- #1
Andrusko
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Homework Statement
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.
Homework Equations
Poiseuille's equation
[tex] Q = Av_{avg} [/tex]
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.