Calculating pressure needed in a misting system.

[X1Y1Z1]

Not a homework problem, personal project.

High all, this is my first post. I am seeking information on how to calculate the pressure needed in a single pipe, closed at its end. The pipe will be used in a misting system for aeroponics [veggies, not cannabis! :-) ].

I am assuming a fixed radius for the main pipe, and misting nozzles with a radius of about half that (however, the total flow will be restricted heavily by the porous exits of each valve). Currently, my misting pipe will have two valves, evenly separated from the open and closed ends of the pipe and from each other.

The pipe will run parallel with the ground. Valves are attached to the top of the pipe, facing upward.

My question is how to go about roughly calculating the total pressure required for causing the valves to mist, and the pressure drop across each valve. I am assuming laminar flow, and that friction and gravity effects are mostly negligible (I will be multiplying the required pressure by some factor and selecting a pump based on this).

 

[aiwarrior]

Take a look at the Bernoulli equation. The Bernoulli principle states that the sum of static and dynamic pressure is constant for an incompressible non viscid fluid. Static pressure is about the pressure that the fluid would exhibit at rest. On the other hand dynamic pressure relates to the speed of the fluid.

The concepts you should learn about are:


So what you want is to increase the speed of the fluid by decreasing the pipe (valve) section area. Because the static and the dynamic pressure is constant if you increase the speed the pressure decreases. If the water pressure decreases below the vapor pressure point it will turn into vapor, which makes the misting effect that you want.

The concepts you should look are:
http://en.wikipedia.org/wiki/Bernoulli%27s_principle
http://en.wikipedia.org/wiki/Vapor_pressure#Boiling_point_of_water_in_nature

For more advanced concepts:

There is also a point which is that the assumption of an inviscid fluid might not hold for really small orifices since the boundary layer might have to be accounted for, making the calculations a bit harder, even though i doubt it would make significant problem.
Also if the orifice is opened at high angles, say more than 10 angular degrees, there might be separation the can cause the water not to go out evenly.

The concepts for this are:
Viscosity
Reynolds number
Stall/flow separation
Boundary Layer


Hope that helps a bit