= Solution
For steady inviscid <incompressible flow> subject to a conservative body force, <Bernoulli's theorem> states that $p/\rho+u^2/2+gz$ is constant along a streamline. The same constant applies across streamlines only with an additional condition, such as an irrotational connected flow with the same upstream head.
Neglect gravity and let the film's free-surface pressure be atmospheric. Its radial speed is then $v$ in the ideal model. <Conservation of mass> equates the incoming flux $\pi r_1^2v$ to $2\pi rt(r)v$, so
$$
\boxed{t(r)=\frac{r_1^2}{2r},\qquad t(r_1)=\frac{r_1}{2}.}
$$
The latter value already warns that the thin-film approximation is poor near impact; the radial expression is most useful beyond that region. The incoming vertical <momentum flux> gives downward force $F_m=\rho\pi r_1^2v^2$ when the outgoing flow is horizontal.
In the stipulated stagnant-rear-layer idealization, the excess rear pressure is the stagnation value $\rho v^2/2$. Its upward force is $\rho v^2\pi r_2^2/2$. Thus, with downward positive and ignoring the water's weight,
$$
F=\rho\pi v^2(r_1^2-r_2^2/2),\qquad\boxed{F=0\text{ at }r_2=\sqrt2r_1.}
$$
For a large plate, the radial-film volume is approximately
$$
\int_{r_1}^{r_2}2\pi rt(r)\,dr=\pi r_1^2(r_2-r_1)\simeq\pi r_1^2r_2.
$$
Its weight therefore changes the model to
$$
F\simeq\rho\pi\left[r_1^2v^2+gr_1^2r_2-\frac12v^2r_2^2\right].
$$
Cancellation occurs near
$$
r_{2,*}=\frac{gr_1^2}{v^2}+\sqrt{\frac{g^2r_1^4}{v^4}+2r_1^2}
\simeq\boxed{\frac{2gr_1^2}{v^2}}\quad(v^2\ll gr_1).
$$
\b[The printed claim of negligible force for every radius above this scale does not follow from this model.] Near the cancellation radius the force is small; for substantially larger radii the quadratic upward-pressure term dominates. The original PDF, not just its transcription, uses that inequality and wording. Moreover, the rear layer's mass and detailed gravity-dependent pressure field are unspecified. The calculation establishes a cancellation scale under the elementary stated pressure approximation, rather than a general large-radius zero-force theorem. A full free-surface flow model would be needed to extend it consistently.
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