1. Euler Turbine Equation
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
An Important Engineering Form of Newton's Laws!!!?!?!?!

2. Simple Turbine : Harvester of Useful Fluid Energy
out T

3. Macro Analysis of A Turbine
Fluid in
Fluid out

4. Cartesian View of Momentum Equation
This is a vector equation and will have three components in x, y and z
Directions.
X – component of momentum equation:

5. X – component of momentum equation:
Y – component of momentum equation:
Z – component of momentum equation:

6. Axial Momentum Equations
A turbomachine cannot tolerate this force doing any work.
The axial force should be completely absorbed by a thrust bearing.
Any remaining traces of this force can cause mechanical or aerodynamic damages.

7. Concurrent Designs for Minimum Axial Thrust

8. Normal Momentum Equations
Resultant radial Force:
The radial force component has little do with steady state aerodynamic performance of a turbo-machine.
Special Casings are designed to reduce this force.
The remaining force is normally absorbed in a journal type bearing.

10. Pump Impeller and casing

11. Radial Force on Impeller

12. Best Efficiency Point (B. E. P
Best Efficiency Point (B.E.P.): The point on a pump's performance curve that corresponds to the highest safe efficiency.
At this point, the impeller is subjected to minimum radial force promoting a smooth operation with low vibration and noise.

13. Euler’s Version of Newton’s Second Law
In turbo-machines much useful information is obtained by employing Newton’s second law in the form where it applies to the moments of forces.
This form is of central importance in the analysis of the energy transfer process in turbo-machines.

14. Euler’s Statement for Second Law
For a system of mass m, the vector sum of the moments of all external forces acting on the system about some arbitrary axis A--A fixed in space is equal to the time rate of change of angular momentum of the system about that axis, i.e.

15. Euler Theory:
Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid = t
Angular momentum is moment of linear momentum of angular velocity, Vq
Define, L as Angular momentum :

16. The Boeing 747 Cruising at an Altitude of 10 km

17. Turbo-jet Engine

18. Even for a steady flow through a turbo-machine:
Inlet rate of angular momentum :
Exit rate of angular momentum at exit:
Change in Rate of angular momentum: