To determine the Head in feet when the pressure in sq. in is known, multiply by 2.3
Friction of water in pipes increases as the square of the velocity.
Doubling the diameter of a pipe increases its capacity 4X.
Pipe is able to deliver water in gallons per min. equal to 0.0408 X the square of the diameter, X the velocity in ft. per minute.
CU. FT. in one foot elevation = R2 X 3.14159 X 12 ÷ 1728
Lbs. in one foot elevation = R2 X 3.14159 X 12 ÷ 1728 X 62.425
The weight of water in a length of pipe is obtained by multiplying the length in feet by the square of the diameter in inches X 0.34
By Tom Conlon CEO, Iron Man Windmill Co. LTD
The result of this formula is in Kw and is theoretical. It does not take into account efficiency losses which must be considered. The Betz factor must be considered and cannot be ignored. Betz can be described as wind seeing all wind energy devices as an imperfect wall - a resistance to the free movement of the wind. A portion of the wind will always move around a wind energy device rather than through it. This factor affects all wind energy devices of every type, including ducted or shrouded devices and is unavoidable. For calculation purposes, wind energy devices with ducts or shrouds assume an area equal to the area defined by the overall dimensions of the shroud or duct. 0.59 is the maximum amount of usable energy available for a wind energy device of perfect design. In the real world, all wind energy devices see losses greater than this. A multi-bladed water pumping windmill of very good design is able to operate with an overall system efficiency of about 30% in lower wind speeds. For comparison, the average modern automobile operates with an overall system efficiency of about 15%! Be sure to understand the efficiency notes below.
Gallons Per Minute x 8.33 (Lbs per Gallon) x Pumping Elevation (in Feet) x 0.0000226 = Kw
Note on the above! The result using this formula is the theoretical amount of energy required to do the work. It does not include mechanical losses, fluid resistance losses, electrical losses etc. The result from this formula will be considerably lower than the amount of energy actually required. Be sure to understand the efficiency notes below.
The modern water pumping windmill is a highly refined invention having made it's first appearance in 1854 and undergone significant improvement for 78 years, and has earned the right to claim a relatively high degree of mechanical efficiency. Let's take a closer look.
Here is a list of the losses that must be considered when designing or evaluating wind energy systems.
1.
Betz - It is an inescapable law of nature that whenever energy is converted from one form to another or is moved, there is loss. When there is movement of air and it comes up against an obstacle, such as a wall, it does the obvious, it simply goes around it. Such is also true regarding all wind energy devices of every type. A wind energy device is not a true wall in that it does not cause all the wind coming into contact with it to go around it. It is in fact an imperfect wall that allows a portion of the wind to pass through it, giving up a portion of its energy in the process. In 1919, the German physicist Albert Betz showed that the MAXIMUM amount of energy that can be RECOVERED from wind is 59.3%. If a wind energy device is not able to convert the maximum amount of energy possible, it will either allow more wind to pass through the device unused, or will provide an excessive obstacle to the movement of wind causing an excess of wind to pass around the device unused. There is no avoiding this. Remember, Betz defines the MAXIMUM amount of energy obtainable with a PERFECT wind energy device! The actual amount recovered will always be less. Some windmills in the past have attempted to use shrouds or ducts to force more wind through a rotor and some have gone on to claim new heights of efficiency, only to have reality smack them in the face. In fact, the working area of the wind energy device is the area of the duct and wind energy device combined, so there is no real improvement, only the added expense and complications imposed by the duct or shroud.
2.
Resistance to the rotation of the wind wheel. If you have a well balanced disc mounted on good bearings and spin it, it will eventually stop spinning. If you place it in a vacuum and spin it, it will spin much longer! The reason there is less resistance to turning in a vacuum is that there is little air to cause aerodynamic friction. A wind energy device is no different. A wind energy device of excellent design works with an efficiency of about 60%. If you want to reduce the resistance to turning, you can reduce the surface area of the wind energy device. Unfortunately, your wind energy device will now allow more wind to pass through unused and the result is actually increased energy losses. You can reduce the amount of supporting structure in the wind wheel, certainly increasing efficiency. Unfortunately, it will also weaken the wind energy device causing failure in unacceptably light winds.
3.
