2D Laminar Jet — Lesson 1

This lesson covers the concept of free shear flows, specifically focusing on two-dimensional laminar jets. The lesson begins with an explanation of free shear flows and their governing equations. It then delves into the assumptions made for large Reynolds number flows, Bernoulli theory, and no separation. The lesson further explains the boundary layer equations and how to find the velocity distribution in a two-dimensional laminar jet. The lesson also covers the concept of similarity transformation technique and how to use it to solve the governing equations. The lesson concludes with the calculation of the volume flow rate per unit width. For instance, the lesson explains how to calculate the velocity distribution of a jet where the velocity becomes almost 1% of the center line velocity.

Video Highlights

01:01 - Explanation of free shear flow and its examples.
03:00 - Introduction to the concept of two-dimensional laminar jet.
04:37 - Discussion on the governing equations and boundary conditions for the jet flow.
10:09 - Derivation of the similarity variable and the stream function.
12:26 - Derivation of the momentum equation in terms of the stream function.
32:42 - Calculation of the width of the jet.

Key Takeaways

- Free shear flows are unbounded regions of a large body of fluid with either excess momentum or momentum deficit.
- The governing equations for free shear flows are derived from the equations for laminar boundary layer flows.
- The assumptions made for large Reynolds number flows, Bernoulli theory, and no separation are crucial in understanding free shear flows.
- The boundary layer equations are used to find the velocity distribution in a two-dimensional laminar jet.
- The similarity transformation technique is a useful tool in solving the governing equations for free shear flows.
- The volume flow rate per unit width can be calculated using the derived equations.