Definitions of jet thrusts

DC
You are of course correct in your statement horsepower is energy per
Unit time

I did not give it the time to consider it

As I have always looked at horsepower as the rate of doing work
work/time
And you use energy per unit time

But as work and energy is the same both are correct

 

Interesting.

 

The rate of useful work done by the jet on the boat would be twice as much if the velocity difference is doubled.

- But -

The power required to move the water would be more than twice as much. The power to move the water would be proportional to:
1/2 x mass flow rate x [ velocity out ^ 2 - velocity in ^ 2]

The ratio of rate of useful work done to the power required to move the water is the efficiency of the jet. The difference between difference in velocity and difference in velocity squared is is why increasing the mass flow rate and decreasing the velocity difference can result in increased efficiency.

Keep in mind this is a simplified analysis. In a real system other effects can eventually cause efficiency to start to drop with increased mass flow rate.

 

so once upon a time I took a physics class, and it turns out the relative position gets confusing for me.

So........

velocity out in relation to what? The boat or the lake?

Velocity in in relation to what? Boat or the lake?

from college, light is the only absolute, and my boat ain't that fast.

Yet.

(smiles)

To be fair, he DID say the mass flow rate was the same, which means that part will be the same.

For such a simple subject (squirt water out the back, boat goes forward), it certainly is confusing as to how it exactly all works mathematically.

 

Not so confusing actually. The easiest to understand frame of reference (and also the commonly used one) is that of the observer moving with the boat.

So you have the observer (you) standing on the deck, and hence the ship is standing still in his frame of reference. What he sees then is a water coming from the stern towards the inlet of the waterjet with a speed Vs (ship speed). At the nozzle he sees the jet expelled at a speed Vj (the jet speed). These are the two speeds used in the thrust equation and for the calculation of the mass flow rate. So all the speeds are referred to the boat as a reference (non-moving) coordinate system.

 

Ok, so if I'm understanding this correctly, one could think of the thrust (out) out the back of the nozzle as "gross thrust", and if we take gross thrust and subtract the inlet velocity we'd have something akin to "net thrust."

Which means Net thrust is indeed a function of the speed of the boat, and diminishes the faster the boat goes.

 

Yes. It looks like my post #13 on the first page went unnoticed.

 

No, I saw it, and appreciated it. And if you look, I said much the same thing at the same time, but it took a bit for others to figure it out.

So, as I read this, if we reach top speed for a jet/boat combo, and we want to go faster, we need to change velocity of the water. But, looking at an impeller curve for a mixed flow pump, that is not a trivial exercise.

Sure would be nice to have a variable displacement pump.

 

So, continuing on.

Thrust is Mass flow * Net Velocity of water.

If the boat is going 35, and the jet stream comes out of the boat at 70, the net thrust will be half as much as if the boat was sitting still.

Also of note, the horsepower consumed is
mass flow rate x [ velocity out ^ 2 )

so, the power consumed is a function of velocity squared, but thrust is a function of only velocity.

Edit> On edit, for horsepower consumed, nothing cares how fast the boat is going. The horsepower consumed is going to be something on the order of
Mass flow rate * (Nozzle velocity squared)

I think.

 

IF the mass flow rate does not change with speed. Depending on inlet configuration and pump characteristics (and other factors) the mass flow rate will increase with increase, perhaps significantly.

The rate of work done on the water is proportional to the mass flow rate x (velocity out ^ 2 - velocity in ^ 2). {I don't remember if there is a factor of 1/2 involved} The velocity in ^ 2 term accounts for the kinetic energy in the water entering the system. "Velocity in" is not the velocity directly at the inlet but rather the approach velocity; ie the boat velocity. Also these equations are based on an assumption of a uniform velocity across the nozzle.

The power input to the system will always be greater than the rate of work done on the water. The velocity across the nozzle will not be uniform, and there will be "system losses" in the ducting and pump.

 

Given a fixed power input (V8 engine), you'd think the max RPM the engine made would change as a function of velocity. In other words, if your argument is right, the faster you go, the more rpm the engine can turn.

With an axial flow pump such as the hamilton 212 this is somewhat true. As speed increases, you can pick up 200 rpm or so which is significant, but not earth shattering.

With a berkeley style mixed flow pump you see very little of this rpm change. To be fair, the mixed flow pumps have a much steeper impeller curve.

Reading on nozzles suggests the velocity is really close to the same across the nozzle. pressures on the order of 300 psi and nozzle diameters on the order of 3 inches means things even out pretty quickly.

Hamilton and others have shown pressure maps on the intake side of the impeller, and those are very much not equal. In general the "top" of the impeller is much less loaded than the bottom at higher speeds (70 mph on up).

Racers using "loaders" report 2-4 mph or more increase with a well placed loader. Generally the higher the RPM, and the higher the mph (horsepower) the more the loader helps. Interestingly, 20 psi seems to generally be "plenty" of pressure. Adding more does not help most boats go faster, and in fact too "much" slows the boat down.

If a racer wanted, they could easily add more pressure on the inlet side of the impeller.
It seems to me if you add more pressure, you are actually causing the water in the inlet (gullet) to slow down in relation to the boat. "slow down" is a change in velocity, which consumes power.

My theory is too low of an inlet pressure allows cavitation at the impeller tips on the top of the inlet. A loader adds enough pressure the cavitation no longer occurs, which makes the pump significantly more efficient. Slowing hte water needlessly past this point reduces pump efficiency.