How Do I Calculate RPM for a Propeller in a Uniform Water Flow?

[dioross]

hi to all!
Say i have a uniform flow of water of 1m/s.. if i put a propeller with known diameter and blade angle...what would be its RPM?...i want to design a flow meter...pls help me!..i need to have basic and approximate formulas on the blade parameters and its RPM..thanks!

Regards
dioross

 

[Gabe21]

assuming the blades are rectangular(the more curves in the blades the more complicated the calculations get) and you had singular movement water flow rate of 1 m/s. take the propeller speed(take the angle of your blade,lets say 45 degrees,and divide by 90. then multiply that by your water rate times 60. ((45 degrees)/90)=.5, (.5*1m/s(60))=30 m/min) divide it by the average blade radius circumference(lets say the beginning of the blade has a radius of .1m and the tip of the blade has a radius of .4m, so your average radius would be .25m. so the circumference would be .25*6.28=1.57m) and that will give you the propeller rpm.((30 m/min /1.57 m)=19.108 rpm.) Now this calculation assumes their will be no friction on the blade whatsoever, and that their is no counter rotation force in opposition of the propeller rotation force. your blade is probably wide at the base and narrows towards the tip with a concave shape, so this will speed up the propeller rpm by as much as 42%. it would be a whole lot easier to just calibrate your machine by recording blade rpms at known water velocities.

 

[rcgldr]

Normally blades are rated with a pitch. That is the distance they would travel through jello with each revolution if there was no compression of the jello. The prop blades are normrally twisted so the pitch (advance rate) is about the same along the radius.

If you know the prop pitch, say 15 inches, and it's speed, 1000 rpm, then it advances 15,000 inches or 1250 feet every minute, or 14.2 mph. This is asumming the prop is free wheeling, (no drag or thrust).

 

[dioross]

thanks for the reply..it really helped me a lot...do you have some basis or references about the calculations?...does the analysis of the propeller in air same as that when it is in water?...does the density of water affect the rpm of the prop?...

 

[dioross]

@Gabe21: the angle of prop in ur example is with respect to the plane of rotation?..why is it that it is divided by 90?..

 

[Gabe21]

you divide by 90 because u have to get your blade angle into a percent. if your blade angle was 5 degrees you would divide it by 90 and get .0556. this means 5.56% of the water flow speed is put into rotational speed of the propeller. assuming no friction or drag of course. think about it on a x,y grid. if you travel from the origin(90 degrees is vertical and 0 degrees is horizontal) at a 5 degree angle moving at a constant speed, then 5.56% of that speed is put into verticle motion and the other 94.44% is put into horizontal motion. the same concept applies to the propeller angle. however, the closer the propeller angle gets to a 90 degrees the less efficient it becomes due to friction.

 

[Gabe21]

and the air calculations would be the same, but i have to say if u r trying to build an airflow meter it would be a lot cheaper to just buy one. because air is so much less dense than water making your own meter would be very impractical. the one i use is very accurate and only set me back 120 bucks, and that was 3 years ago. so I am sure they are cheaper now.

 

[Gabe21]

what is the blade angle of your prop?

 

[Gabe21]

i was thinking about it and the calc for the prop speed is exponential not linear, so my first calc for the rotation speed of the blade is wrong. a 45 degree angle would yield a 1:1 ratio(water rate:prop speed) a 22.5 degree angle= 1:.5 ratio. 67.5 degree angle= 1:2. a 78.75 degree angle= 1:3. 0 degrees is parallel to water flow.

so in my first calc the prop rate should be 60 m/min

 

[dioross]

the angle of my prop is 15 degrees..how about the tip speed ratio TSR?..does it the same with ur formula?..i found this on the internet.. RPM = (60*V*TSR)/(pi*D)..