open or a closed container, which reaches its saturated condition or the transfer of fluid molecules is at equilibrium along its free surface.

• In a closed container, the vapor pressure is solely dependent on temperature. In a saturated condition, any further reduction in temperature or atmospheric pressure below its dew point will lead to the formation of water droplets.

• On the other hand, boiling occurs when the absolute fluid pressure is reduced until it is lower than the vapor pressure of the fluid at that temperature.

• For a network of pipes, the pressure at a point can be lower than the vapour pressure, for example, at the suction section of a pump. Otherwise, vapor bubbles will start to form and this phenomenon is termed as cavitation.

• The very low vapor pressure of mercury makes it particularly suitable for use in Barometers.

Vapor Pressures of Liquids


Thank You.

Engr. Tahir Rafique

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