To estimate the frictional losses you can use the Darcy–Weisbach equation:
$$h_f = f_D \frac{L}{D} \frac{V^2}{2\,g}$$
This head-loss ($h_f$) can be added to Bernoulli's equation:
$$h - h_f = \frac{V^2}{2\,g}$$
In this case the length ($L$) is the same as your height ($h$) so these equations combine like so:
$$h - f_D \frac{h}{D} \frac{V^2}{2\,g} = \frac{V^2}{2\,g}$$
$$V=\sqrt{\frac{2\,g\,h}{1+f_D\frac{h}D}}$$
To get the friction factor ($f_D$) you need the Reynolds number:
$$Re=\frac{V\,D}{\nu}$$
And then you can look it up on the Moody Chart
Plugging our equation for $V$ into our Reynolds number equations we have:
$$Re = \frac{D}{\nu}\sqrt{\frac{2\,g\,h}{1+f_D\frac{h}D}}$$
$$Re=\frac{70mm}{1.0035\frac{m^2}s}\sqrt{\frac{2 \bullet 9.8\frac{m}{s^2} \bullet 3 m}{1+f_d\frac{3m}{70mm}}}$$
$$Re=\frac{81707}{\sqrt{0.0233+f_d}}$$
Now we need two more things to use the Moody Chart, a roughness value ($1.3 \mu m$ new to $30\mu m$ used) and an initial guess.
So lets pick an initial guess of $Re= 10^5$. Looking at the Moody Chart that would give us a friction factor of about 0.023 for a new pipe.
$$Re_{new}=\frac{81707}{\sqrt{0.0233+0.023}}\approx 380000$$
Looks like we were too low. So when we look up the friction factor for the new Reynolds number we get about 0.0205.
$$Re_{new}=\frac{81707}{\sqrt{0.0233+0.0205}}\approx 390000$$
This is about as much accuracy as you will get.
So now we can solve for flow rate:
$$Q=\frac{\pi}4 \nu \, D\,Re \approx 1300 \frac{L}{min}$$
Repeating the procedure for the rougher pipe yields:
$$960 \frac{L}{min}$$
One big warning of this analysis however, is that many pipes can get debris in them severely limiting their flow capacity. Rain gutters are typically as large as they are, not just to pass high volumes of water, but to allow debris to pass through them.
