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There is a rain pipe in a house. I want to know how many cubic meter rain water can flows through the given pipe in a minute. I need to know the maximum capacity of the pipe. In other words: How many liter water can pass through this pipe in one minute.

Data:
Pipe diameter: 70mm
Pipe length: 3000mm
Pipe angle: 90°
Height of the top hole: 3000mm
Height of the bottom hole: 0mm
Pipe material: Copper
Time: 1 minute
Fluid: Water

Can anyone describe me or suggest me an online tool to calculate that?

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  • $\begingroup$ What have you looked for so far? What size pump? What material for the friction factor? Surface roughness? $\endgroup$
    – Solar Mike
    Mar 21 '18 at 8:24
  • $\begingroup$ @Solar: I made some changes. I hope I gave enough info. $\endgroup$
    – Solarinoos
    Mar 21 '18 at 8:38
  • $\begingroup$ A search gives online calculators such as pipeflowcalculations.net/pipediameter.xhtml $\endgroup$
    – Solar Mike
    Mar 21 '18 at 9:37
  • $\begingroup$ Or this one : pipeflowcalculations.com/pipe-valve-fitting-flow/… $\endgroup$
    – Solar Mike
    Mar 21 '18 at 9:37
  • $\begingroup$ The first tool wants me an input that I am exactly looking for: "volume flow rate". Can you help me please how to use it? The second link is too complex for me. Thanks anyway. $\endgroup$
    – Solarinoos
    Mar 21 '18 at 11:39
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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.

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