Navier Stokes Equation Problems — Lesson 5

This lesson covers the application of Navier Stokes equations in solving various fluid dynamics problems. It begins with a recap of the exact solutions of Navier Stokes equations, assumptions made, and how to derive the velocity distribution and volumetric flow rate. The lesson then delves into solving example problems involving viscous incompressible immiscible fluids flowing in separate layers between two infinite parallel plates. It also discusses the velocity profiles in the two layers and how to find the volume flow rate per unit width. The lesson further explores problems involving oil leakage from a barge and a viscous oil leak onto a horizontal surface. The lesson concludes with the application of these principles to solve engineering problems.

Video Highlights

01:03 - Explanation of the first problem involving viscous incompressible immiscible fluids.
20:44 - Introduction and explanation of the second problem involving a viscous liquid flowing down a stationary vertical wall.
33:19 - Introduction and explanation of the third problem involving an oil-filled barge with a crack.
37:32 - Introduction and explanation of the fourth problem involving a viscous oil leaking onto a horizontal surface.

Key Takeaways

- Navier Stokes equations can be used to solve various fluid dynamics problems.
- The velocity distribution and volumetric flow rate can be derived using these equations.
- The equations can be applied to scenarios involving viscous incompressible immiscible fluids flowing in separate layers.
- The velocity profiles in different layers can be determined using these equations.
- The equations can also be used to solve problems involving oil leakage from a barge and onto a horizontal surface.