Fundamentals of turbomachines -The Euler’s equation

Fundamentals of turbomachines -The Euler’s equation:
Rotating machines are called as turbomachines.
Turbomachines are a device, in which the rotating fluid interacts with the rotor which rotates about an axis.
When a fluid interacts with a rotor, two things take place
  1. The energy transfer and
  2. The energy transformation
The energy transfer takes place in the rotating parts( i.e) it may be transferred from the fluid to rotor or vice versa
In case if the energy is transferred from fluid to rotor it is called as a turbine
If the energy is transferred from rotor to fluid it is called as a compressor.
Energy transfer takes place only in the rotating parts
Whereas the energy transformation takes place both in the rotating and stationary parts.
Energy transformation means the change of kinetic energy to the pressure energy.
The forces developed in the turbomachines is because of Newton’s second law of motion or the combined action of both newtons second and third law.
Newton’s second law states that the rate of change of momentum is directly proportional to the force applied.
In case of turbomachines, the angular momentum takes place,
Therefore the rate of change of angular momentum is directly proportional to the applied torque.
fundamentals of turbo machines - the Eulers energy equation
Consider a fluid of mass m and interacts with the rotor with a tangential velocity C1 at a distance r1 from the axis of the rotor and leaves the rotor with a tangential velocity c2 at a distance r2 from the rotor. as this fluid (gas) interacts with the rotor which rotates about the axis A-A, there comes an angular momentum which is directly proportional to the torque applied.
The angular momentum at the inlet is mc1r1
The angular momentum at the exit is mc2r2
Applying Newton’s second law,
The applied torque = mc2r2 -mc1r1
The energy transfer E = T×ω(energy = torque * angular momentum)
E=(mc2r2 -mc1r1ω
E=m(c2r2 -c1r1ω
E=m(c2r2ω -c1r1ω)
E=m(c2u2 -c1u1) (u=rω )
If m=1
 E=(c2u2 -c1u1)
this is the Euler’s energy equation.
where u2 and u1 is the  tangential velocity of the rotoe and c2 and c1 is the tangential velocity of the gas.
c2u2 >c1u1 the energy transfer is positive and is a Turbine
If c2u2 < c1u1 the energy transfer is negative and is a compressor
Energy transfer equation of a Turbine is ET=(c2u2 -c1u1)
Energy transfer equation of a compressor is Ec=(c1u1 -c2u2)
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A complete guide for GATE AEROSPACE 2018 preparation.

How to study effectively for GATE AEROSPACE 2018?

As the big day is nearing, all those GATE aspirants are Working hard to step into a great future.All your dreams come true when you work smart rather than hard for your GATE AEROSPACE 2018. There are few effective strategies, I teach my students, When you follow with this method, you can increase your success rate.

Here is my complete guide for GATE AEROSPACE 2018 preparation. these are my best-known ways to prepare for an exam.

I have got 100% success rate with this methodology, even I use to teach using this methodology.

Planning your study time effectively for GATE AEROSPACE 2018:

So, when you come to the point of “time management “.You frequently  hear the boring proverb “time and tide waits for none “.However, I believe “time is just an illusion” all you need to do is concentrate. Even if you read for half an hour, just try to understand the context. A deeper understanding of the context helps you learn the application techniques.

Therefore, it is not that how many hours you read; it is how well you read that matters.

I call this technique as O-BAD”.

Yup, it’s really bad, because it gives you big bang results when you follow it seriously.

O-BAD Technique:

  1. Outline the” big Chunks”
  2. Break down and list the subtasks
  3. Analyze the tasks and subtasks
  4. Decide when each subtask has to be completed.

Outline the” big Chunks”:

Start with analysing in which subject you are strong. The subject that you choose will be your Big Chunk.Check for the major topics in that subject, these will be TASKS now.

For example, Big chunks in  GATE AEROSPACE are Aerodynamics, Aircraft Propulsion, Aircraft Structures, Mathematics.

If you are good at Aerodynamics, it will be your Big chunk now. you have to sort down the topics in that, to find out your tasks.

In Aerodynamics, tasks will be

  1. Task No:1 -Fundamentals
  2. Task No:2-Inviscid Incompressible Flow,
  3. Task No:3-Inviscid Compressible Flow,
  4. Task No:4-Viscous flow.

now you are done with the first step of this technique. Let’s move to the next step.

Breakdown and list the subtasks :

Identify and list the steps that need to be taken in order to completely Cover each task.

Example: if aerodynamics is the Big chunk, and choosing task 2 -Inviscid Incompressible Flow as your task, now you have to list down the subtasks in that particular chapter and analyse the importance of each subtask with the previous year questions asked in that topic.and list down all the subtopics.

so for the task 2 Inviscid Incompressible flow, Sub tasks are

  1. Introduction to Bernoulli’s equation
  2. Introduction to Pitot tube
  3. Introduction to Laplace equation
  4. Types of Flows
  5. Kutta-Joukowski theorem
  6. d’Alembert’s Paradox
  7. Kutta condition
  8. Kelvin’s circulation theorem
  9. Classical Thin Airfoil theory
  10. Induced drag and Downwash
  11. The vortex filament
  12. The biot savart law
  13. Helmholtz theorem
  14. Prandtl’s lifting line theory
  15. Three-dimensional flows.


Hope you have understood.

Analyze the tasks and subtasks:

Take out and dust the previous year questions for it is much needed to analyze and Segregate the important topics.

Ask: which section-or concept has got more problems?

And which section you struggle the most?

(highlight and remember these topics. Since you need more attention )

Example: when you analyze the previous year question papers, on the Subject of aerodynamics, boundary layer problems have got a subsequent place.

If you are weak in this you need to have deeper learning in this boundary layer topic.

Decide when each subtask has to be completed :

 Follow the seven-day rule for GATE AEROSPACE 2018 Preparation:

Day 1: organize your study material, that is you have to allow for a particular subject.Aerodynamics what are the materials you Have. Textbook or class lecture notes or some other, Downloaded from the web.

Day 2: Study with lecture notes

Day 3: Prepare with textbook

Day 4: Solve if you have got problems in class

Day 5: Try solving problems in book

Day 6: Go with previous year questions on the subtask chosen

Day 7: Review everything. If it is a highlighted topic all you have to do is to allot extra time on it.

Example: if you have chosen Classical thin airfoil theory as a subtask in Aerodynamics

You have to follow the seven-day rule allotting half an hour each day. If it is a Highlighted topic ( your weaker area) you have to allot one hour each day.

Make your own study timetable with this technique and follow it.This method will give you 100% success in GATE AEROSPACE

The books that I recommend for aerodynamics are

Last but not least tips
Study a maximum of 2 hours a night . Try to study 10-12 hours a day.

Review constantly before the test or exam.

you have signed for any paid mock tests, then try to accomplish the test

Try to complete all the topics you have planned for the day before you go to bed.

Sleep at least 6 hours in the night.

Exercise every day to begin fresh.

“Health is wealth”, eat healthy foods.Drink more water, stay hydrated.

Don’t multitask , try to avoid chatting while you are studying.

Vary your study location to boost your preparation.

The method I have followed to prepare the study materials for GATE AEROSPACE 2018 propulsion.


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