How Does Tube Diameter Affect Reynolds Number in Gravity-Driven Laminar Flow?

[emac8585]

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Consider the fully developed laminar flow due to gravity of water in a vertical circular tube. Assume atmospheric pressure at inlet and outlet. Show that the relationship between diameter and Reynold's number is

D = (32*Re*v²/g)^⅓

I know that Re = ρvD/μ

I was thinking that perhaps I have to use Bernoulli's equation,
v₁²+P/ρ+gz₁ = v₂²+P/ρ+gz₂

But beyond that I'm not sure. Thanks in advance!

 

[boneh3ad]

@emac8585 So what are the things you know about laminar flows and any flow where the Reynolds number makes sense. Then compare that with what you know about Bernoulli's equation and the requirements for its use.