Chapter 2: Fluid Statics

Chapter 2 Fluid Statics

Engineering Mechanics

Fluid Mechanics (Week 4)

Hsin-Yuan Miao, Ph. D.

Assistant ProfessorDepartment of Mechanical EngineeringNational Kaohsiung University of Applied Science

415 Chien-Kung Road, Kaohsiung, 80778, Taiwan R. O. C.TEL : 886-7-381-4526 ext. 5351FAX : 886-7-3831373Mobile : 886-937-215-638E-MAIL : kenymiao@cc.kuas.edu.twhttp://www2.kuas.edu.tw/prof/kenymiao/index.html

Chapter 2: Fluid Statics

Introduction

1. 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.

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

Chapter 2: Fluid Statics

Figure 2.1 Forces on an arbitrary wedged-shaped element of fluid

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

重力(weight)

Free-body diagram

Chapter 2: Fluid StaticsChapter 1: Introduction ---1.4 Measure of Fluid Mass and Weight

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

Chapter 2: Fluid StaticsChapter 1: Introduction ---1.4 Measure of Fluid Mass and Weight

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

Chapter 2: Fluid Statics

Figure 2.2 Surface and body forces acting on small fluid element

2.2 Basic Equation for Pressure FluidHow about the “Pressure” from point to point in a fluid?

Surface force

Body force

p = f (x, y, z)

Chapter 2: Fluid Statics

( 壓力的統御方程式 )

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) 。

Chapter 2: Fluid Statics 2.3-1 Incompressible Fluid

2.3-1 Incompressible Fluid

2.3-2 Compressible

Chapter 2: Fluid Statics

Figure 2.3 Notation for pressure variation in a fluid at rest with a free surface

2.3-1 Incompressible Fluid

1. 因為 γ=ρg 。 g設為定值， ρ 設為不變 === Incompressible Fluid

Chapter 2: Fluid Statics

Chapter 2: Fluid Statics

Example Figure 2.1

Chapter 2: Fluid Statics

Chapter 2: Fluid Statics 2.3-2 Compressible

γ=ρg + (2-4 式 )