Flow Through Rectangular Duct — Lesson 1

This lesson covers the concept of steady pressure driven flow of incompressible Newtonian liquid through a rectangular duct. It explains the use of separation of variables method to solve partial differential equations. The lesson further discusses the assumptions made for simplifying the X momentum equation and the use of superposition technique to decompose the problem into two sub-problems. It also provides a detailed explanation on how to calculate the volumetric flow rate and the maximum velocity.

Video Highlights

00:30 - Introduction to the topic of steady pressure driven flow of incompressible Newtonian liquid through a rectangular duct.
03:50 - Introduction to the superposition technique to split the problem into two sub-problems.
11:16 - Application of the boundary conditions to find the solutions for the two sub-problems.
45:33 - Calculation of the volumetric flow rate through the rectangular duct.
53:58 - Determination of the average velocity and maximum velocity.

Key Takeaways

- The separation of variables method is a powerful tool for solving partial differential equations.
- The superposition technique can be used to split a complex problem into simpler sub-problems.
- The assumptions made in the problem, such as considering the flow as fully developed and neglecting gravity effects, can simplify the equation.
- The boundary conditions play a crucial role in solving the equations.
- The solution of the problem can be found by applying the separation of variables method to the two sub-problems.