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Just had to do this.. it's been bugging me as to how this exit force
from a centrfugal nozzle head could produce overunity. So here is
some math (sorry Engineer here) that will explain what a Normal
"sprinker head" would achieve in power. Forgot you said this.. but
the raduis squared does come into play.. however.. still do not
see where the "kick over" occurs for over unity.
OK.. make believe we have a sprinkler (twisted L shaped on each
side) which is feed water in the center of it. THis sprinker is turning
at a velocity of "w" and the length of the arms (in the L forms) are
"L". The exit velocity realitve to the nozzles are "Ve" for exit =
velocity,
and the area of the exit nozzle is "A". I think that now covers it.
Assumptions have to be made now.. and we concider that laminer
flow is occuring and no resistance is taken in to account (friction or
heating). What we want to find is the power produced from this
sprinkler. So..the moment around the z-axis.. will be the summations
of all (r xV)*p*V*A . Opps now "r" is radius, and "p" is density of=20
water. p*V*A is called the mass efflus of the nozzle.. or lets say "m"
for now. The moment going into the hub.. enterance of water... is
zero cause the radius "r" is zero. Thus the equation reduces to only
one sum.. or (r x V)*m. Now we have to take into account for the
rotational velocity and the velocity of the zozzle exit jet... in to the
normal atmosphere. Now we can subsitute r X V =3D -r*(Ve - w*r).
Thus the moment applied to the system by the generator would
be -r*(Ve - W*r)*m. BUT the moment applied to the generator is the
negative of the moment of the generator on the arms. So the equation
becomes positive... no biggy!
The power now is simple...one we have the moment.. It is the moment
time the rotational velocity.. (M =3D moment) or M*w =3D P for Power!
For all who would like the in to one equation .. here...
P =3D (w*r*Ve - w*w*r*r)*m
ENSURE.. that proper mks units are used for example ... RPM has
to be changed to RPS.. etc etc.. and don;t forget 2*pi for rotational
velocity! =20
v/r Ken Carrigan
PS.. NOW... WHERE IS THE OVERUNITY!!!
Help me understand...
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