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Formula's and other Scientific Stuff

To Calculate the Net Energy in Small Hydro Applications

An easy formula for figuring the net energy in a falling stream of water is the head multiplied by volume in usgpm divided by 3960 = horsepower multiplied by .746 (convert hp to kW) and then multiplied by 60% ( turbine, generator and waterline losses etc). e.g. (200 feet head times 300 usgpm = 60,000 divided by 3960 = 15.15 hp multiplied by .746 = 11.3 gross kW multiplied by 60% efficiency = 6.78 net kW.

Losses are attributed to 80% turbine efficiency,  85% generator efficiency, and 10% friction losses in the penstock. (e.g.  .8 x .85 x .9 = 61.2%)

The same formula expressed in a metric equivalent would be Flow (Q expressed in Liters/sec) x H (expressed as Head in Meters) x net losses (factor of 6,   {60% efficiency},  depending upon exact losses)
e.g.    .1 m3 (100 L/s) x 10 M x 6 = 6 kW Net

To Calculate the water flow in CFS over a Suppressed Weir

To calculate the discharge flow of water over a suppressed weir, the following formula is a good approximation.
3.33 x W (width in feet) x D 3 (depth in feet), and Depth  is expressed as the square root of D to the third power.
                                               2                           (depth is cubed first and then the square root is taken)

e.g. 3.33 x 8 feet wide x 2 feet discharge over weir = 3.33 x 8 x 2.828 = 75.38 CFS   or 2nd e.g.

3.33 x 6 feet wide x 8 inches overflow = 3.33 x 6 x .64952 (square root of .75 x.75 x .75) = 12.97 CFS

Note: The water level must be measured a good 3-4 feet before the discharge weir, and there should be a clear drop of the water into a lower pool of water to be fairly accurate.

Rules Relative to the Circle

To find Circumference: Multiply diameter by 3.1416, or divide diameter by 0.3183

To Find Diameter: Multiply circumference by 0.3183, or divide circumference by 3.1416

To Find Radius: Divide diameter by 2, or multiply circumference by 0.15915, or divide circumference by 6.23318

To Find Area: Multiply circumference by 1/4 of the diameter, or multiply the square of the diameter by 0.07958, or multiply the square of 1/2 diameter (radius) by 3.1416

To Find Surface of a Sphere: Multiply the diameter by the circumference, or multiply the square of the diameter by 3.1416, or multiply 4 times the square of radius by 3.1416

To find the Volume of a Sphere:  4/3 pi r3  e.g.  A four foot balloon= 4 x 3.1415927 x 2 x 2 x 2 = 33.51 cubic ft

To Find the Curvature of the Earth: Take the radius of the earth squared, plus the distance you are measuring
squared, and take the square root of that value minus the radius of the earth.  ( square root of R 2 + D 2 minus radius.) For an example, suppose you wish to know what the curvature of the earth is 100 kilometers distant, expressed in differential altitude. The differential altitude is then:  the radius of the earth is half the diameter (measured from the center of the earth to the surface) = 6,378 km squared + 100 km squared= the square root of  this value minus the radius  e.g.  6,378 x 6,378 =40,678,884 + 100 x 100 = 10,000     (40,678,884 + 10,000 =40,688,888) The square root of this value is 6,378.7838 - 6,378 (the radius of the earth ) = .7838 km.  This is 783.8 meters of differential altitude. That is to say that at 100 km distant, you should be able to see a light on the horizon that is on a tower or a hill 784 meters high.  Using this same formula, theoretically, you should be able to see Mt. Everest, from over 200 miles away. Or, on a flat prairie, a 2 km distance has 30 cm of differential altitude due to the curvature of the earth. A little over a foot in every 2 miles. The earth is not flat.

Metric Conversion Tables
Approximate Conversions to Metric and Imperial Measures

When you know                          Multiply by                          To Find                          Symbol

                            Imperial                                 Length                   Metric

                             Inches                                       2.54                                  centimeters                       cm
                             Feet                                          0.30                                   Meters                             m
                             Yards                                        0.91                                   Meters                             m
                             Miles                                        1.61                                   Kilometers                       km
                            Metric                                      Length                        Imperial

                            centimeters                                .39216                                Inches
                            Meters                                       3.33333                              Feet
                            Meters                                       1.099                                  Yards
                            Kilometers                                 .62112                                Miles


                  Square Inches                         6.45                             Square Centimeters                  cm2
                           Square Feet                            0.09                              Square Meters                         m2
                           Square Yards                          0.84                              Square Meters                         m2
                           Square Miles                          2.59                              Square Kilometers                   km2


                Ounces (avoir.)                        28.35                          Grams                                          g
                        Ounces (troy)                           31.10                          Grams                                          g
                        Pounds                                       0.45                           Kilograms                                   kg
                        Short Tons (2000 lbs.)               0.91                          Tones                                         t


                        Fluid Ounces                          28.41                          Milliliters                                       ml
                        Pints                                         0.57                           Liters                                            l
                        Quarts                                      1.14                           Liters                                            l
                        Gallons                                     4.55                           Liters                                            l
                        Cubic Feet                               0.03                           Cubic Meters                               m3
                        Cubic Yards                             0.76                           Cubic Meters                               m3


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