# Euler's Turbomachinery Formula

I would like to know why exactly is only tangential velocity considered in Euler's turbomachinery formula, specifically for torque. I understand that you can use rotational velocity to find torque but why is this not the case for this circumstance?

More specifically, in this case provided by my textbook, what does it mean when the position vector r is purely radial so only the tangential velocity component counts? Thank you

• If you're going to reproduce a bit of the textbook like this, you should cite it, The typographic style looks like something published by Pearson, perhaps Fluid mechanics by Douglas et al.. Oct 28 '21 at 17:17
• May I ask what book is this?
– Algo
Oct 29 '21 at 4:35
• Fluid Mechanics 7th Edition by Frank M. White Nov 1 '21 at 19:29

"The position vector is purely radial" means that the position vector is aligned along the direction from the origin (or rather, the $$z$$ axis) to the location of interest.