I'm going to add snips from a couple of other posts here since they are
all related.

Snip from Rusty's other post:

I presume you meant GPM rather than GPH in  your
chart, right?

Yes, I did mean GPM.

I'm an electronics guy, so I've been comparing the pump to a battery. I
will interchange the terminology between the two fields somewhat freely
here.  In the battery, we have a voltage and an internal impedance.  The
internal impedance limits the maximum current flow available from the
battery or the 'short circuit current'.  In the pump we have pressure
(psi) and flow (GPM).  I can deduce the internal impedance of the pump
by dividing pressure by flow.  (I wonder if the fluid flow guys have a
unit for this?) For this pump pressure (6 PSI), and flow (16 GPH)  gives
an internal impedance of 0.375.

On Fri, 12 Nov 2004 20:56:09 -0600
"Russell Duffy" <13brv3@bellsouth.net> wrote:

Hi again.  I was just thinking about this, and wondering how they get
the flow ratings that they give.  What would happen if you connected
the inlet, and outlet together, with a hose, completely filled with
water.  Of course you could only measure the flow with a flow meter,
but would this condition show a higher flow than pumping from one
container to another?

If it would be higher, then it could actually be a more relevant test,
since that's about what we do with the engine.  We certainly have more
restriction than a simple pipe would have.

snip from Ernest's post:

Second, I think Rusty has a good point here.  There is a significant
amount of energy invested in accelerating the water in these static
test.  Energy that is lost when it drops in the bucket.  In
the closed circuit of the engine, SOME of it will be recovered, but the
drag through the engine is unknown, varies with the amount of flow, and
is  very non-linear.

NOTE:  I don't know how non-linear the flow vs pressure is.  For this
analysis, I'm making a grand assumption that it is linear.  I'm sure
this is wrong so nothing here will give "the answer".  The pressure vs
flow is linear in a non-turbulent system, but if I'm not mistaken, a
cooling system is designed to be turbulent.  Also, the analysis should
be OK if the flow is restricted to a particular value.  If all
measurements were made at 20 GPM for example, the math would be OK, but
not for comparing 20 GPM to 10 GPM.  I'm also neglecting any restriction
caused by the 3 foot 3/4 inch ID hoses used on the input and output

I Think Rusty does have a good point. The 'short circuit current' should
have the output connected directly to the input. This would likely
result in a higher flow rate.  There is some indication that that may be
true in this data.  The flow rate for two pumps in series is higher
than for the single pump, which indicate that the internal impedance is
less than twice the impedance for one pump.

I would expect the current flow to decrease in the closed loop also as
the pump will be doing less work.  That could give me the 20 GPM at 5 A.
I can set the system up while monitoring the current, then connect the
hoses together in the big container.  If I see the current drop, that
will indicate we are on the right track.

Looking at Bill Schertz' flow chart for the Mazda 13B pump (attached),
at 5594 rpm, the pump is flowing 29 GPM with an 11 PSI drop across the
pump. The zero flow pressure of the pump is 19 psi, therefore, total
impedance for the system would be 19/29 = 0.66, the internal impedance
of the pump would be (19-11)/29 = 0.28 and the external impedance of the
system would be 11/29 = 0.38.

This is an important number.  It will determine whether I want to put
the pumps in series or parallel for maximum flow.  For the following, I
am going to make another assumption that Mezarie did their max flow test
as Rusty has suggested and got the 20 GPM flow rate they advertise.
This would give the Mezarie an internal impedance of 6/20 = 0.3.


Example 1:  One WP136

Pressure (P) = 6 psi
internal impedance (Zi) = 0.3
external impedance (Ze) = 0.38

expected flow (F) = 6/(0.3 + 0.38) = 8.8 GPM

Example 2:  Two WP136 in series

P  = 12 psi
Zi = 0.6 (0.3 + 0.3)
Ze = 0.38

F = 12/0.98 = 12.2 GPM

Example 3:  Two WP136 in parallel

P = 6 psi
Zi = 0.15
Ze = 0.38

F = 6/0.53 = 11.3 GPM

Using these assumptions, the series pumps would provide slightly more
flow.  There is enough uncertainty in all of this that it would be hard
to predict which one was actually better.  If Ze were lower, it would
favor the parallel pumps, and higher would favor the series pumps.

If there is a point to all of this, it's that choosing parallel vs
serial for max flow isn't a given.  It all depends on the rest of the
system.

In looking over some other information Bill has published, I don't
believe he had a radiator in the circuit when he did the flow tests.  Is
that correct Bill?  There is another chart showing the pressure drop
across two evaporator cores (calculated from one core).  at 12 GPM, the
drop is about 1.6 psi.  at 29 GPM, it's around 7.2 psi. Impedance of
radiator (Zr) at 12 GPM  = 1.6/12 = .13, at 29 GPM Zr = 7.2/29 = .25.

So much for linearity.  Whatever the impedance, it will increase the
total impedance, and push the system toward series pumps.  On the other
hand, the actual impedance at 12 psi is probably lower than the
impedance at 29 psi, because of the non-linearity in the pressure/flow
curves.

OK, I haven't decided on series vs parallel yet, but I'm leaning toward
parallel for the first try.

Now I will take this data and work from Bill's charts.  All of Bill's
slides are available in a pdf file at:
http://www.bob-white.com/ACRE/Water_Cooling_an_Aircraft_Engine.pdf

To see a similar analysis of Todd Bartram's EWP cooling system go to:
http://www.bob-white.com/ACRE/schertz/EWP_analysis.html

I will assume I can get a 12 GPM flow rate.  Looking at page 9 I see
that I will need a 50 deg temp differential across the radiator to cool
150 HP with a 12 GPM flow.  Bruce Turrentine has set an upper limit of
200 deg with short periods at 210 deg.  If I use the 200 deg limit, the
water needs to cool to 150 deg while passing through the radiator.

The output air from the radiator has to be somewhat less than 150 deg.
For this analysis, let's say I can heat the incoming air to 140.  On a
90 deg day, that give me a 50 deg temp rise thru the radiator.  (Bill's
chart only goes to 50 deg. anyway)  According to the chart I need
slightly less than 5000 cubic feet per minute of airflow = 5000/60
ft^3/m = 83 ft^3/s.

Now I will work form the direction of how large the air intake will have
to be to accommodate that flow.  If I'm climbing out at 120 mph and I
get 60% of that velocity through the input duct, that would be 72 mph or
105 ft/s.  Now I have 83 ft^3/s / 105 f/s = 0.8 ft^2.  using two ducts
of 0.4ft^2 each, I need two opening .63 ft X 0.63 ft, or 7.6 in X 7.6
in. Let's just say 8 in X 8 in.  These are pretty large openings.

I will have to hope that some of the assumptions have been too
conservative.  Todd's success with his turbo installation leads me to
think that might be so.

Finally, I would like to thank Bill for his slides and the analysis he
did on Todd's data.  Without that, I couldn't have done any of the
above.  I have used his analysis as a guide, but done some calculations
from a different direction.  I've made so many assumptions, I'm up to my
ASSumption limit.:) I have no idea how many mistakes I've made, but I'm
sure many of you will find them, and I don't know how far I've strayed
from reality.  One of these days I hope to fire up the engine and get
some real data.  All of you who are flying your rotaries and shared your
experiences give me some hope. Thanks to all of you.

Bob White



-- http://www.bob-white.com
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