Chapter 1 Fluid statics 流体静力学
1. 连续介质假定(Continuum assumption)：The real fluid is considered as no-gap continuous
media, called the basic assumption of continuity of fluid, or the continuum hypothesis of
fluid.流体是由连续分布的流体质点(fluid particle)所组成，彼此间无间隙。它是流体力学中最基本的假定，1755年由欧拉提出。在连续性假设之下，表征流体状态的宏观物理量在空间和时间上都是连续分布的，都可以作为空间和时间的函数。
2. 流体质点（Fluid particle ）: A fluid elementthat is small enough with enoughmoles to make
sure that the macroscopic meandensity has definite valueis defined as a Fluid Particle.宏观上足够小，微观上足够大。 3. 流体的粘性（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.流体在运动状态下抵抗剪切变形的性质，称为黏性或粘滞性。它表示流体的内部流动阻力，也可当做一个流体摩擦力量。The viscosity of a gas increases with temperature, the viscosity of a liquid decreases with temperature.
4. 牛顿内摩擦定律（Newton’s law of viscosity ）：
5. The dynamic viscosity （动力黏度）is also called absolute viscosity （绝对黏度）. The kinematic
viscosity （运动黏度）is the ratio of dynamic viscosity to density.
6. Compressibility （压缩性）：As the temperature is constant, the magnitude of
compressibility is expressed by coefficient of volume compressibility (体积压缩系数) к , a relative variation rate （相对变化率） of volume per unit pressure.
The bulk modulus of elasticity (体积弹性模量) E is the reciprocal of coefficient of volume compressibility к.
7. 流体的膨胀性(expansibility; dilatability)：The coefficient of cubical expansion (体积热膨胀
系数) αt is the relative variation rate of volume per unit temperature change.
8. 表面张力Surfacetension : A property resulting from the attractive forces between
du dz
τμ=μ
νρ
=
molecules.σ-----单位长度所受拉力
9. 表面力 Surface force ——is the force exerted on the contact surface by the contacted fluid
or other body. Its value is proportional to contact area.作用在所研究流体外表面上与表面积大小成正比的力。Stress （应力） is the surface force on per unit area.
10. 质量力Mass force ——The force acting on every fluid mass particle within the control body.
Its value is proportional to its mass. Mass force is also known as body force. 作用在流体的每一个流体质点上，其大小与流体所具有的质量成正比。 11. Euler Equilibrium Equations 欧拉平衡微分方程（分量式） 1775年
Physical Meaning:
For the fluid in equilibrium, surface force components per mass fluid are equal to mass force
components per mass fluid. Pressure variation rate in axes directions are equal to mass force components per unit volume in axes directions respectively
12. constant-pressure Surface(等压面)——a surface that the pressure of every point in liquid
is equal. Common constant-pressure surfaces are free liquid surface and interface of two
unmixed fluids in equilibrium.平衡流体中压强相等的点所组成的平面或曲面。
13. Pressure Distribution in the Static Fluid
Conclusions:
1. Pressure at a point in a static fluid under gravity increases linearly with depth.
2. Pressure at a point in a static fluid under gravity is equal to the sum of the pressure at the free surface and the fluid specific weight timing depth.
3. constant-pressure surface in a static fluid under gravity is a horizontal plane.
4. Extended: while the pressure at a point and the depth difference between two points are known, the pressure at another point can be calculated.
14. Absolute pressure(绝对压力), Gage pressure(相对压力, 又称“表压力”), and Vacuum(真
空度): 表压力＝绝对压力－大气压力; 真空度＝大气压力－绝对压力
15. Fluid in Relative Equilibrium (相对静止流体) Equation of constant-pressure surface(等压面
方程):
a) Uniform Linear Acceleration 等加速度直线运动流体: (,,)p p p
x y z
∂∂∂∂∂∂(,,)x y z f f f ρρρ 0
p C dp ==或cos d (sin )d 0
a y a g z αα+-=
