ABSTRACT
In the classic fluid mechanics, the topic of external flows is focused on the drag and lift forces acting on a macroscale object immersed in a fluid. The forces are caused by a relatively motion between the fluid and the object, which generates nonuniform shear stresses and pressures on the surface of the object. The forces depend on the relative velocity, the shape of the object, and the properties of the fluid, such as density and viscosity. Lift forces are of particular importance mainly in aeronautical engineering. Drag forces, however, have wide applications in a variety of areas. For the drag force, the only case that has an analytical solution is the flow over a sphere at a low Re, for which the drag force is given by the Stokes law, F D = − 6 π μ R V https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315266244/672b9542-e833-4e22-ac0a-37bd5613502c/content/C007_equ_0001.tif"/> (see Equation 1.11a). For other shapes, such as cylinders, or at a high Re, theoretical expressions for the drag force are unavailable.
