Understanding Stokes Second Problem — Lesson 2

This lesson covers the concept of Stokes' first and second problems in fluid dynamics. It begins with a recap of Stokes' first problem, where a stationary fluid medium is suddenly set into motion by a plate moving at a constant velocity. The lesson then delves into Stokes' second problem, where a plate oscillates over time, causing disturbances in the fluid medium. The lesson also discusses the concept of an oscillating flat, semi-infinite Newtonian liquid, and laminar unsteady incompressible Newtonian fluid flow. It further explains the governing equations, initial conditions, and boundary conditions for these problems. The lesson concludes with the calculation of velocity profiles and shear stress distributions in different flow situations.

Video Highlights

01:40 - Explanation of the Stokes second problem, which involves the flow of liquid set in motion by an oscillating plate.
03:59 - Calculation of the velocity profile for the Stokes second problem.
19:49 - Explanation of the concept of the penetration depth and shear stress distribution for the Stokes' second problem.
32:27 - Explanation of the Stokes-Couette flow and the velocity & shear stress distribution.
39:06 - Discussion of pulsating flow between parallel surfaces.

Key Takeaways

- Stokes' first problem involves a stationary fluid medium suddenly set into motion by a plate moving at a constant velocity.
- Stokes' second problem involves an oscillating plate causing disturbances in a fluid medium.
- The governing equation for these problems is Del U by Del T = nu del 2U by del Y square, where U is a function of T&Y.
- The velocity profile and shear stress distribution can be calculated for different flow situations.
- The penetration depth of the disturbances in the fluid medium is limited by the frequency of the oscillating plate.