Deriving Bernoulli's Equation for Steady Flow in a Faucet

[bray d]

[SOLVED] Bernoulli's Equation Prob?

Homework Statement

EXACT PROBLEM:
Water emerges from a faucet of diameter 'd' in steady, near vertical flow with speed 'v'. Show that the diameter of the falling water column is given by D = d[v^2/(v^2+2gh)]^(1/4), were 'h' is the distance below the faucet.

Homework Equations

I'm not positive where to start but I think Bernoulli's Equation may have something to do with it:

pressure+.5(density)(velocity)^2 + (density)(gravity)(height) = pressure+.5(density)(velocity)^2 + (density)(gravity)(height)

maybe the conservation of mass plays a role:
velocity * area = velocity * area

The Attempt at a Solution

I'm terrible at deriving equations. Once I get started I can usually take off but I need that first little push to get me goin. Looking at this problem I see we have the initial diameter, and initial velocity. The water falls due to the acceleration of gravity, creating a higher velocity, and thus a smaller area due to the conservation of mass eqn. That all makes sense to me but I don't really see where I can make any equations out of it. Maybe this is wrong, I need a good understanding of what it happening before I can dive in and try to create the proof.

 

[andrevdh]

use this relationship

...

maybe the conservation of mass plays a role:
velocity * area = velocity * area

...

and consider the water to be in free fall in order to determine the velocity of the water when it has fallen through a height h below the fuacet.

 

[bray d]

thanks!