1b. introduction

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 tension

CE-224

Engr. Fazal-E-Jalal

Prepared by: Engr. Fazal-E-Jalal

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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Distinction between a Solid & Fluid

• 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.


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.

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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.


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.


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.

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• 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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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).


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• 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.


Fluid Mechanics-I 9


• 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 meterPrepared by: Engr. Fazal-E-Jalal

Fluid Mechanics-I 10

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)


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.

Page# 21(Fluid Mechanics with engineering applications)

Sample problem 2.4


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.



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.Prepared by: Engr. Fazal-E-Jalal

Sample Problem 2.1 & 2.2Page# 15, 16 (Fluid Mechanics with engineering applications)


Practice Problems

• 2.3.1• 2.3.2• 2.3.3• 2.3.4• 2.3.5• 2.3.6• 2.3.7


(Fluid Mechanics with engineering applications)


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.


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.


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.



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.


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.

Fluid Mechanics-I 17Prepared by: Engr. Fazal-E-Jalal

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.



Surface Tension

• Surface tension effects are generally negligible in most engineering situations. However, they can be important in problems involving capillary rise.


As in soil water zone, without capillary most forms of vegetable life would perish. Similarly, while calculating pressures and taking reading one shall keep in mind that reading is correct if and only surface tension effect is zero.


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.


Page# 39 (Fluid Mechanics with engineering applications)

SAMPLE PROBLEM: 2.10


Practice Problems

• 2.12.1• 2.12.2• 2.12.3• 2.12.4• 2.12.5


(Fluid Mechanics with engineering applications)


Standard Atmosphere

• First adopted in 1920’s in USA and Europe to satisfy need for standardization of aircraft instruments and aircraft performance.

• ICAO (International Civil Aviation Organization) Standard Atmosphere– Upto 32 km

• ISO (International Standards Organization) Standard Atmosphere.– Upto 50 km



Standard Atmosphere

• U.S Standard Atmosphere: (Last revised in 1976). Incorporates ICAO and ISO standards.– Upto 86 km (and extends as far as 1000 km for

some quantities)


The standard absolute pressure behave very differently from temperature, decreasing quite rapidly and smoothly to almost zero at an altitude 30 km.


Standard Atmosphere

1. Troposphere: In the lowest 11.02 km. The temperature decreases rapidly and linearly.

2. Stratosphere: About 9 km thick. The temperature remains constant at -56.5 degree Celsius.

3. Mesosphere:At an altitude of 50 km. Here T increases first slowly and then rapidly.

4. Ionosphere:This is the upper part of mesosphere. T decreases here

U.S Standard Atmosphere



Vapor Pressure of Liquids

• All liquids tend to evaporate or vaporize, which they do by projecting molecules into the space above their surfaces.

• If this is a confined space, the partial pressure exerted by the molecules increases until the rate at which the molecules re-enter the liquid = the rate at which they leave, we call the vapor pressure as Saturation pressure.



Vapor Pressure of Liquids

• At any given temperature, if the pressure on the liquid surface falls below the saturation pressure, a rapid rate of evaporation results, known as Boiling. – Thus we can refer to the saturation pressure as

the Boiling pressure for a given temperature, and it is of practical importance for liquids.


We call the rapid vaporization and recondensation of liquid as it briefly passes through a region of low absolute pressure cavitation. This phenomenon is often very damaging and so we must avoid it.


Vapor Pressures of Liquids

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


Fluid Mechanics-I 28Prepared by: Engr. Fazal-E-Jalal

Education

1b. introduction