Calculating output force of wind funnel

In summary: This is not rocket science. But, I am guessing that, unless I am missing something, the people doing this type of optimization are not just going to tell me the optimum diameter for the wind turbine, but they will also tell me the pressure and backpressure that is needed to achieve that optimal diameter. I am guessing that these are numbers that are not easily found.
  • #1
ed shaw
2
2
Part one:
Supposed: A wind funnel. Circular Input radius = 600" Windspeed = 24 ft/sec
Air weight = 2 lbs/yd3 Circular Output radius = 60" Disregard = backpressure.
1 HP = 560 ft lb/ sec
Solve for = (1) Theoretical Wind speed at output (2) HP at output.
Part two:
Backpressure will limit air speed at output and restrict input. Using same input size as above, determine the smallest output diameter that would still allow available wind unrestricted flow through funnel.
Solve for = Output diameter.
Solve for = How did you determine Pressure and Back Pressure?

Thank you.
Ed Shaw
 
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what do you think about it yourself? any clues?
 
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My drawing of this funnel shows a 12" deep flat collar. When R=600" the volume of the first 12" of the funnel is 13,564,000 in3 or 290 cu yds. Weight of air in that volume is 600 lbs of air. At about 15 mph (2 feet per second) that mass of air generates 23 HP as it moves through the funnel, at the head.
Now, as the funnel narrows, the intake air speed remaining the same, the air inside will begin to gradually speed up. Ignoring back pressure, the same volume and weight of
air must exit the small end of the funnel as is entering the large end, over the same time period. Now, there is a little mistake in the way I stated the problem here. I was trying to keep things simple, but, overlooked that air volume is a square of the radius (V=pi x r2 x Length) of a cylinder. So, my small end of 1/10 radius of the large end does not translate into 1/10 of the volume over that one foot length. So that was a mistake on my part. But, I am guessing that the air speed at the small end is proportional to the respective volumes. If the airspeed going in is 15mph, the airspeed going out of 1/10 sized (in volume) outlet should be 150 mph. I could sit down and figure the volumes.

Now, at a certain point, the pressure of the air moving in is going to be equalized by the backpressure of the air being squeezed. Just like water being poured into a funnel, the air will overflow. Unless I have made an oversight in the first part of the problem, this is where things begin to get tricky for me. The solution to the optimal funnel design is going to depend, I think, on the nature of the medium, in this case, air.
It should be clear to someone working this problem that what I am looking for is the diameter to fit a wind turbine, to produce work.
 
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What is the purpose of calculating the output force of a wind funnel?

The output force of a wind funnel is calculated to determine the potential energy that can be harnessed from the wind. This information is important for designing and optimizing wind turbines and other renewable energy technologies.

How is the output force of a wind funnel calculated?

The output force of a wind funnel is calculated by multiplying the density of air, the velocity of wind, the cross-sectional area of the funnel, and the coefficient of lift. This formula is known as the Betz limit and is used to estimate the maximum possible power output of a wind turbine.

What factors affect the output force of a wind funnel?

The output force of a wind funnel is affected by several factors including wind speed, air density, funnel size and shape, and the angle of the funnel relative to the wind direction. These factors can change the amount of wind energy that can be harnessed and should be considered in the calculation.

Can the output force of a wind funnel be increased?

Yes, the output force of a wind funnel can be increased by increasing the wind speed, increasing the funnel size, and optimizing the shape and angle of the funnel. However, there is a limit to how much the output force can be increased, known as the Betz limit.

How accurate is the calculation of output force of a wind funnel?

The calculation of output force of a wind funnel is an estimate based on various assumptions and simplifications. Therefore, the accuracy of the calculation may vary depending on the specific conditions and factors involved. It is important to use accurate and up-to-date data and to consider any limitations of the calculation method.

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