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The RW Physics of the Decantur of Endless Water
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<blockquote data-quote="tomBitonti" data-source="post: 1639088" data-attributes="member: 13107"><p>Here are my rough calculations:</p><p></p><p>The physics of an jug of endless water;</p><p></p><p>The following works out the momentum transfer</p><p>from a jug of endless water assuming an orifice</p><p>1 1/2 inches in diameter and flow rates of one,</p><p>five, or thirty gallons per round.</p><p></p><p>The following use pounds as mass.</p><p></p><p>I use momentum transfer, assuming that the momentum of the</p><p>water expelled by the jug must be balanced by a gain of</p><p>momentum in the jug (or the holder of the jug). I also</p><p>assume that the water expelled from the jug need not pay</p><p>for the effective momentum gain because it is expelled in</p><p>the jug's frame of reference.</p><p></p><p>One pint weigh 1 pound (Remember, "A pint a pound the world around.")</p><p>One gallon has 8 pints, weighing 8 pounds.</p><p></p><p>One round has 6 seconds.</p><p></p><p>So:</p><p> One gallon / round gives</p><p> 8 pounds / 6 seconds == 1 1/3 pounds / second</p><p> Five gallons / round gives</p><p> 40 pounds / 6 seconds == 6 2/3 pounds / second</p><p> Thirty gallons / round gives</p><p> 240 pounds / 6 seconds == 40 pounds / second</p><p></p><p>Each pound of water carries momentum according to its velocity out of</p><p>the jug.</p><p></p><p>Working from: </p><p></p><p> 1 lb == 454 gm</p><p> 1 cu in == 2.54 ^ 3 cc</p><p></p><p>So, with 16.39 cc / cu in</p><p></p><p> Water Mass Water Volume</p><p> 1 lb 27.7 cu in</p><p> 1.33 lbs 36.8 cu in</p><p> 6.67 lbs 185 cu in</p><p> 40.0 lbs 1110 cu in</p><p></p><p>(Alternatively, water weighs about 62 pounds / cu ft,</p><p>which gives 27.9 cu in for one pound.)</p><p></p><p>A circle 1.5 inches across has 1.77 sq in.</p><p></p><p>For 27.7 cu in of water to flow through 1.77 sq in in one second</p><p>the water must flow at 15.6 in / sec, or 0.89 mi / hour.</p><p></p><p>For 36.8 cu in of water to flow through 1.77 sq in in one second</p><p>the water must flow at 20.8 in / sec, or 2.4 mi / hour.</p><p></p><p>For 185 cu in of water to flow through 1.77 sq in in one second</p><p>the water must flow at 105 in / sec, or 6.0 mi / hour.</p><p></p><p>For 1110 cu in of water to flow through 1.77 sq in in one second</p><p>the water must flow at 627 in / sec, or 36 mi / hour.</p><p></p><p>Momentum transfer is at the rates:</p><p></p><p>One gallon / round:</p><p> 1 1/3 pounds / second * 0.89 mi / hour ==</p><p> 1.2 pound miles / hour</p><p></p><p> 200 lbs @ 0.000275 g</p><p> 100 lbs @ 0.00055 g</p><p> 50 lbs @ 0.0011 g</p><p> 5 lbs @ 0.011 g</p><p></p><p>Five gallons / round:</p><p> 6 2/3 pounds / second * 2.4 mi / hour </p><p> 16 pound miles / hour</p><p></p><p> 200 lbs @ 0.0037 g</p><p> 100 lbs @ 0.0073 g</p><p> 50 lbs @ 0.015 g</p><p> 5 lbs @ 0.15 g</p><p> </p><p>Thirty gallons / round:</p><p> 40 pounds / second * 36 mi / hour </p><p> 1440 pound miles / hour</p><p></p><p> 200 lbs @ 0.33 g</p><p> 100 lbs @ 0.66 g</p><p> 50 lbs @ 1.32 g</p><p> 5 lbs @ 13.2 g</p><p></p><p>These values vary inversely to the square of the radius, that is,</p><p>doubling the radius divides the values by four, while halving the</p><p>radius multiplies the values by four.</p><p></p><p>For example, a 5 pound jug with a 1/2 inch orifice jetting 30 pounds</p><p>of water per round would be subject to 13.2 * 9 or about 120 g's of</p><p>acceleration.</p><p></p><p>Thx,</p><p></p><p>Tom Bitonti</p></blockquote><p></p>
[QUOTE="tomBitonti, post: 1639088, member: 13107"] Here are my rough calculations: The physics of an jug of endless water; The following works out the momentum transfer from a jug of endless water assuming an orifice 1 1/2 inches in diameter and flow rates of one, five, or thirty gallons per round. The following use pounds as mass. I use momentum transfer, assuming that the momentum of the water expelled by the jug must be balanced by a gain of momentum in the jug (or the holder of the jug). I also assume that the water expelled from the jug need not pay for the effective momentum gain because it is expelled in the jug's frame of reference. One pint weigh 1 pound (Remember, "A pint a pound the world around.") One gallon has 8 pints, weighing 8 pounds. One round has 6 seconds. So: One gallon / round gives 8 pounds / 6 seconds == 1 1/3 pounds / second Five gallons / round gives 40 pounds / 6 seconds == 6 2/3 pounds / second Thirty gallons / round gives 240 pounds / 6 seconds == 40 pounds / second Each pound of water carries momentum according to its velocity out of the jug. Working from: 1 lb == 454 gm 1 cu in == 2.54 ^ 3 cc So, with 16.39 cc / cu in Water Mass Water Volume 1 lb 27.7 cu in 1.33 lbs 36.8 cu in 6.67 lbs 185 cu in 40.0 lbs 1110 cu in (Alternatively, water weighs about 62 pounds / cu ft, which gives 27.9 cu in for one pound.) A circle 1.5 inches across has 1.77 sq in. For 27.7 cu in of water to flow through 1.77 sq in in one second the water must flow at 15.6 in / sec, or 0.89 mi / hour. For 36.8 cu in of water to flow through 1.77 sq in in one second the water must flow at 20.8 in / sec, or 2.4 mi / hour. For 185 cu in of water to flow through 1.77 sq in in one second the water must flow at 105 in / sec, or 6.0 mi / hour. For 1110 cu in of water to flow through 1.77 sq in in one second the water must flow at 627 in / sec, or 36 mi / hour. Momentum transfer is at the rates: One gallon / round: 1 1/3 pounds / second * 0.89 mi / hour == 1.2 pound miles / hour 200 lbs @ 0.000275 g 100 lbs @ 0.00055 g 50 lbs @ 0.0011 g 5 lbs @ 0.011 g Five gallons / round: 6 2/3 pounds / second * 2.4 mi / hour 16 pound miles / hour 200 lbs @ 0.0037 g 100 lbs @ 0.0073 g 50 lbs @ 0.015 g 5 lbs @ 0.15 g Thirty gallons / round: 40 pounds / second * 36 mi / hour 1440 pound miles / hour 200 lbs @ 0.33 g 100 lbs @ 0.66 g 50 lbs @ 1.32 g 5 lbs @ 13.2 g These values vary inversely to the square of the radius, that is, doubling the radius divides the values by four, while halving the radius multiplies the values by four. For example, a 5 pound jug with a 1/2 inch orifice jetting 30 pounds of water per round would be subject to 13.2 * 9 or about 120 g's of acceleration. Thx, Tom Bitonti [/QUOTE]
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