Fluid Physics Help: Find Water Distance at 10mm Diam.

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Homework Statement



Water flowing out of a 16-mm diameter faucet fills a 2L bottle in 10s. At what distance below the faucet has the water stream narrowed to 10mm diameter?

Homework Equations



A1v1=A2v2 Q=vA

The Attempt at a Solution


edit: this is what I TRIED to do:(*note: i ignored some unit conversions at this time)

Q=2L/10s=2x10^-3 m^3/s.

v= Q/A = 2x10^-3 m^3/s / pi(5mm)^2 = 2.54x10^-5

x=vt = 2.54x10^-5 * 10s = 2.54*10^-4.
lol this is so wrong, it doesn't make any sense.
 
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Discussion

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The presumption is that as the water falls it will narrow because of it's increase in speed?

Calculate the velocity of the water coming from the opening - 2 liters flowing through the area of the opening in 10 seconds - and then figure what velocity will be required to flow through an area that is reduced to 10 mm. That velocity should occur from gravity at v² = Vo² + 2 g*x where x is the distance below shouldn't it?