Fluid Mechanics (Week 4) Engineering Mechanics Fluid Mechanics (Week 4) Chapter 2: Fluid Statics Chapter 2 Fluid Statics Hsin-Yuan Miao, Ph. D. Assistant Professor Department of Mechanical Engineering National Kaohsiung University of Applied Science 415 Chien-Kung Road, Kaohsiung, 80778, Taiwan R. O. C. TEL : 886-7-381-4526 ext. 5351 FAX : 886-7-3831373 Mobile : 886-937-215-638 E-MAIL : kenymiao@cc.kuas.edu.tw http://www2.kuas.edu.tw/prof/kenymiao/index.html

Introduction The problem in this chapter : Chapter 2: Fluid Statics Introduction The problem in this chapter : No matter the fluid is either at rest or moving in such a manner that there is no relative motion between adjacent particles. 2. There is no shearing stress in fluid, and the only forces that develop on the surface of the particle will be due to the pressure. 3. All have to investigate are pressure and its variation throughout a fluid, and the effect of pressure on submerged surface.

2.2 Basic Equation for Pressure Field Chapter 2: Fluid Statics 2.1 Pressure at a Point 2.2 Basic Equation for Pressure Field 2.3 Pressure Variation in a Fluid at Rest 2.4 Standard Atmosphere 2.5 Measurement of Pressure 2.6 Manometry 2.8 Hydrostatic Force on a Plane Surface 2.9 Pressure Prism 2.10 Hydrostatic Force on a Curved Surface 2.11 Buoyancy, Flotation, and Stabilityotion 2.12 Pressure Variation in a fluid with Rigid-Body Motion

Figure 2.1 Forces on an arbitrary wedged-shaped element of fluid Chapter 2: Fluid Statics 2.1 Pressure at a Point How about “Pressure”? The normal force per unit area at a given point acting on a given plane within the fluid mass of interest Free-body diagram 重力(weight) Figure 2.1 Forces on an arbitrary wedged-shaped element of fluid

1.4.2 Specifics Weight (lb/ft3, N/m3)(比重量) Chapter 1: Introduction ---1.4 Measure of Fluid Mass and Weight Chapter 2: Fluid Statics 1.4.2 Specifics Weight (lb/ft3, N/m3)(比重量) = γ (gamma) = is defined as its weight per unit volume. = is related to density through the equation γ= ρg = is used to characterize the weight of the system. 1.4.3 Specific Gravity(沒單位) = SG = is defined as the ratio of the density of the fluid to the density of water at some specified temperature. = SG = ρ/ ρH2O 4ºC ρHg = (13.55)(1.94 slugs/ft3) = 26.3 slugs/ft3 ρHg = (13.55)(1000 kg/m3) = 13.6x103 kg/m3 Hg 20 ºC SG= 13.55

1.4.1 Density 密度 (sluds/ft3, kg/m3) Chapter 1: Introduction ---1.4 Measure of Fluid Mass and Weight Chapter 2: Fluid Statics 1.41 Density 密度 1.42 Specific weight 比重量 1.43 Specific gravity 比重 1.4.1 Density 密度 (sluds/ft3, kg/m3) = ρ (rho) =is defined as its mass per unit volume. = used to characterize the mass of a fluid system. = 不同流體，其值變化極大 = 但對單一流體，隨壓力與溫度之變化極小(氣則不然)

Chapter 2: Fluid Statics

Figure 2.2 Surface and body forces acting on small fluid element Chapter 2: Fluid Statics 2.2 Basic Equation for Pressure Fluid How about the “Pressure” from point to point in a fluid? Figure 2.2 Surface and body forces acting on small fluid element p = f (x, y, z) Surface force Body force

Chapter 2: Fluid Statics (壓力的統御方程式)

2.3 Pressure Variation in a Fluid at Rest Chapter 2: Fluid Statics 2.3 Pressure Variation in a Fluid at Rest 1。(2-4)是為靜態流體的方程式，可計算隨高度改變時的壓力值。 2。負值表往下壓力變小。 3。 γ不一定為定值(水為定值)。如氣体，可先求得γ對高度的變化函 數後，再代入(2-4)。

2.3-1 Incompressible Fluid 2.3-2 Compressible Chapter 2: Fluid Statics 2.3-1 Incompressible Fluid 2.3-1 Incompressible Fluid 2.3-2 Compressible

2.3-1 Incompressible Fluid Chapter 2: Fluid Statics 2.3-1 Incompressible Fluid 1. 因為γ=ρg。g設為定值，ρ設為不變 === Incompressible Fluid Figure 2.3 Notation for pressure variation in a fluid at rest with a free surface

Chapter 2: Fluid Statics

Chapter 2: Fluid Statics Example Figure 2.1

Chapter 2: Fluid Statics