Compressible Flow Through Varying Area Passage — Lesson 1

This lesson covers the concept of compressible flow through a passage with varying cross-sectional area, which is representative of flow through nozzles, diffusers, and blade passages in turbo machines. The lesson explains how the area of the stream tube appears in the governing equation due to the finite and varying cross-sectional area of the passage. It also discusses the concept of quasi one-dimensional flows, where the flow is not strictly one-dimensional but is treated as such for simplification. The lesson further elaborates on the area-velocity relation and the area-Mach number relation, which are crucial in understanding the behavior of flow through varying area passages. The lesson concludes with the concept of 'choking' in the context of flow through nozzles.

Video Highlights

01:29 - Discussion on the concept of one-dimensional and two-dimensional flow
06:00 - Discussion on the concept of normal shock and isentropic flow
14:34 - Discussion on the concept of choking and the conditions for it to occur
21:24 - Derivation of the area Mach number relation for choked flow of a calorically perfect gas
31:15 - Explanation of how the mass flow rate can be controlled in a nozzle

Key Takeaways

- Compressible flow through passages with varying cross-sectional areas is representative of flow through nozzles, diffusers, and blade passages in turbo machines.
- The governing equations for such flows include the continuity equation and the momentum equation.
- Quasi one-dimensional flows are not strictly one-dimensional but are treated as approximately one-dimensional.
- The area-velocity relation is a crucial concept in understanding the behavior of these flows.
- The area Mach number relation for choked flow of a calorically perfect gas is a key relation in gas dynamics.
- Once the flow in a nozzle is choked, the mass flow rate becomes a constant and is no longer dependent on the downstream pressure.