# Petroleum Engineering Dept. Fluid Mechanics Second · PDF fileFluid Mechanics ... * Fluid...

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Continents

Chapter 1. Fluid Mechanics -Properties of fluids -Density , specific gravity, specific volume and Viscosity -Newtonian and non Newtonian fluids -Surface tension Compressibility -Pressure -Cavitations Characteristic of perfect gas Problems

Chapter 2 . Fluid Statics - Pressure Distribution in a Fluids - Pressure of fluid at rest - Hydrostatic pressure in gases - Manometers - Buoyancy

Chapter 3 . Fundamental of flow - Movement of the flow - Acceleration Field of a Fluid - Rotation and spinning of a fluid - Circulation - problems

Chapter 4 . Control volume relation for fluid analysis - Conservation of mass - Conservation of energy

Application of Bernoullis equation

Petroleum Engineering Dept.

Fluid Mechanics

Second Stage

Dr. Ahmed K. Alshara

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- Equation of momentum

- Pitot tube, Venture meter, Orifice meter and Rota metere

- Application of momentum equation - Problems

Chapter 5 . Dimensional Analysis , Similarity and Modeling - Dimensional analysis - Similarity and modeling - Problems

Chapter 6. Viscous Internal Flow - Fully Developed Pipe Flow - Darcy Friction Factor - Minor Losses - Multiple Pipe System

Chapter 7. Flow Measurements

Chap8. Turbomachinry

Classification of pumps, pumps connection and Cavitations in Centrifugal Pumps

Chapter 9: Two Phase Flow

Chapter 10: Incompressible Flow

Stagnation Condition, Speed of Sound Isentropic Flow and Flow Cases

in Converging (Truncated) Nozzle

REFERENCES * Fluid Mechanics Frank M. White * Fluid Mechanics V. L. Streeter * Fundamentals of Fluid Mechanics B. R Munson * Fluid Mechanics fundamental and application Y. A. Gengel & J. M. Cimbala

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Conversion Factors

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CHAP 1. FLUID MECHANICS

Fluid Mechanics : Study of fluids at rest , in motion , and the effects of

fluids on boundaries. This definition outlines the key topics in the study of

fluids: (i) fluid static (ii) fluids in motion and (iii) viscous effects and all

sections considering pressure forces (effects of fluids on boundaries).

Fluid: Fluids are divided into liquids and gases. A liquid is hard to compress

and as in the ancient saying Water takes the shape of the vessel containing

it, it changes its shape according to the shape of its container with an upper

free surface. Gas on the other hand is easy to compress, and fully expands to

fill its container. The re is thus no free surface. Consequently, an important

characteristic of a fluid from the viewpoint of fluid mechanics is its

compressibility. Another characteristic is its viscosity . Whereas a solid

shows its elasticity in tension, compression or shearing stress, a fluid does so

only for compression. In other words, a fluid increases its pressure against

compression, trying to retain its original volume. This characteristic is called

compressibility. Furthermore, a fluid shows resistance whenever two layers slide

over each other ,this characteristic is called viscosity. In general , liquids are

called incompressible fluids and gases compressible fluids. Nevertheless, for

liquids , compressibility must be taken into account whenever they are highly

pressurized, and for gases compressibility may be disregarded whenever the

change in pressure is small. Meanwhile, a non-existent, assumed fluid without

either viscosity or compressibility is called an ideal fluid or perfect

fluid. A fluid with compressibility but without viscosity is occasionally

discriminated and called a perfect fluid too. Furthermore, a gas subject to

Boyles-Charles law is called a perfect or ideal gas.

Properties of fluids: Density, specific gravity and specific volume

The mass per unit volume of material is called the density, which is generally

expressed by the symbol . The density of a gas changes according to the

pressure , but that of a liquid may be considered unchangeable in general. The

units of density are kg/m3 (SI). The density of water at 4C and 1 atom (101

325 Pa, standard atmospheric pressure) is 1000 kg/m3. The ratio of the

density of a material to the density of water w , is called the specific

gravity, which is expressed by the symbol s.g :

The reciprocal of density, i.e. the volume per unit mass, is called the specific

volume, which is generally expressed by the symbol :

s.g

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Viscosity As shown in blow Fig .1, suppose that liquid fills the space between two parallel plates of area A each and gap h, the lower plate is fixed, and force F is needed to move the upper plate in parallel at velocity U. Whenever Uh/v < 1500 ( v = / : kinematic viscosity ) , laminar flow is maintained, and a linear velocity distribution, as shown in the figure , is obtained. Such a parallel flow of uniform velocity gradient is called the Couette flow. In this case, the force per unit area necessary for moving the plate, i.e. the shearing stress (Pa) , is proportional to U and inversely proportional to h. Using a proportional constant , it can be expressed as follows:

The proportional constant is called the viscosity , the coefficient of viscosity or the dynamic viscosity. Such a flow where the velocity u in the x direction changes in the y direction is called shear flow. Figure 1 shows the case where the fluid in the gap is not flowing. However, the velocity distribution in the case where the fluid is flowing is as shown in Fig. 2. Extending above equation to such a flow, the shear stress z on the section dy, distance y from the solid wall, is given by the following equation:

This relation was found by Newton through experiment , and is called Newton's law of viscosity.

Fig.1 Fig.2

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In the case of gases, increased temperature makes the molecular movement more vigorous and increases molecular mixing so that the viscosity increases. In the case of a liquid , as its temperature increases molecules separate from each other , decreasing the attraction between them , and so the viscosity decreases. The relation between the temperature and the viscosity is thus reversed for gas and for liquid. Figure 3 shows the change wi