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work moving water into a tank?
I had a physics/calculus problem to calculate the lesser of 2 work problems moving water into a tank.
I think their answer is wrong, or at least short sighted... what is correct? Here is the problem...
"Pumping water from a lake 15-ft below the bottom of the tank can fill the cylindrical tank shown here. (See figure 1) There are two ways to go about it. One is to pump the water through a hose attached to a valve in the bottom of the tank. The other is to attach the hose to the rim of the tank and let the water pour in. Which way will be faster? Give reason for answer."
Though it was not stated, I can only assume that the rate of work performed is constant for either example in order to make the comparison fair. They claim that pumping the water to the bottom of the tank requires less work and therefore faster. They integrate over the height of the tank, being 6 ft. and 2 ft. radius. Their integrand for pumping to the bottom is (62.4 lb/ft^3 water weight) * 62.4 * 4pi * (15 +y) dy
The integrand for pumping to the top is 62.4 * 4pi * 21 (total height to top of tank) dy .
The bottom method equals less work, buy I claim that it is leaving out an important factor.
That is, the total force on the water being pushed into the tank increases as the tank fills up.
You not only have to push against gravity, but against the increasing water pressure building up from the water above the bottom of the tank. That increasing factor increases the force in the integrand over the range of integration. Accounting for this the total work done by pumping to the bottom of the tank is greater.
Is this the correct thinking for this problem? Does the weight of the water in the tank contribute to the force required to pump the water up to the tank?
4 Answers
- 8 years agoFavorite Answer
Pumping into the bottom of the tank is faster. 15 ft of total discharge head from the lake surface to the bottom of the empty tank, and gradually increasing to a maximum of 21 ft of TDH when full.
Pumping over the top of the tank is 21 ft of TDH all the time.
- morningstarLv 78 years ago
"You not only have to push against gravity, but against the increasing water pressure building up from the water above the bottom of the tank. That increasing factor increases the force in the integrand over the range of integration. Accounting for this the total work done by pumping to the bottom of the tank is greater."
The amount of pressure depends on the height of the column of water above you. It does not depend on the volume of water or in any way on the shape of the container. When pumping the water over the top rim of the tank, you have to work against the column of water *inside* the hose. Therefore, the pressure from the water in the hose going to the top of the tank is the same as the pressure from the water in the *full* tank. Therefore when pumping the water to the top of the tank, the pressure is actually *more* or equal at all times vs. pumping to the bottom of the tank.
When pumping into the bottom of the tank, whatever work you do against the water pressure inside the tank *is* doing work against gravity. Work done against the pressure is lifting the water that's already within the tank.
- zee_primeLv 68 years ago
Your reasoning is correct, but remember that if you pump the water to the tank rim and allow it to fall into the tank, then the work you're doing to raise the water above the water level in the tank is wasted; it's converted into heat when the water falls into the tank. So for a given amount of work, you'll fill the tank faster by pushing the water up through a valve in the bottom.
- Anonymous4 years ago
If it replaced into an entire water substitute you have shocked the fish. you are able to substitute basically a third of the water at a time and transfers could be achieved by utilising putting the fish in a open bag with the previous water into the nice and comfortable tank and letting the water blend slowly to assist ease the temperature and water ask your self.
