So here is the thing. The best way to calculate the pressure required to achieve a certain ends is by using the modified Bernoulli equation below:
\dfrac{p_1}{\rho g} + \dfrac{V_1^2}{2g} + z_1 = \dfrac{p_2}{\rho g} + \dfrac{V_2^2}{2g} + z_2 + h_{\ell}.
In this case, ##h_{\ell}## is the head loss and represents all the losses due to friction and valves and pipe bends and the like. ##p_2## is the exit pressure and is going to be equal to atmospheric pressure, and ##p_1## is going to be your "supply pressure" at some given reference point (either just after your pump or at some other known location in the system. The ##z## terms are heights of the two points to account for gravity.
So you are basically looking for a pressure required to meet your requirements. If you solve for that pressure drop (aka the supply gauge pressure, you get something like this:
p_1 - p_2 = \Delta p = \dfrac{1}{2}\rho\left(V_2^2-V_1^2\right) + \rho g \left(z_2 - z_1\right) + \rho g h_{\ell}.
The other thing is that you rarely know velocity, but flow rate, ##Q=VA## is pretty common to know, so you can replace those velocity terms with areas and ##Q##,
\Delta p = \dfrac{1}{2}\rho Q^2 \left[\left(\dfrac{1}{A_2}\right)^2-\left(\dfrac{1}{A_1}\right)^2\right] + \rho g \left(z_2 - z_1\right) + \rho g h_{\ell}.
And then finally, you actually do have a velocity requirement in that you want a specified ##V_2##, so go ahead and use ##Q=V_2 A_2## to get a final, useful equation,
\boxed{\Delta p = \dfrac{1}{2}\rho V_2^2 \left[1-\left(\dfrac{A_2}{A_1}\right)^2\right] + \rho g \left(z_2 - z_1\right) + \rho g h_{\ell}}.
So, that is the final equation you should be working with here (barring any algebra errors I may have made). You will notice that the pressure you need has several dependencies, all of which require information about changes from one point to another. In your first question, you only gave us one, so these terms are all at best zero and at worst (and in reality) have no defined value. What you need is some indication of the height change and area change between your source pressure (##p_1##) and your outlet. If you had those two things, you could get some sense of the pressure drop required if you assume ##h_{\ell}## is zero or negligible, and your later post seemed to indicate that you do have those values available (though I don't think you provided height). You have to be careful here, though, because ##h_{\ell}## is non-negligible in most cases and will probably be a fairly substantial portion of the pressure requirement here.
The final takeaway here is that you need ##A_2/A_1## and ##z_2-z_1## to get any semblance of an answer, and you really need to consider the ##h_{\ell}## term if you want a good answer. You need to have some way of measuring ##p_1## or providing it at a point, and the remainder of the terms need to take into account everything between that point and the nozzle. Usually that point is located downstream of a pump or at a spigot or other supply line. The ##h_{\ell}## term is actually the sum of many terms for bends and expansions and valves and the like, and you can look up the various forms in books and manuals and handbooks and such. They may all have their own dependencies on velocity, though, so the problem can get messy.
I will also mention that plugging the nozzle end to measure the pressure is not necessarily a valid way to do it. At best, that will give you a good estimate of your supply pressure provided there are no other outlets in the system and that you take height change into account. If there are other outlets, it isn't going to tell you much as far as I can tell.
