EULER'S TURBOMACHINERY

Hi, it is group 1 from university of Zaragoza, and it is a one video of principles of turbomachinery´s collection in the subjet fluid installations.
Understanding principles of turbomachinery is the first step we must take to the machines design.
With some basic assumptions we can understand the operation of turbomachinery, so this video will be dedicated to explain by a simple way Euler's theorem of turbomachinery.
First of all, imagine the blade of a turbomachinery. Have you done it? Excelent, there it is:
Pointed with number 1 is the input of the blade, and pointed with number 2 is the output of the blade.
Now we are going to draw the path that would follow a fluid particle whatever.
As many forces in physics we are able to split those two paths (which are absolutes velocities) in a tangencial and a radial one.Currently, and with second's Newton law of motion help, we are able to calculate the generated torque using this simple equation.This equation is known as EULER'S TURBOMACHINE EQUATION, and is one of the most important equation in turbomachinery's world.
But, we know that the rotor of the turbomachine is rotating with an omega (w) velocity. So that, if we consider this detail in the previous equation, we will transform the torque into a power.
The term omega plus r, is called drift velocity.
If the power term is positive, it is because we are talking about a compressor, in which fluid takes energy from the turbomachine. And, if power term is negative it is because the fluid is giving energy to the rotor, so, it is a turbine.
The power of the turbomachine is related with hydraulic height throught the next equation:
In order to introduce velocity triangles concept, it is important to undesrstand the relative velocity concept. Imagine you are one of the billion of fluid particles that are entering in a simple turbomachine. You (the particle) have a velocity (the absolut velocity v), but the rotor has ones too, u. Now it is easy to realize the relative velocity; relative velocity is which you (the particle) feel regarding rotor's ones.
Now that it is clear the relative velocity concept we are able to introduce triangles of velocity, so there it is a simple example: the angle between the absolute velocity and velocity of the rotor is called alpha, and the angle between rotor's velocity and relative velocity is beta.
If in a pump the fluid enters without centrifuged prerotation the angle alpha is 90º, so it is easy to see that there wouldn't be a V1Ɵ component of velocity, and the hydraulic height would be simplified by the next way:
In the case of a turbomachine without output rotation the fluid will exit without rotation energy (like the case os most of turbines), so V2Ɵ is zero. The hydraulic hegiht would be simplified by the next way:
With these simple concepts you would have to be able to face on easy-medium level problems of turbomachinery.
We wish you have enjoyed the video, and that it has been helpful to you to have more curiosity about turbomachinery world.