[工学]流体力学英文课件chap2.pptVIP

Fluid Mechanics 2010 CN Chapter 1 Basics ofFluid MechanicsChapter 1: § 2ViscosityMarc Henn Some Examples of technical applications that are based on the concept of shear flow … A cylindrical piston with diameter “d” is moving at the velocity U horizontally inside a pipe. The width of the radial annular gap between the piston and the wall of the pipe is δ. The gap is filled with a fluid. Because δ is small compared to the diameter d ( δ) the velocity distribution in the gap is considered linear and decreases in radial direction from U at the piston surface to zero at the wall of the pipe. 1. Physical characteristics 2. Shear Flow, Example 1 (1)Piston moves inside a cylinder Minus sign: U is decreasing in positive radial direction 1.同心环形缝隙中的直线运动 如图，假定缝隙 ， 则缝隙中液流的速度分布规律 近似为直线关系。 速度梯度为 切应力为 摩擦面积为 流体对柱塞的摩擦力为 柱塞克服摩擦力所需要的功率为 §1- 2 流 体 的 粘 性 Shear force area Power 「例题1-2」如图长L=10cm、直径d=8cm的柱塞在缸筒中作往复运动，在柱塞与缸筒的同心环形间隙?=0.5mm中充满动力粘度 的油液。柱塞位移为简谐运动规律 柱塞最大行程a=20cm，柱塞往复频率为每分钟n=360次。忽略柱塞惯性力，试求柱塞克服液体摩擦所需要的平均功率。 §1- 2 流 体 的 粘 性 Application: Inside a Piston Engine a piston carries out sinusoidal movements in a cylinder. The annular gap between the piston and the cylinder is filled with oil for lubrication. The lubricating film thickness is δ. 1. Physical characteristics 2. Shear Flow, Example 1 (2)Piston moves inside a cylinder a lubricating film (simplified model) Sliding bearing: A cylindrical shaft of diameter d is revolving at the angular speed ω (omega) in a bore of the length l. 1. Physical characteristics 2. Shear Flow, Example 2Shaft rotates inside a bore The linear tangential velocity at the surface of the shaft of the diameter d is: The length of arc Δa at a radius r from the center included by the angle Δα is: r Δα Δa Δs = Δa t t+Δt 2.同心环形缝隙中的回转运动 如图，同心缝隙 ， 速度分布 假定近似为 直线规律 。 轴表面速度梯度为 切应力为 摩擦面积为 流体作用在轴表面上的摩擦力为 流体作用在轴上的摩擦力矩为 轴克服摩擦力所需要的功率为 §1- 2 流 体 的 粘 性 Shear force Torque Power Two circul