Calc 2 help... (extra credit)

[Danos]

Given: A cylindrical tank standing upright with an open top and a valve at the bottom. Dimensions: radius = 2 feet, height = 6 feet.

Question:
The cylindrical tank shown here can be filled by pumping water from a lake 15ft below the bottom of the tank. There are two ways to go about it. One is to pump the water through the hose attached to the valve at the bottom of the tank. The other is to attach the house to the rim of the tank at the top and let the water pour in. Which way will be faster? Give reasons for your answer.

After putting some thought into this in a group study thingie. Most agreed that pouring through the top would be faster. Now after some thought without a bunch of people yapping. In terms of faster, would it really matter because I believe the hose will pour water at the same rate, regardless if it was higher or not (all things being equal that is. But this question is in a section about work so I assume they phrased it wrong.

I believe the overall answer should be that pouring the water through the valve at the bottom would be the method requiring the least amount of work. Reasoning behind this is that if you pour the water from the top, that means you would have to take the full volume of the container up to 6ft and drop it in. Thus your work would be the total weight of the water by the distance traveled of 6ft. But if you fill it from the bottom, only some water would travel the full distance of 6ft, some would travel 5ft...etc and the rest would just move into the bottom of the tank.

[Elmer the Pointy]

Is there extra force needed to pump water into the bottom of the tank when there's 5ft of water already in there?
Pouring in the top means you're just working against gravity, but pumping in the bottom means you're fighting gravity and the weight of the water.

I may be wrong, though

[Daydreamer]

Is there extra force needed to pump water into the bottom of the tank when there's 5ft of water already in there?
Pouring in the top means you're just working against gravity, but pumping in the bottom means you're fighting gravity and the weight of the water.

I may be wrong, though

Yeah if you're pouring from the top then gravity is going to help you do it faster, if it's from the bottom the gravity will weigh what is already in there down and require more pressure.

[Danos]

Yea thats what I we discussed first as well but then now we need to take into consideration things such as pressure, size of the hose/valve. Those things aren't given. I'm pretty sure we can't calculate something exactly but need to give a really good explanation... or I could just admit I'm dumb.

I also think that taking into the consideration of pressure and such, that pouring from the top would be faster. The only reason I started to think about it from the other viewpoint was this:

Instead of a hose, I imagined lemmings carrying buckets of water then pouring it in from the top. Thus the whole volume having to travel the 6ft distance. From the other end, the lemmings would climb up and stand in their individual spot. This method of thinking does definitely take out the additional pressure building at the bottom of the tank. I'm starting to think that I might be putting too much thought into it.

[Devek]

Something else to think about..

An odd feature of all pumps is the fact that they produce their greatest flow at their least pressure. The maximum pressure rating of a pump is when your thumb is on the outlet of the pump, not letting anything out. In other words, no flow. On the other side of the coin, the maximum flow of the pump occurs when it is free to pump with no restriction (no thumb).

[Jefe]

I think the hose will fill up the thank faster from the top. Don't remember this sh!t very well, but iirc, when the pressure is consistent (as in a hose, hence, increasing the speed), the pressure decreases - less work. Then again the radius and size of the tank were given for a reason <_<

[Maguspk]

What kind of Calc2 class is this extra credit for, and why could you work in groups on extra credit, that's awesome lol. But ya, you're assumption is correct, Top is best.

[Mysterio]

another homework thread?

[Osede]

What kind of Calc2 class is this extra credit for, and why could you work in groups on extra credit, that's awesome lol. But ya, you're assumption is correct, Top is best.

I'm guess it some kind of take home exam.

And yea top best. Due to if you pump from bottom, beside the weight and gravity, u also need to taking care of the air pressure that exert on the surface of the water in the tank.

[Ichthyos]

Most of the replies above are using the right intuition. The right answer depends on the characteristics of the pump being used, though.

When you're pumping a liquid through a hose, the orientation of the hose with respect to gravity affects the pressure required to maintain a given rate of flow. This is due to the hydrostatic pressure of the liquid in the hose being pulled downward by gravity. The higher the end of the hose is, the more pressure is required to counteract that pressure and maintain that rate of flow. So, when the end of hose is at the top of the tank the pump would have to be providing more pressure in order to maintain the same rate of flow, compared to when the end of the hose is at the bottom of the tank (when the tank is empty).

As others have alluded to above, when the hose is attached to the bottom of the tank, the increasing weight of the water in the tank gradually increases the pressure required to maintain a constant rate of flow into the tank. This is also due to hydrostatic pressure, but now instead of just the water in the hose, you have the water in the tank to worry about.

The reason there isn't a clear-cut answer to the question is that we don't know how the pump works. If we had both the cross-sectional area of the hose and an equation relating the hydrostatic pressure at the pump's end of the hose to the observed rate of flow of the pump, then we would be able to figure out which is faster.

[zoobernut]

At the begining when the tank is empty filling the tank from the bottom will be more efficient because the pump does not have to push the water up as far. When the tank is empty the vertical distance the water must be pumped at the bottom of the tank is 15 ft which is the distance from the lake to the tank however it is 21 ft from the lake to the top of the tank.

