# Fluid flow in pipe.

#### welshman2010

Hi,

I have what I'm sure is an easy question for a maths genius. However I need to know the answer for an insurance claim:-

"How much water in litres will flow through a 20mm pipe in one hour with the water pressure at 3 bar"

Any answers will be much appreciated.

Thank you

welshman2010

p.s. I hope I've posted this in the right section

#### hollywood

You might be able to find a table somewhere that gives flow rates for pipes of various sizes and various pressures. Once you get that, you just have to convert the units.

I think you need to know the length of the pipe. The water will flow more slowly through a longer pipe, right?

If you can't find a flow rate online, I think it's possible to calculate it. You'd need someone who knows more about fluid dynamics than I do.

- Hollywood

• welshman2010

MHF Hall of Honor
Hello welshman2010

Welcome to Math Help Forum!
Hi,

I have what I'm sure is an easy question for a maths genius. However I need to know the answer for an insurance claim:-

"How much water in litres will flow through a 20mm pipe in one hour with the water pressure at 3 bar"

Any answers will be much appreciated.

Thank you

welshman2010

p.s. I hope I've posted this in the right section
The equation that gives the volume, $$\displaystyle V$$, of fluid flowing through a pipe in time $$\displaystyle t$$ is:
$$\displaystyle V = \frac{\pi P r^4 t}{8\eta l}$$
where:
$$\displaystyle P$$ is the pressure difference between the ends of the pipe

$$\displaystyle r$$ is the radius of the pipe

$$\displaystyle \eta$$ is the viscosity of the fluid

$$\displaystyle l$$ is the length of the pipe

This is known as Poiseulle's Law.

So, you will need to know the length of the pipe and, to get an exact answer, the approximate temperature of the water (since this affects its viscosity).

You need to use the correct units to get a sensible answer. In the case you mention:
Pressure $$\displaystyle P=3$$ bar = $$\displaystyle 3\times 10^6$$ dynes per square cm

$$\displaystyle r = 1$$ cm (assuming the $$\displaystyle 20$$ mm refers to the diameter of the pipe)

$$\displaystyle t = 3600$$ seconds

At $$\displaystyle 20^o$$ C, $$\displaystyle \eta \approx 1\times 10^{-2}$$ dyne-sec per square cm

So I reckon that for a 1 metre length of pipe, this works out at about $$\displaystyle 4.2\times 10^8 \text{ cm}^3 =4.2\times 10^5$$ litres per hour.

If you double the length of the pipe, you'll halve the rate of flow.

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