How can I find the mass of the object being held up by the water?

[5mmgridbok]

Hi, I was wondering if anyone would be able to help me with this problem:

Homework Statement

I have a mass, that is being held in the air by several downwards pointing jets of water. I know the diameter of the nozzles from which the jets are flowing, and the flow (Q) from each jet, which is the same for each jet. The water is being provided by a pump.
How can I find the mass of the object being held up by the water?

Thank you

Homework Equations

Continuity
Bernoulli equation
Momentum (ΣF (external) = ρQ(Uout-Uin)

where Q is the flow

The Attempt at a Solution

Say I have n nozzles.

I thought this might be an equation I could use:

nF-mg = ρQ(Uout-Uin)

where F is the force provided by each of the jets.
But I'm unsure as to how to proceed.

I've attempted using the Bernoulli equation to find out the maximum height, but don't seem to be getting anywhere.

 

[strive]

From the nozzle diameter calculate the exhaust water velocity:
water_volume/nozzle_area

water_velocity * mass_flow = force_of_jet (at height 0 (at nozzle exit))

Use the equation for vertical throw to calculate where the force of jets and mass*g amount to 0
(i take it your mass is given and this is what you have to do)

note: Here is presumed that the entire kinetic force is being transferred to your mass (othervise subtract the remaining velocity)...

This is 1 way to do it but at least 2 exist to my knowledge