流体力学与工程教学课件 Chapter 2 Fluid Statics.pptVIP

Fig. The equal pressure surfaces A group of paraboloids of revolution Free surface equation Fig. Pressure Formula CONCLUSION The pressure formula for the liquid in a rotating container at a constant angular velocity is the same as that in the absolute static fluid. h is measured from the free surface in the weight direction. Fig. Example 2 A cylindrical container is filled with water, then rotates at 60r/min about its axis. It is 1m high, and its diameter is 60cm. Determine (1) water volume overflowed (2) gauge pressure at a distance of 20cm to the center on the bottom. Solution (1) Paraboloid height Then water volume overflowed is equal to the volume of paraboloid. (2) when r =20cm Hence 上节小复习 1）等压面方程 1、相对平衡的物理意义 2、等加速水平运动容器中液体的相对平衡 把容器中液体作为一个整体，它相对地球有运动，但各液体质点彼此之间及液体与容器之间无相对运动。 2）自由表面方程 3）压强分布规律 4）均质液体在作等加速直线运动并处于相对平衡时： 垂直方向的压强分布规律与静止液体相同。 水平方向的压强分布沿加速度相反方向压强随距离线性增大。 上节小复习 1）等压面方程 3、等角速旋转容器中液体的相对平衡 2）自由表面方程 3）压强分布规律 4）均质液体在作等角速度旋转运动 并处于相对平衡时： 垂直方向的压强分布规律与静止液体相同。 水平方向的压强分布与半径的二次方成正比。 上节小复习 4、此类问题的具体分析方法： 1）先写出流体的单位质量力， 2）再列出等压面方程（压差公式）， 3）推导出流体静压强分布规律（静压强一般分布规律）， 4）得出最终的流体压强分布公式。 3.5 Forces Exerted on Plane Area by Static Liquid 3.5.1 Magnitude of the Resultant Force on Plane Because the forces of atmospheric pressure on object is usually counteracted，only forces exerted by gauge pressure are taken into account. b c d a p a A ? a b A ? p a d c c A b ? a p a d b a p a A c ? d h As for d A CONCLUSION 1) The magnitude of resultant force on plane surface is in direct proportion to the pressure at the center of plate and the area of plate, and has nothing to do with the shape and the magnitude of oblique angle of plate. 2) The resultant force is perpendicular to the surface. 3.5.2 Action Point of Resultant Force ( Pressure Center ) The resultant moment about x axis Suppose the coordinates of pressure center P is（xP，yP）