北京航空航天大学：《工程流体力学》课程PPT教学课件（双语版）Chapter 2 Pressure Distribution in a fluid

82.2 Equilibrium of a fluid element Consider a cube in a static fluid Pressure at the center is p, Body forces are R=Xi+Yj+Zk ap dx Pleft=P Ox ap dx Pleft=p+ OX left d dy dx

6 Consider a cube in a static fluid Pressure at the center is p; Body forces are R Xi Yj Zk     = + + dx dy dz right p left p p        = +   = − 2 2 dx x p p p dx x p p p left left § 2.2 Equilibrium of a Fluid Element

Pressure Op dx d dx Body force: )Zdxdyd pkdxdydz dx

7 dx dy dz Xdxdydz ZdxdydzYdxdydz dx dy dz 2 dx xp p  + 2 dx xp p  − p Pressure: Body force:

In x direction plhh-、parh+phe=0 Ox 2 个 Force on Force on Body force in left surface right surface direction Op- pX Euler Equilibrium Equations ax (Euler 1775) P qp=p(kax+Ya小y+z) z

8 0 2 2  + =         − +        − dydz Xdxdydz dx x p dydz p dx x p p  In x direction: Force on left surface Force on right surface Body force in x direction X x p =             =   =   Z z p Y y p   Euler Equilibrium Equations (Euler 1775) dp = (Xdx +Ydy + Zdz)

pi+ Opk=p(Xi +Yj+Zk) ax Our O p=0 Pressure increase in the direction of body force Equipressure surface(等压面) Surfaces in fluid with same pressure, vertical to body force everywhere, in gravity field it is a horizontal plane

9          =   =   =   Z z p Y y p X x p    Pressure increase in the direction of body force. Surfaces in fluid with same pressure, vertical to body force everywhere, in gravity field it is a horizontal plane. Equipressure surface（等压面） p R   =  k (Xi Yj Zk ) z p j y p i x p       = + +   +   +   