### Re: Relative Velocity In Relation to Water Resistance

Date: Fri Apr 6 13:30:38 2007
Posted By: michael pierce, Post-doc/Fellow, Materials Science Division, Argonne National Lab
Area of science: Physics
ID: 1169317767.Ph
Message:
```
ok, I have a minor point of possible confusion over what you mean by "at
rest in a flowing stream."  So depending upon what you mean by the
statement, there are two different answers.  Pick the one that applies.

************

CASE A) you mean that it's at rest relative to the ground so that water
must flow around the stick.  Then ...

You're correct that the water resistance is the same for the stick being
"pulled" and the stick held fixed to the ground.  However, the force
holding the stick fixed to the ground is also the same force as that
exerted by the person pulling the stick through the water.  In each case
there must be exactly the same amount of force applied to the stick to
counteract the water resistance.  In one case it's a force being applied by
whatever is pulling and in the other it's a force applied by the ground (or
whatever the stick is stuck to).

Now, in actual streams and flowing water things will be a little different.
For slow, smooth flowing water and low speed sticks things will be nearly
equivalent.  But for fast (turbulent water) and a fast moving stick the two
examples will begin to differ.  In turbulent conditions, there will be eddy
investigate turbulent and "laminar" flows.

Or, said in different words, at low velocity the water doesn't care if it
has to go around a fixed stick in the stream or if it's being pushed out of
the way by a moving stick.

************

CASE B) you mean that it's at rest relative to the flowing stream, ie
relative to the moving water.  So the stick is moving continuously with the
water.  Then ...

Actually, your intuition is correct that something isn't right.  They are
not the same!

The resistance of the stick floating in the stream (with the water) is
going to be close to zero (assuming the stick is moving at the same rate as
the water).  If it is moving at the same speed as the average velocity of
the fluid, then there will be no net force exerted on the stick to cause it
to move at a different rate than the stream of fluid(let's ignore buoyancy
for the moment as well as ebbs and flows of the stream).  In this case the
stick does not need to displace any water.  (Ideally) the water in front of
the stick will always remain in front and the water behind it will always
remain behind.  In practice, this isn't actually the case as the stick will
move at a slower rate than the stream and streams do not flow smoothly.

A stick being pulled through water at a constant rate has two opposite
forces being exerted on it.  First it has the force of whomever is pulling
it through the water.  Secondly it has the resistance force of the water
opposing it.  When the two forces are equal, then it will be moving at a
constant rate.  However, in the case the stick has to displace the water in
its path.  This displacement causes the resistance.

Think of it this way : Contrast the difference between swimming forwards in
a pool and just floating along in a stream.

```

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