Creeping Flow Around a Sphere — Lesson 1

This lesson covers the concept of lubrication theory, which is the analysis of fluid flow in thin layers, such as the motion of fluid flow in the thin layer in a bearing of a shaft. The lesson starts with an explanation of creeping flow, where the Reynolds number is very small. It then moves on to derive the governing equation for creeping flow and discusses Stokes flow past a sphere. The lesson also explains the continuity equation and momentum equations in Cartesian coordinates for laminar incompressible fluid flow with constant fluid properties. The lesson concludes with the calculation of pressure drag and viscous drag, explaining that one-third of the total force comes from pressure drag and two-thirds from viscous drag.

Video Highlights

01:46 - Explanation of Stokes flow past a sphere.
07:25 - Explanation of flow over a sphere and the use of spherical coordinates.
15:57 - Explanation of the bi-harmonic equation for the stream function.
24:53 - Explanation of the pressure distribution on the sphere.
33:01 - Calculation of the drag force acting on the sphere.
39:02 - Explanation of the pressure variation over the surface of the sphere.

Key Takeaways

- Lubrication theory is the analysis of fluid flow in thin layers.
- Creeping flow is a type of flow where the Reynolds number is very small.
- The governing equation for creeping flow is derived, and Stokes flow past a sphere is discussed.
- The continuity equation and momentum equations are explained in Cartesian coordinates for laminar incompressible fluid flow with constant fluid properties.
- The calculation of pressure drag and viscous drag is explained, with one-third of the total force coming from pressure drag and two-thirds from viscous drag.