Solving Flow Rate Problem to Increase Pipe Diameter by 5.3

[Andrusko]

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

$$Q = Av_{avg}$$

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:

$$Q = \pi r^{2}v_{avg}$$
$$Q = \pi(\frac{d}{2})^{2}v_{avg}$$
$$d = 2\sqrt{\frac{Q}{\pi v_{avg}}}$$

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 $$v_{avg}$$ is a function of diameter. And this is where I am stuck.

Thanks in advance.

 

[Irid]

Probably you need to assume something like "The force of pump, which drives the water around, is constant". Then you get, by Bernoulli's law:

$$F = PA = \frac{A\rho v^2}{2} = \text{const.}$$

Thus, the new velocity is

$$v_2 = \sqrt{\frac{A_1}{A_2}} v_1$$

 

[Andrusko]

Okay, I'm just getting more and more confused.

Apparently the solutions were wrong and the actual answer is 1.52. Now I can't get this as an answer no matter what I do with the problem, when I had it coming out before to 5.3.

Can someone else please do the problem and tell me what factor of diameter increase they get? It's kinda urgent, the test on this stuff is in a matter of hours.