1b. introduction

Fluid Mechanics-I
ppt Presentation

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

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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 2

3. 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 3 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.

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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 4 Therefore a liquid may have FREE SURFACE i.e. a surface from which all pressure is removed, except that of it’s own vapor.

5. Distinction between a Gas and a Liquid 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 5 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.

6. Distinction between a Gas and a Liquid 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 6

7. 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/ft 3 (B.G system) and kg/m 3 (S.I system). Also, can be expressed as lb.sec 2 /ft 4 or N.s 2 /m 4 Units of Specific weight : lb/ft 3 (B.G system) and N/m 3 (S.I system). Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 7

8. 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 8

9. 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/ft 3 )/( ft/s 2 ) = lb.sec 2 /ft 4 = mass/Vol. = slugs/cubic feet In S.I System: Ƿ = ɣ/g = ( N/m 3 )/( m/s 2 ) = N.s 2 /m 4 = mass/Vol. = kg/cubic meter Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 9

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) Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 10 Unless otherwise specified or implied by a given temperature, the value to use for water is 62.4 lb/ft 3 or 9.81 kN/m 3 . 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/ft 3 . Page# 21 (Fluid Mechanics with engineering applications) Sample problem 2.4

11. 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: ft 3 /slug In S.I: m 3 /kg It is reciprocal of density. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 11

12. Specific Gravity Denoted by “s”, the specific gravity of a liquid is the dimensionless ratio. S liquid = ƿ liquid / ƿ water 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/cm 3 (or 1.00 g/mL 3 ), equivalent to 1000 kg/m 3 . Density of fluid varies with temperature. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 12 Sample Problem 2.1 & 2.2 Page# 15, 16 (Fluid Mechanics with engineering applications)

13. Practice Problems 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.3.7 Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 13 (Fluid Mechanics with engineering applications)

14. 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 14 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.

15. 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 15

16. 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 16 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 .

17. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 17 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 2 rcos = r 2 hɣ h = ( 2 cos) / (ɣ.r) Where; = Surface tension (sigma) in units of force / L = Wetting angle ɣ = Specific weight of liquid r = Radius of tube h = Capillary rise Meniscus Capillary Rise

18. Surface Tension The expression h = ( 2 cos) / (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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 18

19. Surface Tension Surface tension effects are generally negligible in most engineering situations. However, they can be important in problems involving capillary rise. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 19 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.

20. 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 20 Page# 39 (Fluid Mechanics with engineering applications) Sample problem: 2.10

21. Practice Problems 2.12.1 2.12.2 2.12.3 2.12.4 2.12.5 Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 21 (Fluid Mechanics with engineering applications)

22. 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 Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 22

23. 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) Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 23 The standard absolute pressure behave very differently from temperature , decreasing quite rapidly and smoothly to almost zero at an altitude 30 km.

24. Standard Atmosphere Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 24

25. 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 . Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 25

26. 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. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 26 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.

27. Vapor Pressures of Liquids The very low vapor pressure of mercury makes it particularly suitable for use in Barometers. Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 27

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