Fluid Mechanics Fundamentals and Applications Cengel 3rd Edition Solutions Manual
Fluid Mechanics Fundamentals and Applications Cengel Cimbala 3rd Edition Solutions Manual
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Name: Fluid Mechanics Fundamentals and Applications
Author: Cengel Cimbala
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Fluid Mechanics Fundamentals and Applications Solution Manual
Fluid Mechanics Fundamentals and Applications Cengel Cimbala 3rd Edition Solutions Manual ISBN: 0073380326
INTRODUCTION AND BASIC CONCEPTS
PROPRIETARY AND CONFIDENTIAL
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Introduction, Classification, and System
Solution We are to define a fluid and how it differs between a solid and a gas.
Analysis A substance in the liquid or gas phase is referred to as a fluid. A fluid differs from a solid in that a solid can resist an applied shear stress by deforming, whereas a fluid deforms continuously under the influence of shear stress, no matter how small. A liquid takes the shape of the container it is in, and a liquid forms a free surface in a larger container in a gravitational field. A gas, on the other hand, expands until it encounters the walls of the container and fills the entire available space.
Discussion The subject of fluid mechanics deals with ball fluids, both gases and liquids.
Solution We are to determine whether the flow of air over the wings of an aircraft and the flow of gases through a jet engine is internal or external.
Analysis The flow of air over the wings of an aircraft is external since this is an unbounded fluid flow over a surface. The flow of gases through a jet engine is internal flow since the fluid is completely bounded by the solid surfaces of the engine.
Discussion If we consider the entire airplane, the flow is both internal (through the jet engines) and external (over the body and wings).
Solution We are to define incompressible and compressible flow, and discuss fluid compressibility.
Analysis A fluid flow during which the density of the fluid remains nearly constant is called incompressible flow. A flow in which density varies significantly is called compressible flow. A fluid whose density is practically independent of pressure (such as a liquid) is commonly referred to as an “incompressible fluid,” although it is more proper to refer to incompressible flow. The flow of compressible fluid (such as air) does not necessarily need to be treated as compressible since the density of a compressible fluid may still remain nearly constant during flow – especially flow at low speeds.
Discussion It turns out that the Mach number is the critical parameter to determine whether the flow of a gas can be approximated as an incompressible flow. If Ma is less than about 0.3, the incompressible approximation yields results that are in error by less than a couple percent.
Solution We are to define internal, external, and open-channel flows.
Analysis External flow is the flow of an unbounded fluid over a surface such as a plate, a wire, or a pipe. The flow in a pipe or duct is internal flow if the fluid is completely bounded by solid surfaces. The flow of liquids in a pipe is called open-channel flow if the pipe is partially filled with the liquid and there is a free surface, such as the flow of water in rivers and irrigation ditches.
Discussion As we shall see in later chapters, different approximations are used in the analysis of fluid flows based on their classification.
Solution We are to define the Mach number of a flow and the meaning for a Mach number of 2.
Analysis The Mach number of a flow is defined as the ratio of the speed of flow to the speed of sound in the flowing fluid. A Mach number of 2 indicate a flow speed that is twice the speed of sound in that fluid.
Discussion Mach number is an example of a dimensionless (or nondimensional) parameter.
Solution We are to discuss if the Mach number of a constant-speed airplane is constant.
Analysis No. The speed of sound, and thus the Mach number, changes with temperature which may change considerably from point to point in the atmosphere.
Solution We are to determine if the flow of air with a Mach number of 0.12 should be approximated as incompressible.
Analysis Gas flows can often be approximated as incompressible if the density changes are under about 5 percent, which is usually the case when Ma < 0.3. Therefore, air flow with a Mach number of 0.12 may be approximated as being incompressible.
Discussion Air is of course a compressible fluid, but at low Mach numbers, compressibility effects are insignificant.
Solution We are to define the no-slip condition and its cause.
Analysis A fluid in direct contact with a solid surface sticks to the surface and there is no slip. This is known as the no-slip condition, and it is due to the viscosity of the fluid.
Discussion There is no such thing as an inviscid fluid, since all fluids have viscosity.
Solution We are to define forced flow and discuss the difference between forced and natural flow. We are also to discuss whether wind-driven flows are forced or natural.
Analysis In forced flow, the fluid is forced to flow over a surface or in a tube by external means such as a pump or a fan. In natural flow, any fluid motion is caused by natural means such as the buoyancy effect that manifests itself as the rise of the warmer fluid and the fall of the cooler fluid. The flow caused by winds is natural flow for the earth, but it is forced flow for bodies subjected to the winds since for the body it makes no difference whether the air motion is caused by a fan or by the winds.
Discussion As seen here, the classification of forced vs. natural flow may depend on your frame of reference.
Solution We are to define a boundary layer, and discuss its cause.
Analysis The region of flow (usually near a wall) in which the velocity gradients are significant and frictional effects are important is called the boundary layer. When a fluid stream encounters a solid surface that is at rest, the fluid velocity assumes a value of zero at that surface. The velocity then varies from zero at the surface to some larger value sufficiently far from the surface. The development of a boundary layer is caused by the no-slip condition.
Discussion As we shall see later, flow within a boundary layer is rotational (individual fluid particles rotate), while that outside the boundary layer is typically irrotational (individual fluid particles move, but do not rotate).
Solution We are to discuss the differences between classical and statistical approaches.
Analysis The classical approach is a macroscopic approach, based on experiments or analysis of the gross behavior of a fluid, without knowledge of individual molecules, whereas the statistical approach is a microscopic approach based on the average behavior of large groups of individual molecules.
Discussion The classical approach is easier and much more common in fluid flow analysis.
Solution We are to define a steady-flow process.
Analysis A process is said to be steady if it involves no changes with time anywhere within the system or at the system boundaries.
Discussion The opposite of steady flow is unsteady flow, which involves changes with time.
Solution We are to define stress, normal stress, shear stress, and pressure.
Analysis Stress is defined as force per unit area, and is determined by dividing the force by the area upon which it acts. The normal component of a force acting on a surface per unit area is called the normal stress, and the tangential component of a force acting on a surface per unit area is called shear stress. In a fluid at rest, the normal stress is called pressure.
Discussion Fluids in motion may have both shear stresses and additional normal stresses besides pressure, but when a fluid is at rest, the only normal stress is the pressure, and there are no shear stresses.
Solution We are to discuss how to select system when analyzing the acceleration of gases as they flow through a nozzle.
Analysis When analyzing the acceleration of gases as they flow through a nozzle, a wise choice for the system is the volume within the nozzle, bounded by the entire inner surface of the nozzle and the inlet and outlet cross-sections. This is a control volume (or open system) since mass crosses the boundary.
Discussion It would be much more difficult to follow a chunk of air as a closed system as it flows through the nozzle.