Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 75 / 3 / a / Solution

For steady nonzero flux, $Aw=Q$, so $A=Q/w$. Substitution in the slender viscous thread force balance givesIf $f=w_z/w$, thenHence $\boxed{\frac{1}{2}(w_z/w{)}^2=U/w+c}$. This argument does not divide by $w_z$, so it also applies at turning points of the axial velocity. The symbol $U$ here has dimensions inverse length-time; it is not itself a speed.