Fluid statics Phm B p2 Figure2-1 unit body in Figure 2-2 the infinitesimal the static fluid wedge-shaped in the equilibrium fluid
11 p n p m Figure2—1 unit body in the static fluid z x y py pz f pn px → n A B C Figure 2—2 the infinitesimal wedge-shaped in the equilibrium fluid
流功学 p x 图21静止流体中的单元体图22平衡流体中的微元四面体 12
12 p n p m 图2—1静止流体中的单元体 z x y py pz f pn px → n A B C 图2—2平衡流体中的微元四面体
2. On any points in the static fluid the static pressures in all directions are equal without relations to the azimuth of acting face Select a infinitesimal wedge-shaped OABC in the equilibrium fluid whose length of sides are dx, dy and dz. As shown in Figure 2-2 Assume that the pressure at a random point of each surface of the wedge-shaped is expressed by px, Py and p: respectively Then the surface force acting on the infinitesimal wedge-shaped is 13
13 2. On any points in the static fluid the static pressures in all directions are equal without relations to the azimuth of acting face. Assume that the pressure at a random point of each surface of the wedge-shaped is expressed by , and respectively. Then the surface force acting on the infinitesimal wedge-shaped is x p py pz dx dy dz Select a infinitesimal wedge-shaped OABC in the equilibrium fluid whose length of sides are , and . As shown in Figure 2—2
流功学 静止流体中任何一点上各个方向的静压强大小相等,与作 用面方位无关。 在平衡流体中任取边长为y、c的微元四面体OABC。 如图2—2所示。 设四面体每个面上任意一点的压强分别用p2、P,、P2及 表示,则作用在微元四面体表面力为
14 二、静止流体中任何一点上各个方向的静压强大小相等，与作 用面方位无关。 设四面体每个面上任意一点的压强分别用 、 、 及 表示，则作用在微元四面体表面力为 x p py z p 在平衡流体中任取边长为 dx 、 dy 、 dz 的微元四面体OABC。 如图2—2所示
dP=(p dydz-p,AABC cos(n, x)) 2 +(p,-dxdz-p, AABC cos(n, y)j +(p. dxdy-p,AABC coS(n, z)k 2 =(PxPn)ddi+(Py-Pn)x与+(P:-Pn)d水 (2—3) 15
15 p p dydzi p p dxdzj p p dxdyk p dxdy p ABC n z k p dxdz p ABC n y j dP p dydz p ABC n x i x n y n z n z n y n x n 2 1 ( ) 2 1 ( ) 2 1 ( ) cos( , )) 2 1 ( cos( , )) 2 1 ( cos( , )) 2 1 ( = − + − + − + − + − = − （2—3）