(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An irrigation pipe of diameter 20cm carries water at an average speed of 0.1 m/s. By what factor must the pipe diameter be increased to achieve a flow rate of 1.00 m^3/min?

The answer given is a factor of 5.3.

2. Relevant equations

Poiseuille's equation

[tex] Q = Av_{avg} [/tex]

3. The attempt at a solution

I converted the desired flow rate to m^3/s by multiplying by 1/60. Then using Poiseuille's equation I did a bit of manipulation and came up with:

[tex] Q = \pi r^{2}v_{avg}[/tex]

[tex] Q = \pi(\frac{d}{2})^{2}v_{avg}[/tex]

[tex] d = 2\sqrt{\frac{Q}{\pi v_{avg}}}[/tex]

Substituting in the desired flow rate I get an answer of 0.46, which is a factor of 2.3. Which isn't 5.3.

I actually realize this method is wrong from the get-go, as [tex]v_{avg}[/tex] is a function of diameter. And this is where I am stuck.

Thanks in advance.

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# Homework Help: Flow rate problem

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