Bearings - Yes, as good as bearings can be, there are still energy losses here that must be considered. Traditional windmill bearings were almost always made of Babbitt metal, which has a very long life, improves with age as journals become finely polished in use and are actually quite efficient. Babbitt is still the bearing material of choice used in the large percentage of internal combustion engines today, and for good reason. Ball and roller bearings have been used since they first became available in the last century, but early on, it was found that they simply do not have the lifespan as experienced with Babbitt bearings for reasons beyond the scope of this writing. Since ball and roller bearings are being used in almost all new windmill designs today, we will discuss the efficiency of these bearings. A good ball or roller bearing that is accurately mounted and properly lubricated should be 95% to 97% efficient
per bearing! The more bearings, the lower the efficiency. A windmill with 2 bearings will have about half the bearing loss as a windmill with 4 bearings. Fewer bearings = lower cost - increased performance - reduced maintenance = good design.
4.
Gears - of excellent quality with an accurate tooth design and very fine finish operate with an efficiency of about 95% per set of gears. Increased loads increase the losses. Like bearings, fewer gears = lower cost - increased performance - reduced maintenance = good design. The use of gears is required to provide the leverage required to allow pumping from deep wells.
5.
Other Power Transmission related energy losses - such as pump rod guides, arm bearings, fluid resistance on the pump rod contribute to more losses. These losses vary significantly from design to design and can run from about 5% in a good system to 20% in a poor system.
6.
Pumps - are always a significant concern regarding efficiency. The traditional windmill pump made of brass or bronze tubing with a highly polished bore and uses treated leather seals. They are highly dependable and have a long life. They are also suffer from an overall efficiency of about 50%! Still, due to their other desirable qualities, they continue to be the most widely used of any pump type with windmill pumping systems. Improved materials increases efficiency, but usually with a reduction of pump and seal life. For many years, Iron Man Windmill Co. has worked to minimize pump losses and improve performance and has achieved considerable success. Windmills using Iron Man Pumps are seeing an increase in pump performance of 50% for a total efficiency of 75%.
7.
Fluid Friction - The movement of water in pipes, through valves and around restrictions eats up energy. In an excellent system with smooth pipe of the proper size and the best check valve design, fluid efficiency can be quite high - 95% or so. Most windmill systems when pumping from deep wells, through long pipelines or at high speeds can have a much lower efficiency and a fluid efficiency in such systems can drop by as much as 50%, if the pipe used is of insufficient size.
8.
Electrical - early in the 1970's we did much work developing 3 bladed electric generating windmills. While such electric generating windmills can operate efficiently and do a very good job of providing electricity in strong winds, they provide little if any usable power in lower wind speeds, which are the most common wind speeds at most locations. With the electric generating windmill, the power of the wind is converted to mechanical energy. The mechanical energy is then converted to electrical energy. The electrical energy is then transmitted to a control panel and then either stored in batteries or connected to the utility power grid by processing the power generated by a synchronous inverter. If the power is to be used for pumping, the energy must then be converted or regulated into a usable form and then transmitted to the electric motor that operates the pump. Then the electric motor converts the electricity to back to mechanical energy. The mechanical energy is then used to operate a pump. Pumping water with an electric generating windmill is an expensive and highly inefficient effort that results in little water for the investment. While there have been many recent attempts at accomplishing this using modern electronics, such systems still fall far short of being practical.
Ok, now take the total of the losses described above and assuming a wind energy device of very good design with a standard pump, you will make an interesting discovery!
0.60 (wind wheel) x 0.95 (bearings) x 0.95 (gears) x 0.50 (pump) x .90 fluid and pump rod losses = mechanical system efficiency = 0.24 or 24%
The same windmill using an Iron Man Windmill Pump will see an efficiency of:
0.60 (wind wheel) x 0.95 (bearings) x 0.95 (gears) x 0.75 (pump)* x 0.90 fluid and pump rod losses = mechanical system efficiency = 0.37 or 37%
* The pump efficiency shown is obtained with Iron Man Windmill Pumps using our proprietary seals and valves.
For other makes of pumps, an efficiency of 0.50 or 50% should be used.
It is interesting to note, that most modern automobiles have an operating efficiency of about 15%!
