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I'm trying to design a system that requires relatively high pressure (for spraying) however, I do not want to invest money in pumps, piping, gear etc. I'd rather try find a way to figure out a combination of criteria before I do this.

For this, I'm assuming that the flow regime is laminar. I have found an equation that I think may give me what I need, however I am unsure how I can apply it in this situation.

Hagen-Poiseuille equation:

Flow rate = πr4(P−P

_{0})/8ηl

where r is the radius of the pipe or tube, P

_{0}is the fluid pressure at one end of the pipe, P is the fluid pressure at the other end of the pipe, η is the fluid's viscosity, and l is the length of the pipe or tube.

I am unsure what pressure I should set the input (pump end) of the equation, P

_{0}?

Any help would be appreciated, thanks.