 Solution

Choose a control volume containing the small impingement region, with an inlet section across the incident jet and an outlet annulus across the conical sheet. The remaining boundary follows free surfaces and the wetted cone. Subtract atmospheric pressure and neglect gravity. Bernoulli's equation gives the same speed $U$ in the outgoing sheet as in the incoming jet, and its total volume flux is $AU$.

The incoming axial momentum rate is $\rho A{U}^2$. The outgoing velocity makes angle $\alpha$ with the cone axis, so its axial momentum rate is $\rho A{U}^2\cos \alpha$; transverse components cancel by axisymmetry. The integral momentum equation says that the cone's axial force on the water is their difference, $-\rho A{U}^2(1-\cos \alpha )$. By equal and opposite reaction, the jet's force on the cone is along the incident jet, with magnitudeThe outlet control surface is across the sheet, not along it, so its entire outgoing volume flux is counted.