Reactive thrust of submerged waterjet

Hi,

I'm sure that this question has been posted before in many different guises but ......

I am looking at a jet propulsionpositioning system for a small floating platform. I have calculated the thrust issued from an array of water jet nozzles.

I know what forces I want to act on the platform and roughly what drag is present.

I want to work out the reactive thrust developed by these submerged nozzles? Reviewing rocket equations is fine but they are all firing exhausts into an immovable ground plane and receiving an equal & opposite reaction. My waterjets are firing into a body of water (they are submerged below the platform) and I'd like to get a lead on how to work out the resultant reactive force received by the platform.

Any ideas?

Many thanks in advance.

 

I'm sure Baeckmo will be along with the magic formula in a mo ,however you have not made it clear if these are actually deeply submerged nozzles ,or commercial waterjets at rest,and therefore in a submerged state.The two will not behave in the same way.

 

Reactive thrust

Anthony,

thanks for prompt reply. The nozzles are positioned flush with the bottom surface of the platform and angled at 20deg below this horizontal plane. I can't deeply submerge them.

Many thanks

Mark

 

Well after that point I am out of my depth but I'm sure that information will be helpful to the hydrodynamicists when they arrive. Bit like buses really ,you wait all day for one and then they all arrive together.

 

I'm probably wrong but I believe Newtons laws of action reaction apply. It doesn't matter what the jets push against, air, water, etc. it's the reaction that make the propulsion.

Thrust should be the same above or below the waterline.

Steve

 

Feel the thrust from a garden hose with your thumb at the end. Adjust the speed of water exiting and feel the equal and opposite motion, then feel the less thrust when doing the same experiment under water.

 

It's the counter pressure of the water diminshing some of the jet velocity so smaller nozzles help.. anyway so me thinks.. waiting also to hear some real expertise.

 

Of course it is, the water absorbs the velocity therefore no equal velocity.

To every motion is an equal and opposite motion.

 

I have a feeling you're all going to get a good telling off in a minute.

 

Ha ha,-- probably.

 

Yes it will work, and no, it isn't an good way to power a vessel.

V=body velocity, Vj=jet velocity, rho=mass density, A= jet nozzle area

mass flow rate= Q = rho*Vj*A
change in velocity = (Vj-V)
Thrust = change in momentum = T= Q*(Vj-V)
Useful work done on the hull= T*V
Work (kenetic energy) required to accelerate jet internal to the hull= 1/2 m del v^2 = 1/2*Q*(Vj-V)^2
effeciency = eta = useful work/total work = T*V/(T*V+1/2*Q*(Vj-V)^2)
reducing
eta= 2V/(Vj+V)

So we can see that to have maximum efficency Vj=V which means T=0 or A = infinity. And we haven't even started talking about real fluids and internal losses.

What it really means is that a similar sized propeller external to the hull is far better than having a hole through the vessel.

 

you're probably right anthony, thats why I started with "I'm probably wrong" but....

I've been down this road before. A looong time ago on an island far away the US Navy posted a fleet of Pegasus Hydrofoil Gunboats....

http://wn.com/Pegasus-class_PHM_hydrofoil

I was a vendor to the Naval detachment on that island and I had opportunity to tour the first vessel to arrive just hours after she docked.

I asked the Captain if the power would be more efficient if it "pushed" against water instead of air because the waterjet nozzles are on the transom and not submerged. This launched a discussion involving the previously long deseased Mr Newton and of action reaction with examples of why spaceship's work in space with rocket nozzles "pushing" against a vacuum.

I was told reaction was same / same and it was the reaction that caused the motion and what it "pushed against" was irrevelant.

But...like I said, "I'm probably wrong"

Steve

 

Realisticly you aren't pushing against a vacuum, you are pushing against the mass you are expelling. Think of a projectile gun recoil...it is caused by the throwing (i.e. changing the momentum) of a small mass really fast.

For the really geeky, see if you can come up with what happens if you change from an axial jet (as describe above) to a right angle one (like a Tees White Gill thruster or Hero's engine).

 

Will check these thrusters tomorow. reading this on my mobil. Best explenation I once read was on a jet site that mentioned the waterjet only took flight when someone took it out of the water and pointed the nozzle on the water surface hitting it. Action reaction? forget now why but that was easy to understand for me, will read the form tomorrow. JH, have a thought on a pulsed (hard to get a pulse but thrust may ne up?) waterjet?

 

JH is right in that a large slow moving prop is good for bollard pull .However don't disregard the jet, in this respect ,they punch well above their weight in static thrust, The reason for this is that a good waterjet ,when stationary ,can absorb in excess of 90% of engine revs and power,{to the limits of cavitation},whereas a standard propeller needs to advance in order to do this.