FAN laws, RPM, REYNOLD's NUMBER ALL CONFUSING
 

Hi everyone, please am new to using forums help but I need help seriously, I only don't know if I will get it here.
I am an Agricultural student writing his final year project on tree air-assisted crop sprayer, am working on a component part just as my other mates, am working on the air blast mechanism which is a fan which is going to have a duct which other part will be mounted on.
I thought it will be kind of easy working with those FAN LAWS but it looks like it not applicable or It is just not working for my own case, working from the reynolds number is large thereby making my RPM too to be unnecessarily large, 16720 rpm!!! Also the torque and the power too is not right making my shaft diameter to even be larger than the size of my cylindrical duct.
I know am missing it but I don't know where, those material have consulted couldn't provide me with the answers I needed.
Will appreciate anyone with any info that can be of help.
Am working on a duct of 1 m DIA
Need to develop a fan that can produce air that can reach a distance of 18 m
Calculating the effective length of the duct I got it to be 2.53 m
The inlet of the duct will be 1 m DIA but the outlet will be semi-circular, giving the outlet a rectangular view from the plan, which gives a lenght of 1 m and assumption of the breadth to be 0.4 m was made.
Thanks

Can anyone having the mathematically solved example problem for navier stokes equation , to find Pressure and velocity at specific time. IF so please post me immediately and also Stream vorticity approach to find pressure and velocity.

Regards
K.Rajashekaran