When a person gets stuck in the aorta and pulls out the weapon blood comes literally flying out. Has it ever been measured how fast? Or does it depend on different arteries how they are measured?

"stuck"=stabbed

You could probably use fluid dynamics, pressure, and flow rates to figure this out. It would also depend on the size of the injury.

This diagram might help

I think the relevant equations are Bernoulli's and volumetric flow rate, but I'll leave that up to someone else to clarify

I'm not a scientist but i've dealt with some leaky stuff before. I think it all comes down to (blood) pressure and wound size, and to a lesser extent, wound shape.