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FLUID MECHANICS (CE 204)

FLUID MECHANICS (CE 204). Lecturer: Othman K. Mohammed University of Salahaddin – Hawler College of Engineering Civil Engineering Department. 1. Set by: Othman K. Mohammed. INTRODUCTION.

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FLUID MECHANICS (CE 204)

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  1. FLUID MECHANICS (CE 204) Lecturer: Othman K. Mohammed University of Salahaddin – Hawler College of Engineering Civil Engineering Department

  2. 1

  3. Set by: Othman K. Mohammed INTRODUCTION Fluid Mechanics is the science that deals with the action of forces on fluids (liquids and gases), either at rest (statics) or in motion (dynamics). A fluid is a substance that will continuously deform under the action of a shear stress. History of Fluid Mechanics • Archimedes(287-212 B.C.):buoyance theory. • Leonardo da Vinci (1452-1519): He described wave motions, hydraulic jump, jet and vortex motion. • Torricelli (1608-1647): He is well known for measuring atmospheric pressure.

  4. Blaise Pascal (1623 – 1662) Finally clarified principles of barometer, hydraulic press, and pressure transmissibility. • Newton (1643 - 1727): He explained his famous second law in motions. He also provided the idea of linear viscosity describing the relationship between fluid deformation and shearing forces. • Bernoulli (1700 - 1782): Bernoulli equation. • Euler (1707 - 1783): Euler equation. • William Froude (1810 – 1879) Developed many towing-tank techniques, in particular the conversion of wave and boundary layer resistance from model to proto type scale. • Reynolds (1842 - 1919): Pipe flows, Reynolds stress, turbulence theory. 2

  5. Set by: Othman K. Mohammed Units of Measurement Main quantities are: Length (L), Mass (M) and Time (T). Most of the other quantities like force, pressure, power and more can be derived from the main three quantities: L M T. The International System of Units (SI)

  6. Acceleration due to gravity, g in SI units =9.806 m/sec2. Commonly used prefixes for SI units: 3

  7. Set by: Othman K. Mohammed Properties of Fluid Density (ρ) The mass per unit volume of material is called the density, which is expressed by the symbol (ρ) rho. The density of a gas changes according to the pressure, but that of a liquid may be considered unchangeable in general. The maximum density of water (which occurs at 4 °C and 101325 Pa, standard atmospheric pressure) is 1000 kg/m3.

  8. Specific weight (γ) The specific weight of a fluid is defined as its weight per unit volume and expressed by the Greek symbol (γ) gamma. Thus, specific weight is related to density through the relation: 4

  9. Set by: Othman K. Mohammed Relative Density (r) Is defined as the ratio of mass density of a substance to the standard mass density. For solids and liquids this standard mass density is the maximum mass density for water. Pressure (P) Pressure results from a normal compressive force acting on an area. Mathematically, it is defined as

  10. Compressibility (E) When fluids are pressurized, the total volume V is changed. The amount of volume change is the compressibility of fluids. In fluid mechanics, we use bulk modulus which is denoted as 5

  11. Set by: Othman K. Mohammed Where: dp represents the small increased in pressure applied to the substance that causes a decrease of the volume by dV from its original volume of V. Note the negative sign in the definition to ensure that the value of E is always positive. For liquids the bulk modulus is very high, so the change of density with increase of pressure is very small even for the largest pressure changes encountered. Accordingly, the density of a liquid can normally be regarded as constant, and the analysis of problems involving liquids is thereby simplified.

  12. Viscosity () Viscosity is a measure of a fluid’s “inner friction” or resistance to shear stress. It is basically defined as the ratio of the shear stress to the velocity gradient. From experiments with various fluids, Isaac Newton postulated that for the straight and parallel motion of a given fluid, the tangential stress between two adjoining fluid layers is proportional to the velocity gradient in a direction perpendicular to the layers. 6

  13. Set by: Othman K. Mohammed • The unit used for viscosity is: N.sec/m2 • Another unit used for the viscosity is the poise, which is 0.1 N.sec/m2. • Viscosity is one of the properties that control the amount of fluid that can be transported in a pipeline during a specific period of time. It accounts for the energy losses associated with the transport of fluids in ducts, channels and pipes.

  14. The viscosity of a gas increases with temperature • The viscosity of a liquid decreases with temperature 7

  15. Set by: Othman K. Mohammed Vapor Pressure At the surface of a liquid, molecules are leaving and re-entering the liquid mass. The activity of the molecules at the surface creates a vapor pressure, which is a measure of the rate at which the molecules leave the surface.

  16. Surface tension (σ) The surface tension manifested itself by a rise or depression of the liquid at the free surface edge. Surface tension is also responsible for the creation of the drops and bubbles. It also responsible for the breakage of a liquid jet into other medium/phase to many drops (atomization). The surface tension is force per length and is measured by [N/m] and is acting to stretch the surface. 8

  17. Set by: Othman K. Mohammed Surface tension is the surface force that develops at the interface between two immiscible liquids or between liquid and gas or at the interface between a liquid and a solid surface. Because of surface tension, small water droplets, gas bubbles and drops of mercury tend to maintain spherical shapes.

  18. Molecular forces Cohesion: Cohesion enables a liquid to resist tensile stress (inner force between liquid molecules) Adhesion: adhesion enables it to adhere to another body (attraction force between liquids, and a solid surface). The adhesion of water to glass is stronger than the cohesion of water. Hence, when water is spilled on a clean glass surface it wets the glass and spreads out in a thin film. On the other hand, the cohesion of mercury is greater than its adhesion to glass. Therefore, when mercury is spilled on glass it forms small spherical droplets or larger flattened drops. 9

  19. Set by: Othman K. Mohammed The difference between the adhesive and cohesive properties of water and mercury explains why meniscus of water curves upwards and that of mercury curves downwards when these liquids are poured into clean glass vessels ( as shown in the following figure).

  20. Capillarity The capillarity phenomenon is due to the rise or depression of the meniscus of the liquid due to the action of surface tension forces. Equating the vertical component of the surface tension force to the weight of the liquid column: 10

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