Water and Funnels
Name: Michael K.
I read the article on "Towing a Funnel"
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
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?
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
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
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
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Update: June 2012