Fluid mechanics Chapter 2 Fluid Statics
1 Fluid Mechanics
流体力学 N□ 件为学
2
Chapter 2 Fluid statics §2-1 Preface D$2-2 Fluid Static Pressure and Its Characters 82-3 Differential Equation of Fluid Equilibrium 82-4 Equilibrium Fluids in Gravity Field s82-5 Calculation and Measure of Static Pressure 82-6 Relative Equilibrium of liquid D$2-7 Total Pressure Acting on Plane of Static Fluids D82-8 Total Pressure Acting on Curved Surface of Static Fluids 2 Exercises of Chapter 2
3 §2–1 Preface §2–2 Fluid Static Pressure and Its Characters §2–3 Differential Equation of Fluid Equilibrium §2–4 Equilibrium Fluids in Gravity Field §2–5 Calculation and Measure of Static Pressure §2–6 Relative Equilibrium of Liquid §2–7 Total Pressure Acting on Plane of Static Fluids §2–8 Total Pressure Acting on Curved Surface of Static Fluids Exercises of Chapter 2 Chapter 2 Fluid Statics
第二章流体静力学 §2-1引言 §2-2流体静压强及其特性 §2-3流体平衡的微分方程式 §24重力场中的平衡流体 §2-5静压强的计算和测量 §26液体的相对平衡 §2-7静止流体作用在平面上的总压力 §28静止流体作用在曲面上的总压力 第二章习题
4 §2–1 引言 §2–2 流体静压强及其特性 §2–3 流体平衡的微分方程式 §2–4 重力场中的平衡流体 §2–5 静压强的计算和测量 §2–6 液体的相对平衡 §2–7 静止流体作用在平面上的总压力 §2–8 静止流体作用在曲面上的总压力 第二章 习 题 第 二 章 流 体 静 力 学
§2-1 Preface Fluid statics researches the mechanics rules and applications of Equilibrium fluids a. fluids have not relative motion The relative Equilibrium to the earth Equilibrium to the b. Fluids have not relative motion coordinate system to the moving container There are not relative motion among the Equilibrium fluids and fluids do not appear having viscosity. The static pressure in the normal direction is the only surface force acting on fluids Main tasks in this chapter: Research distributed regulations of fluid static pressure in space, the total pressure acts on the fixed wall( such as planes or curved surfaces), etc. Moreover solve some factual engineering questions basing on this
5 §2-1 Preface Fluid statics researches the mechanics rules and applications of Equilibrium fluids. Equilibrium a. Fluids have not relative motion to the earth b. Fluids have not relative motion to the moving container. The relative Equilibrium to the coordinate system. There are not relative motion among the Equilibrium fluids and fluids do not appear having viscosity. The static pressure in the normal direction is the only surface force acting on fluids. Main tasks in this chapter: Research distributed regulations of fluid static pressure in space , the total pressure acts on the fixed wall( such as planes or curved surfaces) , etc. Moreover solve some factual engineering questions basing on this
流功学 §2-1引言 流体静力学研究平衡流体的力学规律及其应用 平b流体对运动容器无相对运动对下标系的相 ∫a流体对地球无相对运动:\相对于 平衡流体相互之间没有相对运动,流体不呈现粘性,作 用在流体上的表面力只有法向的静压强。 本章主要任务:研究流体静压强在空间的分布规律;平衡 流体作用在固壁(平面或曲面)上的总压力等。并在此基础上 解决一些工程实际问题
6 §2-1引言 流体静力学研究平衡流体的力学规律及其应用。 平衡 a.流体对地球无相对运动； b.流体对运动容器无相对运动。 相对于坐标系的相 对平衡 平衡流体相互之间没有相对运动，流体不呈现粘性，作 用在流体上的表面力只有法向的静压强。 本章主要任务：研究流体静压强在空间的分布规律；平衡 流体作用在固壁（平面或曲面）上的总压力等。并在此基础上 解决一些工程实际问题
