Fluid Mechanics Chapter 1

1. Fluid Mechanics Chapter 1 Introduction

2. Scope • fluid mechanics is the study of fluids at rest or in motion. • It has traditionally been applied in such areas as the design of canal, and dam systems; • the design of pumps, compressors, and piping and ducting used in the water • and air conditioning systems of homes and businesses, as well as the piping systems needed in chemical plants; • the aerodynamics of automobiles and sub- and supersonic airplanes; • and the development of many different flow measurement devices such as gas pump meters

3. Definition of a Fluid • A fluid is a substance that deforms continuously under the application of a shear (tangential) stress no matter how small the shear stress may be. • Because the fluid motion continues under the application of a shear stress, we can also define a fluid as any substance that cannot sustain a shear stress when at rest

4. Deformation of Fluids • The amount of deformation of the solid depends on the solid’s modulus of rigidity G; • the rate of deformation of the fluid depends on the fluid’s viscosity μ. • We refer to solids as being elastic and fluids as being viscous

5. Basic Equations • The basic laws, which are applicable to any fluid, are: • 1. The conservation of mass • 2. Newton’s second law of motion • 3. The principle of angular momentum • 4. The first law of thermodynamics • 5. The second law of thermodynamics

6. Solids and liquids • A solid can resist a shear stress by a static deformation; • Molecular forces are much higher and they tend to retain their shapes • Solids tend to regain their shapes when applied stress is removed • A fluid cannot resist a shear stress • Any shear stress applied to a fluid, no matter how small, will result in motion of that fluid. • The fluid moves and deforms continuously as long as the shear stress is applied • Fluid at rest must be in a state of zero shear stress

7. Liquids and Gases • A liquid, being composed of relatively close-packed molecules with strong cohesive forces, tends to retain its volume and will form a free surface in a gravitational field if unconfined from above • These are incompressible • A gas has no definite volume, and when left to itself without confinement, a gas forms an atmosphere which is essentially hydrostatic • These could be compressed

8. Solid Liquids and gases

9. System and Control Volume • A system is defined as a fixed, identifiable quantity of mass; • the system boundaries separate the system from the surroundings. • The boundaries of the system may be fixed or movable; • however, no mass crosses the system boundaries • For a piston-cylinder assembly the gas in the cylinder is the system. • If the gas is heated, the piston will lift the weight; • the boundary of the system thus moves. • Heat and work may cross the boundaries of the system, • but the quantity of matter within the system boundaries remains fixed. • No mass crosses the system boundaries as on next slide

10. System and Control Volume • For a piston-cylinder assembly the gas in the cylinder is the system. • If the gas is heated, the piston will lift the weight; • the boundary of the system thus moves. • Heat and work may cross the boundaries of the system, • but the quantity of matter within the system boundaries remains fixed. • No mass crosses the system boundaries as on next slide

11. Equations • For a closed system:

12. Control Volume • A control volume is an arbitrary volume in space through which fluid flows. • The geometric boundary of the control volume is called the control surface. • The control surface may be real or imaginary; it may be at rest or in motion. • Figure 1.3 shows flow through a pipe junction, with a control surface drawn on it. • Note that some regions of the surface correspond to physical boundaries (the walls of the pipe) and others (at locations 1 ,2 , and 3 ) are parts of the surface that are imaginary (inlets or outlets).

13. Control Volume

14. Systems and control mass/volumes • Systems may be considered to be closed or open, depending on whether a fixed mass or a fixed volume in space is chosen for study. • A closed system consists of a fixed amount of mass, and no mass can cross its boundary. It is also called control mass system • That is, no mass can enter or leave a closed system, But energy, in the form of heat or work, can cross the boundary; • And the volume of a closed system does not have to be fixed. • If, as a special case, even energy is not allowed to cross the boundary, that system is called an isolated system.

15. Systems and control mass/volumes • An open system, or a control volume, as it is often called, is a properly selected region in space. It usually encloses a device that involves mass flow such as a compressor, turbine, or nozzle. • Flow through these devices is best studied by selecting the region within the device as the control volume. • Both mass and energy can cross the boundary of a control volume.

16. Systems and control mass/volumes • A large number of engineering problems involve mass flow in and out of a system and, therefore, are modeled as control volumes. • A water heater, a car radiator, a turbine, and a compressor all involve mass flow and should be analyzed as control volumes (open systems) instead of as control masses (closed systems). • A control volume can be fixed in size and shape, as in the case of a nozzle, or it may involve a moving boundary, • Most control volumes, however, have fixed boundaries and thus do not involve any moving boundaries. • A control volume can also involve heat and work interactions just as a closed system, in addition to mass interaction..

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