Erosion and Sedimentation

The analysis of particle motion in inviscid fluids is important because asymmetric objects and large sediment particles will be subjected to large lift forces. In real fluids, the viscous effects can be ignored at large particle Reynolds numbers. At every point on the surface of a submerged particle, the fluid exerts a force per unit area or stress. In Chapter 3, the stress vector was subdivided into a pressure component acting in the direction normal to the surface and two orthogonal shear stress components acting in the plane tangent to the surface. In this chapter, the stress vector for inviscid fluids is always normal to the surface, which means that there is only a pressure component and no shear stress.

The flow of inviscid fluids around submerged particles may be due either to the movement of the fluid, the movement of the particle, or a combination of both. The following discussion considers flow conditions made steady by application of the principle of relative motion of the fluid around a stationary particle. For steady flow of incompressible and inviscid fluids, the Bernoulli equation is applicable as long as the flow is irrotational. The approach in this chapter is first to define the flow field for irrotational flow. The Bernoulli equation applies throughout the flow field and then defines the pressure from the velocity.