1. Analysis of the Simplest Flow
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Identification of Two Extreme Regimes of the Simplest Flow ?!?!?

2. The Simplest Flow Geometryx y z
Main Flow

3. Something inside the simplest flow ???
A control volume for this analysis is shown, and the gas flows from left to right.
The control volume is having a very narrow width.
No chemical reactions.
There is no friction or heat loss across this CV.
NO work transfer is possible as this is so narrow.
The increase of the entropy is fundamental to any thing that happens in this world.

4. System of Equations for 1D inviscid Adiabatic no work transfer Idea Gas Flow

5. Solution of Simultaneous Equations
If the conditions upstream are known, then there are four unknown conditions downstream.
A system of four unknowns and four equations is solvable.
There exist two solutions because of the quadratic nature of the equations.
These two possible solutions may or may not feasible.
Thermodynamics dictates the feasibility of these solutions.
Changes in pressure, temperature, volume cannot detect the possible solution.
The only tool that helps in identifying the possible solution is change in entropy.
For the adiabatic process, the entropy must increase or remain constant.

6. Change in Mach Number between points x & y
Conservation of mass:
Dividing this equation by cx

7. Conservation of momentum:

8. Dividing this through by cx2/g

9. &

10. Conservation of energy
Energy equation in terms for pressure and velocity for a perfect gas
Dividing this by

11. The Unified Equation for the Vorticity Generator
Simplified Energy Equation :
Combined Mass & Momentum Equation :
Combined Mass, Momentum and Energy Conservation :

12. Discovery of Entropy Generator
Reversible flow : No vorticity generation between x & y,