Power requirement to turn blade in free air

[aarothepharo]

Does anybody have any equations that predict the power required to turn an impeller in free air? I am building a wood impeller four blades flat in reference to rotation radiating from central hub. I need to predict the length of the blade to be able match a certain HP.

 

[Legolaz]

You may start with Kinetic energy (KE=1/2mv²) of the wind which would pass through the projected circular area of your blade.
Say area on the blade is A = π(D²-d²)/4

Flow rate of wind passing through that projection is Q = Av (m³/sec) & ρ = m'/Q.
Combining these equations will give you something like this:

KE rate = 1/2 ρQv² = 1/2 ρ(π(D²-d²)/4)v³ (Power J/s) This is the available energy rate that can be utilize at certain wind speed passing through an annulus.

You could also express ρ = P/R_airT, so you have something like
Power=1/2 (P/R_airT)(π(D²-d²)/4)v³
where: P- Atmospheric Pressure;
T -ambient temperature;
R-specific gas constant of air
v - wind speed

 

[OldEngr63]

You can find a lot of this in Marks Mechanical Engineering Handbook under Windmills.

 

[Baluncore]

I am building a wood impeller four blades flat in reference to rotation radiating from central hub.

So this is an impeller, not a propeller or turbine.
As the impeller rotates, air circulates from the inside to the outside.
The mass of air, m, in kg that moves must be accelerated to a velocity, v, in metres per second, sufficient to depart the impeller.
Energy is 0.5 * mass * v². Power is energy in joules per unit time in seconds.

 

[aarothepharo]

Baluncore. I'm building an impeller in a housing however I want to spin it in free air off of a 6.5 HP engine to test if it can spin fast enough without shattering.

 

[Baluncore]

I'm building an impeller in a housing however I want to spin it in free air off of a 6.5 HP engine to test if it can spin fast enough without shattering.

If the impeller is in a housing it will consume less power than if spinning in free air at the same RPM.
It is safer to test it in a housing because that housing may contain some of the splinters.
Do not test it without a housing capable of containing all the fragments.

 

[Legolaz]

If the impeller is in a housing it will consume less power than if spinning in free air at the same RPM.
It is safer to test it in a housing because that housing may contain some of the splinters.
Do not test it without a housing capable of containing all the fragments.

Sounds unsafe to me testing with very little knowledge about a rotating mechanism which could end up in a fatality and destruction both property and life.
I strongly recommend not to test at all.
Do not deal with things you are not well equipped and able to do. Invest more in knowledge first and education, other than doing testing, a "destructive testing" most probably, when it involves " i guess it will work".

 

[Legolaz]

Baluncore. I'm building an impeller in a housing however I want to spin it in free air off of a 6.5 HP engine to test if it can spin fast enough without shattering.

Your thread does not fit any more to the topic. I suggest you read and study Engineering Strength of Materials, specifically about "stress and/or fatigue" on a rotating disc or propeller.

 

[aarothepharo]

If the impeller is in a housing it will consume less power than if spinning in free air at the same RPM.
It is safer to test it in a housing because that housing may contain some of the splinters.
Do not test it without a housing capable of containing all the fragments.

I agree.

 

[aarothepharo]

Sounds unsafe to me testing with very little knowledge about a rotating mechanism which could end up in a fatality and destruction both property and life.
I strongly recommend not to test at all.
Do not deal with things you are not well equipped and able to do. Invest more in knowledge first and education, other than doing testing, a "destructive testing" most probably, when it involves " i guess it will work".

Legolaz: I am a Mechanical Engineer. I have found a lot of formulas and probably could use calculus but was wonder if anyone knew of a formula to prevent me from doing it.

Any test can be conducted safely and any test that can not be conducted safely should not be conducted. I abide by those rules.

 

[aarothepharo]

Your thread does not fit any more to the topic. I suggest you read and study Engineering Strength of Materials, specifically about "stress and/or fatigue" on a rotating disc or propeller.

Legolaz: I understand your concern and have already studied the design with a strength stand point. Thanks for the feed back.

 

[aarothepharo]

It looks like nobody has a formula for me so I will use calculus. Thanks for all the help everone

 

[aarothepharo]

Just in case anyone thinks it can't be done. This guy has been building them out of wood for years.
http://woodgears.ca/dust_collector/blower_build.html