As the tank fills up there is a crossover point in which the pressure of the water in the tank on the hose at the base of the tank is greater than the difference between the force it takes to initially pump the water to the base of the tank and to pump the water to the top of the tank, at this point it will become more efficient to pump water up to the top of the tank. This scenario only works IF you can start pumping one way then switch midway to the other method of pumping. If you can only pick one way to pump then yeah pumping to the top is more efficient.

hmmm. I just re-read the question and Ichthyos is right without anymore knowledge of what type of pump it is we cannot really answer the question the way it is phrased. The question in the OP asks which method of pumping would be faster not which method would be more efficient or take less force. Pumping to the top of the tank would only be faster if you assume the pump would slow down the rate of flow as the pressure on the hose increases.

[Devek]

hmmm. I just re-read the question and Ichthyos is right without anymore knowledge of what type of pump it is we cannot really answer the question the way it is phrased. The question in the OP asks which method of pumping would be faster not which method would be more efficient or take less force. Pumping to the top of the tank would only be faster if you assume the pump would slow down the rate of flow as the pressure on the hose increases.

What type of fluid pump does not create flow when the pressure is increased?

[zoobernut]

hmmm. I just re-read the question and Ichthyos is right without anymore knowledge of what type of pump it is we cannot really answer the question the way it is phrased. The question in the OP asks which method of pumping would be faster not which method would be more efficient or take less force. Pumping to the top of the tank would only be faster if you assume the pump would slow down the rate of flow as the pressure on the hose increases.

What type of fluid pump does not create flow when the pressure is increased?

I think you missunderstood what I meant. Some pumps are powerfull enough that the amount of back pressure from the weight of the water in the water tank as it fills up would not be enough to change the rate of flow of water into the tank from the pump. The pump might have to work harder but it could maintain the same rate of flow into the tank as when the tank was empty.

[Ichthyos]

hmmm. I just re-read the question and Ichthyos is right without anymore knowledge of what type of pump it is we cannot really answer the question the way it is phrased. The question in the OP asks which method of pumping would be faster not which method would be more efficient or take less force. Pumping to the top of the tank would only be faster if you assume the pump would slow down the rate of flow as the pressure on the hose increases.

What type of fluid pump does not create flow when the pressure is increased?

I think you missunderstood what I meant. Some pumps are powerfull enough that the amount of back pressure from the weight of the water in the water tank as it fills up would not be enough to change the rate of flow of water into the tank from the pump. The pump might have to work harder but it could maintain the same rate of flow into the tank as when the tank was empty.

Exactly.

[Devek]

Except for one tiny detail.. a pump "working harder" will always pump less water.

A pump large enough to not be phased at all by that tank would have to be MASSIVE and even then a 1psi increase in pressure will equate to less flow even if it isn't that much less. Less is still less.

[zoobernut]

Except for one tiny detail.. a pump "working harder" will always pump less water.

A pump large enough to not be phased at all by that tank would have to be MASSIVE and even then a 1psi increase in pressure will equate to less flow even if it isn't that much less. Less is still less.

No a pump working harder does not mean less water is pumped it just means the pressure inside of the hose is increased. as the water in the tank increases if the pump works harder it means it also increases its output pressure to counteract the pressure from the tank.

A pump that reaches its output capacity and cannot work any harder would then start to pump less water as the pressure increased.

[Devek]

What type of frictionless world do you live in?

The output capacity of a pump is only reached when there is no pressure.

I can do this all day.

[zoobernut]

What type of frictionless world do you live in?

The output capacity of a pump is only reached when there is no pressure.

I can do this all day.

If you get a problem like this in calc. or physics or mechanics you can only use the information you are given and rule #1 is that unless otherwise stated assume there is no friction. Treating this like a real world problem is impossible with the information given and therefore I treat it like any other physics problem that I had in school. And given standard physics questions format or math one can assume no friction.

If my math and physics books from college were not in storage I would just go look it up, I have had several problems just like this before I just don't know exactly where my notes are right now since I last moved.

[Devek]

It doesn't ask how much faster it would be to fill from the top.. it asks if it would be faster to fill from the top.

A bigger/stronger pump would decrease the difference between filling from the top and the bottom.. but it doesn't ask the difference.

I assert that flow/pressure charts for pumps typically look like this:

http://img369.imageshack.us/img369/262/rightoj5.png

You are asserting that flow/pressure charts for pumps sometimes look like this:

http://img369.imageshack.us/img369/2803/wrongxf4.png

Embarrassingly I don't have any graphing software installed on this machine I am currently on.. but dammit don't make me start pulling out specifications for actual pumps because I can.

[zoobernut]

Devek I am not asserting that the pressure vs. flow chart looks like that. You are way overcomplicating this problem. You are looking at pump efficiency and friction when neither of those things are stated in the problem.

Only using the information in the problem changes how you interpret it.

You are right though in your last post. I am a little bit rusty on this sort of thing because it has been about 3 years since I took a class on mechanics or physics. I just think that it is necessary to only use the information given in the original question.