# Question on fluid jet profile in the limit of zero surface tension

While reading on the Plateau Rayleigh instability of fluid jets, the following thought came to my mind: suppose we have a fluid jet with zero cohesion forces (and therefore zero surface tension) falling under the influence of gravity. My understanding is that since fluid parcels with different vertical coordinate move at different speeds, and there are no intermolecular forces, than the whole jet cannot exist at all! Just think of the molecoles as tiny stones dropped from an orifice at different times - since they all experience uniform acceleration they always keep the same relative speed and therefore get away from each other.

So, in my understanding, surface tension is what keeps the liquid jet a unity and is the cause for it getting narrowed as it is accelerated by gravity. However, after reading the MIT lecture notes on fluid jets that are linked to in the wikipedia article on Plateau-Rayleigh instability, I saw the profile $$r(z)$$ of the jet depends on the Weber number, which is inversely proportional to surface tension. Therefore, in the limit of zero surface tension and infinite Weber number, I thought one should get uniform cross section of the jet. However, this conclusion is wrong according to a formula from the lecture notes, which states:

$$\frac{r}{a} = (1+\frac{2gz}{U_0^2})^{-1/4}.$$

So my question is how to reconcile this formula with the argument I gave before? Is there a fallacy in my argument?