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Underwater Jet Dispersal Rates

A long lance 38mm ID mounted vertically into a pool the last 300mm of the lance is bent 45 deg, so the end of the lance is 305mm above the pool floor.

It is supplied by a submersible pump that is 1m below the pool surface and provides 3.5m/s and 4.25 l/s

I'm trying to figure out how far the water jet will travel in the water, before losing all its momentum
i.e. How far would the water disperse the larger mass of the pool.

The lances function is to disturb and plume a silt like layer of material that is approx 80% dead plant algii
Pond 95 by 35 m by 5m deep

What would the result of doubling the flow to say 9 l/s?

Would fitting a nozzle or several small nozzles to the lance head improve the dispersal rate?

Any other optioneering thoughts would be most welcome? Would an educator be a better method for example?

Also if you could explain your workings as much as possible.

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Solution Preview

Here (below) are the governing equations, from which you will be able to re-arrange the variables (by simple algebra) and solve for items that you are interested in changing or evaluating.

Please carefully consider that your plume of silt/algii is the primary body that is "reacting" the momentum of the volume of fluid that exits the lance. Therefore, by "F=m*a", this is a transient problem. In other words, the increment of time over which these two different fluid volumes interact is an important component for your understanding.

So, you will want to treat your plume as stationary, and your lance fluid volume as being in flux.
And, you will need to take some educated guesses about the effective mass properties of your plume at the depth/elevation of the outlet of the lance.

Conservation of Momentum:
In general-
sum of all external forces acting on the control volume of fluid, which is exiting your lance,
F_ext = m * a

m = mass of the fluid volume
a = acceleration of the fluid volume

F_ext = m * (d/dt * v)

v = velocity of fluid volume
m = (rho)*(dVol)
rho = fluid density
rho = (gamma)/(g_n) ...

Solution Summary

This solution explores the fluid mechanics of interactive flowing and stationary fluid volumes. It also provides the governing equations for applying Newton's Second Law of Motion to the fluid mechanics in step-by-step calculations using Bernoulli's equation.