What is the diameter of each hole in the shower head?

[Galactium]

Homework Statement

In a low-flow showerhead that contains 18 nozzle holes, the volume flow rate of the water is 4.00 L/min and the water maximum speed is 2.70 m/s.

What is the diameter of each hole? Do not ignore viscosity of water.

Homework Equations

Q=Av_max
Q=((pi)r^2)v_max
Q=(pi(r^4)/8nl)*(deltaP)
v_max=2Q/(pi(r^2))
d=2r

3. The Attempt at a Solution
Given:
Q:4L/min = 6.6667E-5 m^3/s
v_max=2.7 m/s
v_average=v_max/2
v_average=1.35 m/s
n(vescosity):8.90E-4

I am not quite sure where to start, I used the v_max equation, but I got the wrong answer. I know at some point I may need to divide by 18 for one nozzle.

 

[Chestermiller]

What is the volumetric throughput rate per hole? What is the average velocity through each hole? How is the average velocity per hole related to the volumetric throughput rate per hole?