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# Pipe Length Calculation

## Pipe Length Calculation

(OP)
Hi,

I'm trying to work out a formula for calculating the heat loss of hot air flowing through a pipe in cold air, so that eventually I can spec the length of pipe needed.
It's been a while since I'v done any thermodynamics so some help would really be appreciated. I've summarised the problem in the image bellow.

Thanks,

Matt

### RE: Pipe Length Calculation

Have you done any searching or research?

Try searching this site for heat transfer from pipe or look elsewhere and gems like this come up

https://www.engineersedge.com/heat_transfer/convec...

Be aware that many simple calculations assume fairly short pipes so pretty constant Delta T.

If your pipe is long or small then the impact on temperature will be greater and a "mid point" temperature will be less and less accurate. You might need to divide your pipe into sections and calculate heat loss / temperature loss to then modify the heat loss in the next section.

Wind velocity makes a massive difference compared to "still air" heat transfer so you need to figure that out.

hot air doesn't have a whole heap of mass so doesn't have a lot of thermal energy to lose. What is this for?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pipe Length Calculation

(OP)
Thanks,

I've been looking at a few things but have been confused about the effect of the moving fluid through the pipe. I've found similar things to what you sent in your link, but will there be different effects because the fluid is moving through the pipe? My initial idea was to "slice up" the pipe and calculate the heat change iteratively for each section, but presumably the mass flow rate would have no effect on this? Or am I missing something?

I thought for these calculations I would assume wind speed=0 and calculate a worst case scenario.

It's for a exhaust filtering system where I need to cool exhaust gasses enough to be able to pass through a carbon filter.

Thanks again,

Matt

### RE: Pipe Length Calculation

"My initial idea was to "slice up" the pipe and calculate the heat change iteratively for each section, but presumably the mass flow rate would have no effect on this?"

cp*mass_flow*delta_T is the net heat flow in the pipe, so each increment chunk of the pipe must have the same relationship to account for the heat loss through the wall of the pipe.

TTFN (ta ta for now)
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### RE: Pipe Length Calculation

(OP)
Okay, sorry if I'm being stupid.

So from the equations for heat transfer coefficients from the link given in the first reply I get the equation bellow. How do I link that with cp*mass_flow*delta_T ?

### RE: Pipe Length Calculation

I think you would be much better off with a proper air cooled heat exchanger or finned pipe.

Depending on your temperatures while mass flow will be constant density will increase and hence velocity decrease so you might need to reduce the size of your section.

You ate trying to do a variable rate thing using steady state equations which often needs sectioning.

Whilst in one sense your worst case is no wind in another you might find the temperature too low if you get a cold wind blowing.

If you want cooling, use a proper cooling device not bare pipe.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pipe Length Calculation

(OP)
Hi,

The pipe runs through a section of open air (although it is shielded top and sides from wind) so we wanted to calculate if this section of pipe allows sufficient cooling so were going to use this calculation to evaluate that. I'd really appreciate some help with it, although I'm sure in the end a proper heat exchanger will be the best solution!

Thanks,

Matt

### RE: Pipe Length Calculation

Just do it in energy

You should be able to get a heat flow rate in m2 and delta T. just chop you pipe into suitable sections, say 10m?

Then work out how much energy has left the pipe at some temperature ( estimate to start with)
Then work out what that energy means in terms of mass in that section. With flowrate you can work out the end temperature because you know the mass of air in that 10m section.

As I said you're trying to use steady state equations for a moving transient variable thing so you will need to do some iterations to get the numbers to work

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pipe Length Calculation

it sound like homework to me but i will still give ou a general advice aside from opening the text book:

For a straight pipe you use the log mean temperature difference. So the heat flux will work out to:

Q=h*A*((dti-dto)/ln(dti/dto))

where h is the combined heat transfer coefficient. If you got a steel pipe with no insulation then most of the resistance will be on the outside. Here its free convection that governs the equation. And free convection ALSO depends on the temperature so it becomes more tricky. I would try google "nusselt number natural convection horizontal cylinder calculator" and you could check this online calculator:
http://www.jalalalhajabed.com/eng/engineering-calc...

Bestregards, Morten

### RE: Pipe Length Calculation

(OP)
Haha, I wish it was homework, if it were homework I'd just not bother doing it!

### RE: Pipe Length Calculation

You should hire an Engineer who understands heat transfer, Trying to bootstrap this will cause many problems

### RE: Pipe Length Calculation

Can you let us in on some data such as

anticipated length
pipe size
inlet temp,
required outlet temp
ambient air temp
Gas density,
gas pressure
gas velocity (start)

Any simple equation will only get you to a ball park figure, but a lot depends on your temp range.

If you're coming in at say 400C and leaving at 50, there are too many changes,

but entering at 150, leaving at 120 is more amenable to using simple equations.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

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