流体力学英文版复习

15
For the two points 1 and 2 in the static fluid
p1 p2 z1 z2 g g
p2 p1 g ( z1 z2 )
For the two points 0 and 1
p1 p0 g ( z0 z1 )
Figure 2.4 A vessel containing liquid at rest
The pressure at a point in liquid at rest consists of two parts: the surface pressure, and the pressure caused by the weight of column of liquid.
2016/2/24
双 语 课 程
General Review 总复习
Chapter 1. FLUID PROPERTIES 第一章 流体性质
Definition of a fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress, no matter how small it is. 流体是一种一受到切力作用（不论多么小） 就会连续变形的物体。
Geometrical meaning
expressed in terms of the length of column of liquid (液柱), and called the head (水头).
z ——the position height or elevation head (位置水头) p/g——the pressure head (压力水头) per unit weight of fluid Sum of the position head (位置水头) and pressure head is called the hydrostatic head ( 静 水 头 ), also known as the piezometric head (测压管水头).
(1.14)
in which is the specific weight of fluid, N/m3; G is the weight of fluid, N.
Or the product of density and acceleration of gravity g.
g
(1.14a)
Predominant Cause: Cohesion is the cause of viscosity of liquid. Transfer of molecular momentum is the cause of viscosity of gas.
2016/2/24
9
Newton‟s law of viscosity In Fig.1.5, a substance is filled to the space between two closely
2016/2/24
11
The angular velocity may also be written as du/dz, so Newton‟s law of viscosity is
du dz
(1.19)
The proportionality factor (比例因子） is called the viscosity coefficient（黏性系数，黏度）. Fluids may be classified as Newtonian or non-Newtonian. Newtonian fluid: is constant. (gases and thin liquids稀液) Non-Newtonian fluid: is not constant. (thick稠的, longchained hydrocarbons长链碳氢化合物)
dp
The bulk modulus of elasticity ( 体积弹性模量 ) K is the reciprocal of coefficient of volume compressibility p.
dp K p dV / V
2016/2/24
1
（Pa）
(1.16)
7
Example 1.1 A mineral oil in cylinder has a volume of 1000cm3 at 0.1MN/m2 and a volume of 998 cm3 at 3.1MN/m2. What is its bulk modulus of elasticity?
16
Physical meaning
z —— the position potential energy per unit weight of fluid to the base level； p/g —— the pressure potential energy (压强势能) per unit weight of fluid. The energy per unit weight of fluid can be also
2016/2/24
5
(3) Relative density and specific gravity The relative density (相对密度) RD of a fluid is the ratio of its density to the density of a given reference material.
integrating
dp dz 0 ρg
Figure 2.4 A vessel containing liquid at rest
p z c (2.7) g
2016/2/24
c is the constant of integration (积分常数) determined by the boundary condition.
Solution:
p K V / V 6 6 3.110 0.110 (998 1000) /1000 1.5 109 (Pa)
8
2016/2/24
(5) Viscosity
Viscosity is an internal property of a fluid that offers resistance to shear deformation. It describes a fluid's internal resistance to flow and may be thought as a measure of fluid friction. The resistance of a fluid to shear depends upon its cohesion( 内 聚 力 ) and its rate of transfer of molecular momentum(分子动量交换).
2016/2/24
3
(1) Density （密度）
Density is the ratio of the mass of fluid to its volume.
m (kg/m3 ) ρ V
(1.12)
Specific volume (比容) : volume occupied by unit mass.
Basic equation of hydrostatics under gravity
Gravity G (G=mg) is the only mass force acting on the liquid fx=0，fy=0，fz= g From (2.5)
dp ρgdz
rewriting
spaced parallel plates（平行板）. The lower plate is fixed, the upper plate with area A move with a constant velocity V, a force F is applied to the upper plate.
AV F h
If the shear stress is =F/A, it can be expressed as
(1.18)
V h
The ratio V/h is the angular velocity of line ab, or it is the rate of angular deformation of the fluid.
Figure 1.5 Deformation resulting from application of constant shear force
2016/2/24
10
Experiment shows that F is directly proportional to A and to V and is inversely proportional （反比）to thickness h.
RD ref
dimensionless quantity无量纲
The reference material is water at 4C i.e., ref=water.=1000kg/m3 The specific gravity (比重) SG of a fluid is the ratio of its weight to the weight of an equal volume of water at standard conditions(标准状态).
SI unit：m2/s U.S. customary unit：ft2/s （英尺2/秒） cgs unit：stokes (St, 斯). 1cm2/s=1St 1mm2/s=1cSt (厘斯)
2016/2/24

13
Chapter 2. FLUID STATICS 第二章 流体静力学
G SG Gwater water
2016/2/24
dimensionless quantity无量纲
6
(4) Compressibility（压缩性） The volume of fluid changes under different pressure. As the temperature is constant, the magnitude of compressibility is expressed by coefficient of volume compressibility (体积压缩系数) p , a relative variation rate（相对变化率） of volume per unit pressure. dV / V (1.15) p （Pa1）
V 1 m ρ
(m3/kg )
(1.13)
The specific volume is the reciprocal (倒数) of density.
2016/2/24
4
(2) Specific Weight （重度）
It’s the weight per unit volume
G V
2016/2/24
12
Dynamic viscosity and Kinematic viscosity • The dynamic viscosity（动力黏度）is also called absolute viscosity （绝对黏度）. From （1.19）
τ du / dz
SI unit ：kg/(ms) or Ns/m2 U.S. customary unit：dynes/cm2 （达因秒/厘米2） cgs unit： Poise (P, 泊). 1P=100cP (厘泊) 1P=0.1Pas (帕秒) • The k百度文库nematic viscosity （运动黏度）is the ratio of dynamic viscosity to density.