流体力学英文版复习

Solution:
p K V / V 6 6 3.110 0.110 (998 1000) /1000 1.5 109 (Pa)
7
2018/10/14
(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).
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
2018/10/14
1
（Pa）
(1.16)
6
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?
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.
integrating
dp dz 0 ρg
Figure 2.4 A vessel containing liquid at rest
p z c (2.7) g
2018/10/14
c is the constant of integration (积分常数) determined by the boundary condition.
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
V 1 m ρ
(m3/kg )
(1.13)
The specific volume is the reciprocal (倒数) of density.
2018/10/14
3
(2) Specific Weight （重度）
It’s the weight per unit volume
G V
Predominant Cause: Cohesion is the cause of viscosity of liquid. Transfer of molecular momentum is the cause of viscosity of gas.
2018/10/14
8
Newton’s law of viscosity In Fig.1.5, a substance is filled to the space between two closely
2018/10/14
10
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)

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)
2018/10/14

12
Chapter 2. FLUID STATICS 第二章 流体静力学
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).
Figure 1.5 Deformation resulting from application of constant shear force
2018/10/14
9
Experiment shows that F is directly proportional to A and to V and is inversely proportional （反比）to thickness h.
G SG G water water
2018/10/14
dimensionless quantity无量纲
5
(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）
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。
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.
2018/10/14
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ints 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
2018/10/14
2
(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.
2018/10/14
11
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 kinematic viscosity （运动黏度）is the ratio of dynamic viscosity to density.
(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)
2018/10/14
4
(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.
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.
15
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