Calc 2 help... (extra credit)

[Evelyn]

think of it this way:

pump does more work based on how much it has to push. more water in the hose = more work done. If you push a 30 pound block, you exert less pressure on it to start movement and continue movement than you would a 300 pound block. Also, assuming the same pressure (IE constant pump pressure) you'd be moving the large block much slower than the smaller one.

Same thing here. If you had to include the water already in the tank, it would take more work to push the water than if you have just the hose to worry about. More work = slower rate = tank takes longer to fill.

[Osede]

pressure that exerted on at the point of connection between the tank and the hose, if connect throught bottom of the tanks is,

"Pa (air pressure) + density*gravity*height(of water which in a function of time)."

if connect from top, will be "Pa" only.


from reading replies above, OP might need to state those assumptions, like
1. flow rate constant or not,
2. does flow rate affect by the pressure and total weight?
3. how does the pump work (which i think it barely affect the assumption 1 and 2)
4. etc


so, state all the reasonable assumptions as many as possible . Then OP may come with conclusion that supported by these assumptions

[Daahan]

I fucking hate optimization problems.

[ozz]

think of it this way:

Same thing here. If you had to include the water already in the tank, it would take more work to push the water than if you have just the hose to worry about. More work = slower rate = tank takes longer to fill.

but the pump has to push that water up the hose to the top if you fill it that way, which if you dont have any pump specs should equate to equal work either way,right? except you lose work pumping from the top, as the water falls back down once it gets there,due to gravity, energy you cant reuse once you exert it

bottom is best,yo

[ozz]

so uh...you ever get the answer from the teacher? <_<

[mikazuki]

the pressure is always greater at the same height in any size hose which is filling from the top than it is from the bottom, therefore the work will always be greater. you could also consider the additional 6'+d column of water remaining in the hose after the completion of pumping (unless the hose is within the tank and has no thickness).
the pressure is a function of height of the hose, not diameter.

on the plus side there is no danger of all the water in the tank returning through a hose filling from the top, ie. you have a more secure intake.

disclaimer: i could be wrong^^

[VZX]

wait... this is calc 2 problem?
looks like high school phyiscs trick question to me :/

[mikazuki]

the question is supposed to be answered by modelling the two circumstances vzx, the calculus is needed for describing the rate of change of pressure in the hose (and subsequently amount of work done) when filling from the bottom, the result is a graph which shows the work done increasing when filled from the bottom, but never reaching the same as the work done filling from the top.
of course comparing the two equations is also an acceptable answer - it's just harder to understand.

[kalenedrael]

Consider the energy it takes, assuming ideal, non-strange pumps (constant flow rate regardless of pressure) and non-viscous fluid. If you pump it in from the top, the pump must lift every drop of liquid to the top of the container, and drop it in. This takes more energy than simply lifting the liquid to the required height to fill the container, as it would do if it pumped liquid in through the bottom. The extra energy that pumping to the top requires is lost through unnecessary liquid motion as it swirls around in the container.