Water column shape

Suppose a water pipe is sprayed vertically downward at a constant flow rate. So what's the shape of the water column? The air resistance is not considered and the interaction between the water molecules is assumed to be negligible.

The shape of the water column does not change over time. Thus, from the exit to the water column at any point, the included flow shape of the volume unchanged. The flow rate at the outlet of the water pipe is represented by $q$, and a cross section is taken. If the distance between the cross section and the outlet is $x$, then there are: $Av =q$. Where $a$ represents the cross-sectional area, $v $ represents the water flow rate, $v _0$ for the initial velocity. According to the Law of Mechanical energy conservation, $\frac 12V_0^2+GX=\FRAC12 v^2$. Thus, $A =\frac q{\sqrt {v_0^2+2gx}}$

Water column shape