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
                                                                                                                                  3

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
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                            Imperial                                 Length                   Metric

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

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

                  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
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   Mass

                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
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                                                         Volume

                        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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