Shaun

snip

If i understand what you're saying here, it sounds prettymuch
counterintuitive. I may be mis-using some of the terms? let me give an
example just to be sure that i understand what you're saying here, and bear
in mind that of course the numbers im going to use are entirely made up in
my head, so they'd be wrong....

It seems counterintuitive if you're thinking in terms of the discharge
stream "pushing against the water".

lets say that you have two identical boats with the same pump on each one,
running at whatever flow you like, say 5,000GPH. Boat A has a huge
outlet... say 5 inches in diameter. for arguements sake, because i dont
know how to calculate the speed of the water for that given outlet, lets say
the speed of the water coming out the back is slow. i dont know how slow,
but lets say it comes out at 3 knots.

Now boat B has the same pump, but the outlet is so small, that even though
its using the same pump, the water is coming out at a speed of 20 knots.
what you're saying is that both boats because they have the same amount of
energy put into them, and the same total force.... they'd go the same
speed?

Yes, that is the case. It's no different than if you used your hands,
and applied the same force to boat A, using only one finger, as you
apply to boat B, using the whole palm of your hand. It would "seem"
that you're pushing much harder with the finger than you have to with
the hand, but you're really not. With the finger, you have to apply a
much greater force *per unit of area* than with your palm (which has a
much larger surface area). For example, if you apply 10 lbf/sq.in. to
one square inch on Boat A, and 1 lbf/sq.in. to 10 square inches on Boat
B, the total force applied to both is the same, and the resulting
acceleration would be the same (assuming the same time interval of force
application).

is there no relationship between the speed the water comes out and
the speed of the boat ie. it seems pretty obvious boat A could never go
faster than 3 knots,

It may seem obvious, but that is incorrect. The discharge water is being
*accelerated* to 3 knots faster than the intake water. So there is a
constant force being applied that is totally independent of boat speed.
If there were no friction (and bow waves, etc.) the boat would
continue to accelerate indefinitely (well...see below). This is for an
axial system, where water comes in the bow, leaves the stern, the only
practical way to do it. As I said earlier, if your intake isn't pointed
forward, then you have Bernoulli effects, and you have pump cavitation
problems that reduce the flowrate. In the axial configuration, the boat
speed increases system efficiency by pressurizing the suction line and
overcoming the intake line pressure drop. At some speed, you'll reach a
point where the pump cannot maintain an acceleration of 3 knots (outlet
vs inlet), and your thrust will drop from that point on.

snip


F = m x a

Where F = Force
m = mass (proportional to the volumetric flow rate)
a = acceleration (proportional to the velocity of the water leaving the
pump versus velocity entering the pump)


ok, wait i should have read this first and thought about it more.... so
there is a direct relationship between water velocity and boat speed, if you
can maintain the same volume of water flowing.... right?

Exactly. It takes more pressure (force per unit area) to get that
higher velocity, so you have to do more work on the system (by the
pump). That additional 'work' is then available in the form of thrust.

so the sweet spot
would be just before the pump starts to be slowed by the backpressure?

Just before the discharge *volume* (mass flow techically) decreases.
Keep in mind that shrinking the nozzle is not "free", since that creates
higher pressure requirements, and thus higher load on the pump (i.e.
more amp draw).

now
this may be pure conjecture on all our behalfs, but assuming you could get
double the pressure (which you probably cant) at the same flow rate by
having pumps in series as opposed to parallel, and for the same current
draw, which boat do you think would go faster, the boat with double the flow
and half the speed, or the boat with double the speed and half the flow?
the total numbers add up the same right, but wouldnt the boat with higher
speed water jet go faster?

Nope, 'cause it's the accelerated mass of water that supplies the
thrust, not the discharge water 'pushing against' anything. Does the
boat you push with your finger (above) go faster than the one you push
with your palm because your fingertip is applying so much more pressure
(over a small area) than your palm is? No, if the total force applied
is the same. It doesn't matter whether it's great force on a small area
(fingertip, small water stream) or a lesser force over a greater area
(palm, large water stream) if the total force is the same, the thrust is
the same.

Keith Hughes