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Name: Michael K.
Status: other
Age: 30s
Location: N/A
Country: N/A
Date: 1999-2001


Question:
I read the article on "Towing a Funnel"

http://www.newton.dep.anl.gov/askasci/gen99/gen99580.htm

If you had a funnel (household funnel) - and it was full of water(upright) -- Water seems to come out very fast for such a small amount of water. Water in other containers of similar size - like a coffee can with a hole in bottom come out slower. Why? And is their a way to calculate this or does it have to be measured?

I am asking why the water comes out faster in a funnel than a coffee can with a hole in the bottom not the side. The holes are on the bottom(underside) NOT in the sides of the containers. If you have a quart funnel and a quart coffee can with same size holes and filled with the same amounts of water....the funnel empties first. Why is this? And can you calculate the pressure or flow rate of the different shaped container(funnel) or does it have be measured. Obviously the funnel is faster... does the same formula used in the article you linked above apply? I do not how it could since the water comes out faster?


Replies:
I am replying to this question purely from a theoretical standpoint - I have no experimental information to back up what I am saying. However, I will suggest experiments to test my assertions as I go along, so that someone experimentally minded can easily check on my account as they go along.

A funnel has a conical cross section. (Actually, two cones - one cone for the body of the funnel and another cone or a cylinder for the stem.) A coffee can has a rectangular cross section. The same volume of water in each will come up to different heights. Most likely, unless the coffee can is very tall and thin, the funnel will need more height to contain the same volume of water as the coffee can.

This is important because, to a first approximation, the velocity of a stream of liquid through a pipe or hole depends on the pressure forcing the liquid through the pipe or hole. The pressure forcing the water through the bottom of your funnel or coffee can is a result of the force of gravity acting on the water. The pressure at the hole depends on the density of the water (the same for both vessels) and the height of the top of the water above the hole. The water level is probably higher in the funnel, so the water pressure at the hole is probably greater there too. Thus, we would expect the water flow out of the funnel to be faster.

So, the thing to check will be the flow rate from the funnel and coffee can when both have the same height of liquid. Since the liquid heights will change differently in these two vessels as water is removed, it may be best to set up the experiment to keep the liquid levels fairly constant. One way I can think of to do this is to begin the experiment with the holes in both the funnel and coffee can plugged, and fill each one to the same height. Then mount over each vessel an inverted, rigid container full of water, such as a wide-mouth glass bottle. Put the opening of the bottle exactly at the water level of the container below. (I'll try to illustrate the set-up below. View in a constant-space font such as Courier for it to be legible.)
   _______
   |      |
   |~~~~~~|-water level or reservoir
   |      |
   |      |
   |      |
   \     /
|  |   |  |
|  |   |  |
|~~~~~~~~~|-water level of vessel
|         |
|         |
|         |
|____ ____|
      |
    opening

As water drains out of the lower opening, an air gap will appear between the water level in the lower vessel and the mouth of the reservoir. Air will rush into the reservoir through its mouth, allowing water to flow into the lower vessel until the water level in the lower vessel again reaches the mouth of the reservoir.

There are other ways you could ensure that the water level in both the coffee can and the funnel stay the same, such as running a siphon between them. The way I've described should give you the added benefit of an easy way to measure relative water flows - if you give both vessels identical reservoirs, whichever one's reservoir empties first is the one with the highest flow.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois



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