To give a concrete example, supposed you had water at 2 bar coming out of a 3 mm circular nozzle, hitting a wall 3 m away. What would be the pressure on the wall from the water?
I think you would need to work out the area of the water hitting the wall first.
This is a mixed of several complexed problems of nozzle flow, jet flow, and slamming. Your conditions are probably not sufficient to formulate a complete solution without assumptions. But your suggestion "to work out the area of the water hitting the wall first" is actually the right start.
Let assume the emitting velocity at the nozzle ($x=0$) is $u_0$, so the momentum at the cut is $J=\rho\pi r^2u_0^2$. Note that the pressure at the edge of the nozzle is atmospheric pressure (not 2 bars). At the distance $x\rightarrow\infty$ from the mouth, the velocity distribution can be expressed in a similarity solution $u(y/x)=u_{max}/\cosh^2(f(y/x))$, with the $u_{max}$ the maximum velocity at the center of the cut and can be stated as $$u_{max}=(\frac{2J^2}{32\rho^2\nu})^{1/3}x^{-1/3}$$ Ref. Boundary Layer Theory-Schlichting and Fluid Mechanics-KUNDU.
Is this velocity you are looking for?
Then for the pressure, by neglecting the tangential component of the jet flow, the slamming pressure on the wall can be estimated as $1/2\rho C_su^2$, with $C_s\approx5.15$ from DNV-RP-C205.
