omg, no, the result is not correct, average velocity is of no interest to anyone here.and i did not correct your grammer, it is perfectly understandable at the moment.
furthermore, if the energy and power are as you suggest, then we can get more out by cascading n systems. this is obviously not true. do you know what this means?
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MATTM said "17.333 pounds per second times 12.68266 feet per second is equal to approximately 220 foot-pounds per second, which is also .4 horsepower."
I see what you are doing, and i'm trying to explain it to you without re-proving newton's laws, you evidently don't understand them.
calculate the kinetic energy: no, i'm not going to derive it for you, but i did in physics class...
- 33 pounds/second x (12.7 ft/sec)^2 x .5 = you figure this out and tell me what you get in imperial units, then compare to mks...
- 87 kg/s * 3.87m/s^2 x .5 = 58.99 watts.
- foot pounds/s = 298 watts.
answer this question: how much power does it take to lift 17.33 pounds of water 10 feet per second?
DEFFINITION: work is done then a force acts over a distance. one horse power is lifting 550 pounds one foot off the ground in one second
lifting 33000 pounds one foot off the ground in one minute
lifting 55 pounds of water 10 feet off the ground in one second,
do you see where this is going?
pushing a car down the road at 15 miles per hour. ~approx~
pushing a train at a few inches per second...~approx~
pounds is a unit of force, i ignored the kinetic energy still in the water, after it got lifted off the ground..
it's a squared function of speed , so we can ignore it for relatively slow moving objects.
OVERUNITY [10 feet, 220 out, 173.33 in], [40.3% at 100, 700 out, 1733 in], what do you get for 10,000 feet?
using you math,
ttf 10,000 feet is 24.99 seconds[i agree, this is elementary]
average speed is 400 feet/second [i agree, this is also elementary]
400 feet/second x 17.33 pounds/second is 6932 foot pound/sec or 12 horsepower
speed at bottom [800ft/sec conveniently always twice the average speed for acc.= constant and V_i = zero] x 17.33 pounds/sec is 24 horsepower.
power needed to lift 17.33 pounds of water per second to 10,000 feet: 173,300 foot pounds/sec or 315 horsepower!
your math results in a 3.8 % out using average speed, and 7.6 % out using peak speed
in fact, if we cascade one thousand of your ten foot drops, and drop 17.33 pounds of water out of an air plane... we get 2.2 million foot pounds out of the system, and we put 173 thousand in.
whereas if we dropped it all the way at the bottom we'd get 13.86 thousand foot pounds by your 'math'
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17. 333 gallons per second times 0.001818 horsepower is 0.031512 horsepower
Now this is for one foot displacement per pound without the effects of gravity. Let's factor in gravity... Using math we can figure the time necessary for the water to fall 10 feet by using the equation for the distance that the object falls in a given time. This equation is d = gt²/2
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you invented more math!
assuming you meant 17.33 pounds/sec
17.33 pounds/sec is a flow rate, a unit of force exerted by the earth, on the water, not mass.
in theory, it would take NO energy to move 17.33 pounds of water per second.
in practice, it takes almost no energy. (joules or less, we don't have to move it again, after it's moving
_ Newtons first law__)
multiply this by height to get work.
divide by time to get power, but since we already did that (pounds/sec), we DO NOT do it again.