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Turbulent flow on a plate element

Turbulent flow on a plate element

Turbulent flow on a plate element

(OP)
Hi,

I am trying to find the force on a (possibly infinitely large) stationary plate element in all directions when hit by a jet from a given angle. The jet is from a propeller/thruster on a ship hull.

If the jet is normal to the plane, i get a force equal to:

F = (Density * Jet_Area * Avg_velocity) * (Avg_velocity)
    (  These combine to a mass flow   ) * (   Speed    )

With the jet at an angle, the force normal to the plate would be :

Fn = sin(angle) * F

Here I have not considered friction, and i can't find a way to incorporate friction into my equations in order to get forces paralell to the plate.

I also wonder if the first equation should have some factor to consider that the jet spreads out after hitting the plate.

And how does dynamic pressure/stagnation pressure work in this case?

I sincerily hope someone can help me shed some light on these topics, especially if my current formulaes are close to correct, or completely wrong..

RE: Turbulent flow on a plate element

Liquid's force parallel to the plate skin shouldn't be higher than the liquid's shear stress (the measure of liquid shear stress is viscosity) x area of liquid in contact with the plate. (I think, I think)

http://virtualpipeline.spaces.msn.com

"What gets us into trouble is not what we don't know, its what we know for sure" - Mark Twain

RE: Turbulent flow on a plate element

(OP)
And shear stress should be possible to find from the velocity field of my jet, right?

I really want to get this working without creating a CFD program :)

Any thoughts on the formula for force from the jet?

RE: Turbulent flow on a plate element

Shear stress = (dynamic viscosity)*(dV/dy)

Calculating dV/dy: ah, there's the rub!

" also wonder if the first equation should have some factor to consider that the jet spreads out after hitting the plate."

Yes.  And that factor is intimately related to shear stresses acting between the jet and the surrounding quiescent fluid.

RE: Turbulent flow on a plate element

(OP)
Hah,

That doesn't sound very easy then... Any chance that someone has already calculated a bunch of these factors for a water jet on a plane at different angles?

The thing is, I really just need approximate figures, around 25% error would probably be ok, and rules of thumb are good for calculation speed.

What I'm looking for is something like: "When the jet hits the plate at an angle of 45%, 70% of the momentum creates a force normal to the plane, 10% creates a friction force paralell to the plane, and 20% remains as speed in the jet, now racing along th plane"

Does anyone know of, or can point me towards sources for any information on this.

And thanks a lot to the two of you that has answered me already :)  

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