What is the relationship between water stream diameter and distance from faucet?

[Corin511]

Homework Statement

Daphne goes to the kitchen for a glass of water. She turns on the faucet so the stream of water is laminar flow. She notes that the diameter of the water steam decreases with distance below the faucet assuming that the water exits the faucet of diameter D with speeds v0, find the diameter of the stream as a function of y.

2. Homework Equations

We have to create a step by stem reasoning for the solution of the problem.
So far we have come up with using:
Bernoulli's principle, continuity principle and and energy diagram.[/B]
Can anyone help break down this problem and actually explain what the principles actually do?

The Attempt at a Solution

 

[mfb]

What do you expect in terms of the water velocity, pressure and the amount of water flowing through the cross-section per time?