7 Fluid’s Surface Shape in a Rotating Cylindrical Tank

In this chapter we will investigate the surface shape of a fluid in a rotating cylindrical tank, as shown in Figure 7.1. Initially, the fluid’s surface is horizontal when the rotational speed of the tank is zero. Also, we will neglect the surface tension at the fluid’s free surface. We will also neglect the viscous forces between the fluid and the walls of the tank. When the tank is rotating with a constant angular speed of ω (rad s⁻¹), the fluid’s surface takes the form of a concave paraboloid which will be shown below when we consider only two forces acting on a fluid’s surface particle, namely the gravity force which draws the particle in the negative Z-direction and the centrifugal force which draws the particle away from the center of rotation.