《流体力学 Fluid Mechanics》课程PPT教学课件（双语版）第六章 不可压缩理想流体的无旋运动

Mechanics of fluid Chanter o Irrotational flow of impressible ideal-fluid

1 Mechanics of Fluid

流体力学 单

2

Chapter 6 Irrotational flow of impressible ideal-fluid 86-1 Introduction 86-2 Dynamic analysis of micelle in liquid 86-3 Velocity potential of irrotational flow 86-4 Stream function of plane flow 86-5 Fundamental potential flow in plane 86-6 Combining theory of potential flow

3 Chapter 6 Irrotational flow of impressible ideal-fluid §6–1 Introduction §6–2 Dynamic analysis of micelle in liquid §6 –3 Velocity potential of irrotational flow §6–4 Stream function of plane flow § 6–5 Fundamental potential flow in plane § 6–6 Combining theory of potential flow

第六章不可压缩理想流体的无旋运动 §6-1引言 §6-2流体微团运动分析 §6-3无旋流动的速度势 §6-4平面流动的流函数 §65基本平面势流 §66势流的叠加原理

4 第六章 不可压缩理想流体的无旋运动 §6–1 引言 §6–2 流体微团运动分析 §6 –3 无旋流动的速度势 §6–4 平面流动的流函数 § 6–5 基本平面势流 § 6–6 势流的叠加原理

Rotational nosy unimpressible ideal-fluid Chapter 6 Irrotational flow of impressible ideal-fluid §6-1 Introduction In this chapter irrotational flow in plane of impressible ideal fluid is studied, velocity field of irrotational flow can be obtained through three approach by calculating velocity potential, stream function and combining potential

5 Chapter 6 Irrotational flow of impressible ideal-fluid §6-1 Introduction In this chapter irrotational flow in plane of impressible ideal￾fluid is studied, velocity field of irrotational flow can be obtained through three approach by calculating velocity potential, stream function and combining potential

不可压包流的元旋动 第六章不可压缩理想流体的无旋运动 §6-1引言 本章主要研究不可压缩理想流体平面无旋运动,平面 无旋运动的速度场可通过计算速度势、流函数及复势这三 条途径来确定

6 第六章 不可压缩理想流体的无旋运动 §6-1 引言 本章主要研究不可压缩理想流体平面无旋运动，平面 无旋运动的速度场可通过计算速度势、流函数及复势这三 条途径来确定

Rotational nosy unimpressible ideal-fluid 86-2 Dynamic analysis of liquid micelle Known from theory mechanics, in rigid body there are two motion forms moving and rotation; but different in liquid motions Due to different velocity of each point of liquid micelle in flow field, but need keep its continuity as well, so besides moving and rotation in liquid micelle, still has deform motions. In following three motion forms of liquid micelle are analyzed Figure 6-1 is plane motion of liquid micelle. Supposing liquid micelle is rectangle ABCD at t, Through dt, it changes into new position and deforms to ' again supposing at t velocity of angle point A is ur, u Thaler progression, obtaining velocity of point B andc suy spreading due to ABCD point B B:u +-xdxu +ydx ax ax point C: u, +dy, u, +dy 7

7 §6-2 Dynamic analysis of liquid micelle Known from theory mechanics,in rigid body there are two motion forms： moving and rotation；but different in liquid motions.Due to different velocity of each point of liquid micelle in flow field,but need keep its continuity as well,so besides moving and rotation in liquid micelle,still has deform motions.In following three motion forms of liquid micelle are analyzed. dy y u dy u y ux C u dx x u dx u x u B u y x y y y x x   +   +   +   + point , point , ： ： Figure 6—1 is plane motion of liquid micelle.Supposing liquid micelle is rectangle ABCD at t ,Through ,it changes into new position and deforms to ,again supposing at t velocity of angle point A is ,spreading due to Thaler progression,obtaining velocity of point B and C ABCD x y u ,u dt

不可忽流的元族运动 §6-2流体微团运动分析 由理论力学可知,刚体有平移和旋转两种运动形式,而流体 运动则不同。由于流体微团在流场中各点的速度不同,但又要保 持流体本身的连续性,因此流体微团除有平移和旋转运动外,还 有变形运动。下面将分析流体微团的三种运动形式。 如图6-1所示的平面运动中的流体微团。设在t时刻流体微 团为矩形ABCD,经过时段后它移动到新的位置并变形为ABCD ,又设t时刻角点的速度为xy,根据泰勒级数展开,得B、 C点的速度分别为 B点: 0 dx.u t-ydx C点:,+ u.+

8 §6-2 流体微团运动分析 由理论力学可知，刚体有平移和旋转两种运动形式，而流体 运动则不同。由于流体微团在流场中各点的速度不同，但又要保 持流体本身的连续性，因此流体微团除有平移和旋转运动外，还 有变形运动。下面将分析流体微团的三种运动形式。 dy y u dy u y ux C u dx x u dx u x u B u y x y y y x x   +   +   +   + , , 点： 点： ABCD x y u ,u dt 如图6—1所示的平面运动中的流体微团。设在 t 时刻流体微 团为矩形ABCD，经过 时段后它移动到新的位置并变形为 ，又设 t 时刻角点A的速度为 ，根据泰勒级数展开，得B、 C点的速度分别为

Rotational nosy unimpressible ideal-fluid D′ +。xd dy +ddt C D B dxdt iOx tu+ dx + dxtaxdxdi B Lnxox-u dt dx x Figure 6-1 Analysis on plane motion of liquid micelle

9 x y A B C D D C B A u dt x dx x u u x x   + dy y u u y y   + dy y u u x x   + dx x u u y y   + dydt y u dy y   + u dt y dydt y ux   dxdt x u dx x   + dxdt x uy     Figure 6-1 Analysis on plane motion of liquid micelle y u x u

不可压包流的元旋动 D′ +。xd dy +ddt C D B dxdt iOx tu+ dx + dxtaxdxdi B Eu +-x dx ax-u dt x 图61分析流体微团的平面运动 10

10 x y A B C D D C B A u dt x dx x u u x x   + dy y u u y y   + dy y u u x x   + dx x u u y y   + dydt y u dy y   + u dt y dydt y ux   dxdt x u dx x   + dxdt x uy     图 6—1 分析流体微团的平面运动 y u x u