8 2-2 Fluid Static Pressure and Its Characters Definition The pressure in the equilibrium fluid is called fluid static pressure. It is expressed byp △PdP (2-1) In the formula A4→0△AdA AA--area of infinitesimal unit △P— the total pressure acting on the surface of△A Vector expression of fluid static pressure on the surface of infinitesimal unit is dP=-pdA (2-2) The minus shows that the direction of fluid static pressure goes along the inner normal direction of the compression face Characters The magnitudes and directions are all have relation to the compression face 7
7 §2-2 Fluid Static Pressure and Its Characters Definition： dA dP A P p A = = →0 lim （2—1） In the formula: ——area of infinitesimal unit ——the total pressure acting on the surface of A P A Vector expression of fluid static pressure on the surface of infinitesimal unit is dP pdA = − （2—2） The minus shows that the direction of fluid static pressure goes along the inner normal direction of the compression face. Characters： The magnitudes and directions are all have relation to the compression face. p The pressure in the Equilibrium fluid is called fluid static pressure. It is expressed by
§2-2流体静压强及其特性 定义: 平衡流体中的压强称为流体静压强,记作P △PdP (2-1) 式中 △4→0△Ad4 △微元面积; △P→作用在△4表面上的总压力大小。 微元表面上的流体静压力矢量表达式为 dP==pdA (2-2) 负号说明流体静压力的方向是沿受压面的内法线方向 特点: 大小与方向均与受压面有关
8 §2-2流体静压强及其特性 定义： dA dP A P p A = = →0 lim （2—1） 式中 ——微元面积； ——作用在 表面上的总压力大小。 A P A 微元表面上的流体静压力矢量表达式为 dP pdA = − （2—2） 负号说明流体静压力的方向是沿受压面的内法线方向。 特点： 大小与方向均与受压面有关。 平衡流体中的压强称为流体静压强，记作 p
Characters of fluid Static Pressure 1. The direction always goes along the inner normal of the compression face. Incise the static fluid into two parts with an arbitrary plane, just as shown in Figure 2-1. Take the shadow part as partition, if the direction of the static pressure at a certain point m on incisory plane doesnt go along the normal direction but arbitrary, then p can be decomposed tangent component t and normal component pn. The static fluid dose not undergo shearing stress and pulling force or else the equilibrium will be destroied. So the only direction of static pressure is consistent with the normal direction on the acting face
9 Characters of Fluid Static Pressure p n p m Incise the static fluid into two parts with an arbitrary plane, just as shown in Figure 2—1. Take the shadow part as partition, if the direction of the static pressure at a certain point on incisory plane doesn’t go along the normal direction but arbitrary, then can be decomposed tangent component and normal component . The static fluid dose not undergo shearing stress and pulling force or else the equilibrium will be destroied. So the only direction of static pressure is consistent with the normal direction on the acting face. 1. The direction always goes along the inner normal of the compression face
流功学 流体静压强的特性: 静压强方向永远沿着作用面内法线方向。 用任意一个平面将静止流体切割分为两部分,如图2—-1,取 阴影部分为隔离体,如果切割平面上某一点m处静压力方向不是 法线方向而是任意方向的,则P可分解为切向分量τ和法向分量Pn ,静止流体即不承受切应力,也不承受拉力,否则将破坏平衡, 所以静压力唯一可能的方向就是和作用面内法线方向一致。 10
10 流体静压强的特性： p n p m 用任意一个平面将静止流体切割分为两部分，如图2—1，取 阴影部分为隔离体，如果切割平面上某一点 处静压力方向不是 法线方向而是任意方向的，则 可分解为切向分量 和法向分量 ，静止流体即不承受切应力，也不承受拉力，否则将破坏平衡， 所以静压力唯一可能的方向就是和作用面内法线方向一致。 一、静压强方向永远沿着作用面内法线方向