流体力学第一章

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FLUID MECHANICS 流体力学符 松清华大学 航天航空学院2011年3月14日 清华大学工程力学系 1

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I.1 Basic Concepts & DefinitionsFluid 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: (1) fluid statics (fluids at rest), (2) momentum and energy analyses (fluids in motion) (3) viscous effects and all sections considering pressure forces (effects of fluids on boundaries).2011年3月14日 清华大学工程力学系 2

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I.1 Basic Concepts & DefinitionsFluid - A substance which moves and deforms continuously as a result of an applied shear stress.The definition also clearly shows that viscous effects are not considered in the study of fluid statics.

Two important properties in the study of fluid mechanics are: Pressure and Velocity2011年3月14日 清华大学工程力学系 3

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I.1 Basic Concepts & DefinitionsPressure - The normal stress on any plane through a fluid element at rest. Key Point: The direction of pressure forces will always be perpendicular to the surface of interest. Velocity -The rate of change of position at a point in a flow field. It is used not only to specify flow field characteristics but also to specify flow rate, momentum, and viscous effects for a fluid in motion.

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I.4 Dimensions and UnitsThis text will use both the International System of Units (S.I.) and British Gravitational System (B.G.). A key feature of both is that neither system uses gc. Rather, in both systems the combination of units for mass * acceleration yields the unit of force, i.e. Newton’s second law yields . S.I. - 1 Newton (N) = 1 kg m/s2 B.G. - 1 lbf = 1 slug ft/s2

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I.4 Dimensions and Units

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I.4 Dimensions and UnitsKey Point: In the B.G. system of units, theunit used for mass is the slug and not the lbm. and 1 slug = 32.174 lbm. Therefore, be careful not to use conventional values for fluid density in English units without appropriate conversions, e.g., for water: ρw = 62.4 lb/ft3 (do not use this value)

Instead, use ρw = 1.94 slug/ft3 .2011年3月14日 清华大学工程力学系 7

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I.4 Dimensions and UnitsFor a unit system using gc, the manometer equation would be written asg P=ρ h gc

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I.4 Dimensions and Units

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清华大学工程力学系

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I.4 Dimensions and UnitsRecommendation: In working with problems with complex or mixed system units, at the start of the problem convert all parameters with units to the base units being used in the problem, e.g. for S.I. problems, convert all parameters to kg, m, & s; for B.G. problems, convert all parameters to slug, ft, & s. Then convert the final answer to the desired final units. Review examples on unit conversion in the text .2011年3月14日

清华大学工程力学系 10

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1.5 Properties of the Velocity FieldTwo important properties in the study of fluid mechanics are: Pressure and Velocity The basic definition for velocity has been given previously. However, one of its most important uses in fluid mechanics is to specify both the volume and mass flow rate of a fluid.

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1.5 Properties of the Velocity FieldVolume flow rate:

Q = ∫ V n dA = ∫ Vn dAcs cs

where Vn is the normal component of velocity at a point on the area across which fluid flows. Key Point: Note that only the normal component of velocity contributes to flow rate across a boundary.2011年3月14日 清华大学工程力学系 12

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1.5 Properties of the Velocity FieldMass flow rate:

m = ∫ ρ V n dA = ∫ ρ Vn dAcs cs

NOTE: While not obvious in the basic equation, Vn must also be measured relative to any motion at the flow area boundary, i.e., if the flow boundary is moving, Vn is measured relative to the moving boundary.2011年3月14日 清华大学工程力学系 13

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1.6 Thermodynamic PropertiesAll of the usual thermodynamic properties are important in fluid mechanics :

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1.6 Thermodynamic PropertiesAlternatives for density

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1.6 Thermodynamic PropertiesExample: Determine the static pressure difference indicated by an 18 cm column of fluid (liquid) with a specific gravity of 0.85.

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Ideal Gas PropertiesGases at low pressures and high temperatures have an equation-of-state ( the relationship between pressure, temperature, and density for the gas) that is closely approximated by the ideal gas equation-of-state. The expressions used for selected properties for substances behaving as an ideal gas are given in the following table.2011年3月14日 清华大学工程力学系 17

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Ideal Gas Properties and Equations

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Properties for Air

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