Ask A Scientist© General Science Archive

 
 >    name         Mik
 >    status       other
 >    age          40s

 >    Question -   My son wants to enter this years science fair. We spent
 > most of friday
 >P.M. searching through your archives and saturday at our county
 >library. This is the question. If you towed a funnel through the water
 >would the resultant flow and P.S.I. from the small end be in direct
 >proportion to the speed at which it is being towed? Or is there a
 >phenomenum created in front of the funnel eliminating flow through the
 >funnel? Could a different shape change the action of the water and
 >improve flow and discharge P.S.I.?

First of all, let's look at this in a few very simple terms.  Instead of
dragging the funnel through water, let's assume that there is a flow of
fluid through the funnel, i.e. a pipe that necks down.  There are two types
of flow that can go through this pipe:  laminar and turbulent.  If we assume
laminar (or smooth) flow, it becomes real easy to see that the flow
characteristics change with Bernoulli's equation.  Bernoulli's equation
simply states that there can be no loss of kinetic energy (velocity of the
fluid) without a change in potential energy (pressure of the fluid).  That
is, if the flow rate is constant, the sum of the potential energy and
kinetic energy is constant.   Flow rate is determined by the area of the
pipe x velocity of the fluid.  So, if we say the flow rate is constant and
we decrease the area of the pipe (smaller diameter) we must increase the
velocity of the fluid to keep the flow rate constant.  If we increase the
velocity (kinetic energy) of the fluid, we must decrease the pressure
(potential energy) because of Bernoulli's principle.  With Bernoulli's
equation and some flow factors, we can accurately predict laminar flow
through a funnel. So the answer to one of your questions is "yes", the psi
is directly related to the flow through the funnel and is predictable if we
assume laminar flow.  When flow becomes turbulent, the equations become a
little more complex, but the same affect is going to happen with a little
stranger results.  There are mathematical models (i.e. finite element
analysis) that can be used to predict the behavior.  Now to make it even
more complex, lets drag your funnel through the water.  There is going to be
additional pressures built up in front of the funnel because you are
dragging something through a fluid and creating drag forces.  There will be
eddy currents behind the funnel due to the flow around the edges of the
funnel, not to mention that there probably some eddy currents from ejection
of the fluid through the small portion of the funnel.  These eddy currents
will also create more drag.  As you can see it gets pretty hairy.
A neat thing for you son to maybe do is like I mentioned at the top.  Create
a recirculating pipe system that has two different pipe sizes.  Maybe
something that looks like this (I hope it comes through OK over e-mail

   P1                     P3
------               ----------
        \     P2     /
         \----------/

          ----------
         /          \
        /            \
------               -----------


Hook a small pump to it and put pressure gauges (maybe a manometer or a
gauge that reads low pressures) at the points P1, P2, and P3.  What you
should see is the same pressure (or close to it) at P1 and P3, and a lower
pressure at P2 because of Bernoulli's principle.  Look in some basic fluid
mechanics books or hydraulic system manuals for an explanation of the
principle.  You may want the pipes to be clear so that the people can see
that there is fluid flowing through it (aesthetics).
Good luck.

Dr. Murphy

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Most of my work in hydrodynamics has been in the use of a wind tunnel
here at Argonne National Laboratory.  I can tell you what I do know about
such obstacles in flows.  As the towing speed increases a number of things
will happen.  Speed of flow through the funnel will not increase linearly
with tow speed.  As the tow speed increase, frictional energy losses along
the inside of the funnel will tend to reduce flow increases through the
funnel.  However, a more important problem is that the resistance to flow
through the small end of the funnel will increase with speed, causing a
buildup of water being pushed by the large end of the funnel to increase
with speed.  This then spills outside the funnel in an increasingly large
wake, producing vortices outside the funnel.  If the vortices are large
enough and strong enough, they could actually push against the water
trying to come out of the small end of the funnel and decrease the flow from
the funnel more.  At some speed, I would expect the combined affects of
resistance to flow and the vortex effect to bring the flow through the
funnel to a stop, particularly for a fluid as viscous as water.  The
affects would probably not be nearly as severe if air were the medium.

Dr. Cook
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