fan laws, angle of climb, angle of attack, reynolds number a

[paulriz43]

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

[rjsa]

Mind to post a pointer to said FAN LAWS and you working hypothesis?

[paulriz43]

Thanks a lot,
Talking about the one which says for constant density and diameters,
CFM I directly proportional to RPM,
The square of CFM is directly proportional to the total pressure Pt, and that
The cube of CFM is directly proportional to the shaft power of the fan.
Workings from continuity equations shows that;
A1 = 0.7855 square meter
A2 = o.4 square meter
V1 = 9.4233 meter/sec
V2 = 18.505 meter/sec and
Discharge Q = 7.402 cubic meter/sec which gives 15,682 cubic feet/min (CFM), which gives a RPM by the facts of proportionality, that is practically too big a value to work with. And after trying to calculate all the loses present in the duct to the total pressure, gives 330.5785 Pa which also by that proportionality fact makes the RPM too small a value to work with too. Maybeam mixing something up or missing something that I don't know, please anyone with information that can shed a light will be highly appreciated.
And thanks again for replying

[Greg Locock]

This the second query I've seen recently about the exhaust pattern/spread from a duct. The conesnus elsewhere (not student friendly) is that you'd need to do an experiment of some form. So, how are you predicting the 18m number? what pressure/flow do you need at that distance? I assume this is on the centreline of the duct.

[rjsa]

Greg has a point, but to see what are you dealing with, which fan are you using for extrapolation? What are it's geometric and perfromance numbers?

[Blanchimont]

Is your project similar to to this?

[Greg Locock]

ah, if the 18m is the length of the distribution tube then OK you might be able to estimate it using conventional formulae. I'd assumed open air. More data required.

[paulriz43]

Thanks greg, rjsa and Blanchimont,
Blanchmont, the differencies are that this one is a boom spray with no direct air assisting mechanism, the one am working on will spray up to the trees wich Is different to the one here which sprays the protection chemicals downward.
I am not actually sure if working towards a certain pressure is the problem am having, from the start of the project assumption was made to have a platation which the tree spacing is 9 m and the maximum height of all trees are also 9 m, so my project is now a sprayer that looks like the one that Blanchimont showed here, but will be spraying up to the trees, having my sprayer motor at a distance 4.5 m to each tree.
So working with Newton' Law of motion, that's how I came by the 18 m distance, which is the point at which the air coming from the fan must reach without causing an overlap or repetition of spray at either sides of the tree.
So I do not know, if I should have started my workings with pressure and not distance but from what ihave been doing, I don't have a pressure am working with now, only trying to get other values and parameters through what I have earlier stated.
Thanks for your replies

[rjsa]

We have real little to go on here. If you want someone to check your numbers please post the whole thing...

Now one thing for sure, pressure in and out the system will always be the same, 1bar. The moment air leaves the last nozle it's pressure is equalized qith the environment. You will then have increased speed.

Now with speed you can use newton to calculate what intial speed you need to have material reaching all the way up.