Personal Water Craft (Jetski, etc)

[ruko]

My question is about the propulsion system used by jet boats or personal water craft sometimes called Jetskis. You see them skimming across the water at high speed and it looks like a blast. My question is this: Does the water propulsion exit the jet nozzle above or below the water surface when the craft is at high speed ? Why?

 

[rcgldr]

Normally below the water level, except when skipping over waves. I think that thrust from a turbine driving water at relatively low speeds (compared to a rocket's thrust) would produce more thrust with the exit in the water than with the exit in the air.

 

[ruko]

Normally below the water level, except when skipping over waves. I think that thrust from a turbine driving water at relatively low speeds (compared to a rocket's thrust) would produce more thrust with the exit in the water than with the exit in the air.

What I have learned about thrust:

Rockets work better in a vacuum - in fact, according to NASA, they develop about 10% more thrust in a vacuum than in the atmosphere. So how can this be? One of the great fallacies about rocket propulsion gasses is that it needs to have something to "push" against to make it go. In fact, atmospheric air partially chokes off or slows down the gasses coming out of the rocket nozzle which, in turn, reduces thrust.. Rockets are a perfect demonstration of Newton's Third Law.

A very similar phenomenon happens with jet boats or personal water craft, Jetski, etc, that use a jet of water for propulsion. Because water is so much more dense than air, it is this very reason all of these types of boats are designed with the jet nozzle above the water surface at plane speed. Jet boat manufacturers learned very early, for a given horsepower input the jet produces much more thrust above the water compared to under it. This is the one and only reason why the jet nozzle exits above the surface of the water at plane speed, not because of drag or any other physical design factors. It is considerably more efficient this way because the jet of propulsion water has only air to resist it's motion.

It is only volume and velocity that determine thrust of a jet or rocket and it doesn't matter if it is gas or water being expelled from the nozzle. If something gets in the way of the thrust medium as it is exiting, thrust is reduced.

 

[rcgldr]

I was aware that rocket engines produce more thrust in space than in the atmoshpere, but it's seems to be more complicated than just the terminal velocity of the spent fuel from the engine. In the atmosphere, the force equals mass flow rate of spent fuel times change in velocity plus mass flow rate of the affected air times change in velocity. In space it's just the spent fuel mass flow rate. It turns out that more thrust and higher pressures occur in space where it's just the fuel mass flow. Another complicating factor is that the exhaust velocity is super sonic, and information about pressure can't travel faster than the speed of sound. I don't know how supersonic flow affects rocket engines in the atmoshpere.

In the case of the jet ski with exit nozzle in the water, the force = mass flow rate of water in turbine times change in velocity plus mass flow rate of affected water outside the engine times change in velocity. If the exit nozzle is in the air, then the realtively small momentum of the air can be ignored, and it's just the mass flow rate of water in the engine times change in velocity. The change in velocity is higher with the exit nozzle in the air, but the mass flow rate is greater with the nozzle in the water.

At relatively low speeds (smaller change in velocity), I would think that exit in the water would be better, but at higher speeds (larger change in velocity), then exit in the air would be better. The issue here is I don't know at what speed it's better to have the exit in the air.

In my previous post, I should have made it clear that I didn't know, but thought the exit in the water case might be better (at low speeds). After posting my response I attempted to edit it but the forum was having problems and I couldn't get back until now.

 

[ruko]

I don't understand how the mass flow rate could be greater with the nozzle under water. Water offers so much more resistance to flow than air and it would take more horsepower to bring the flow rate up to the same level as in air.

Drawing from the basics of rocket propulsion, we know that the thrust is equal to the product of the mass flow rate and nozzle exit velocity plus the product of the nozzle exit area and the difference between the nozzle exit pressure and the ambient pressure.

F = (m dot * V)e - (m dot * V)0 + (pe - p0) * Ae

The product of the nozzle exit area and the ambient pressure is referred to as the back-pressure. Since the density of water is greater than that of air, it follows that the back-pressure in water is greater than in air; and thus, the thrust is less.

 

[Danger]

"[URL=http://img125.imageshack.us/my.php?image=jetskipf8en.jpg[/URL]
[PLAIN]http://g.imageshack.us/img125/jetskipf8en.jpg/1/ [Broken]
http://g.imageshack.us/img125/jetskipf8en.jpg/1/ [Broken]

Sorry... I couldn't resist.

 

[rcgldr]

I don't understand how the mass flow rate could be greater with the nozzle under water.

Because the water outside of the turbine is affected by the flow from the turbine. In addition to acclerating water in the turbine, the surrounding water is also accelerated, so the effect on the surrounding water needs to be taken into account as well.

 

[ruko]

Because the water outside of the turbine is affected by the flow from the turbine. In addition to acclerating water in the turbine, the surrounding water is also accelerated, so the effect on the surrounding water needs to be taken into account as well.

I agree and because it takes more energy to accelerate surrounding water, compared to surrounding air, thrust is less with a given power input.

 

[rcgldr]

It takes more energy to accelerate surrounding water, compared to surrounding air.

On the other hand, the same thrust can be generated with a higher mass flow at a lower rate of acceleration and a corresponding exit velocity, which reduces the power requirement.

 

[ruko]

On the other hand, the same thrust can be generated with a higher mass flow at a lower rate of acceleration and a corresponding exit velocity, which reduces the power requirement.

"the same thrust can be generated"

Not the same thrust. Lower because it is working against water vs air. You can generate the same thrust but you need more HP to push the water out of the way.

Again, all modern personal water craft jet boat manufacturers design their craft with the jet nozzle above the surface of the water at plane speed because it requires considerably less horsepower to go fast. I have devised a simple back yard demonstration of the thrust difference between above and below the surface if you are interested. It involves a 5 gallon pail of water and garden hose with a nozzle attached. Simple but effectual.