# Volume through a pipe



## Chris Scott (Jan 2, 2008)

I'm not sure if I'm asking this question correctly, not being an engineer or physicist. Hopefully it's close enough to be understood. What is the increase in flow/volume through a pipe if the ID of the pipe is increased?

My Garratt has a restricted exhaust creating considerable back pressure limiting its performance; 2 1.7mm ID exhaust pipes combine into 1 blast pipe the same 1.7mm ID. I want to increase the diameter of the blast pipe so its flow/volume is approximately equal to the flow/volume of both exhaust pipes. If I remember correctly the flow/volume is nonlinear to the increase in pipe diameter. 

2 questions;
1. What is the ratio of diameter increase to increase in volume?
2. What should the diameter of the larger blast pipe be?


----------



## rklopp (May 19, 2014)

To a first approximation, make the diameter of the single combined pipe equal to the square root of 2 times the diameter of the incoming pipes. The keeps the area constant. Thus, the single pipe should be approximately 2.4 mm diameter.


----------



## Chris Scott (Jan 2, 2008)

rklopp said:


> To a first approximation, make the diameter of the single combined pipe equal to the square root of 2 times the diameter of the incoming pipes. The keeps the area constant. Thus, the single pipe should be approximately 2.4 mm diameter.


1.7 +1.7 = 3.4 mm
3.4 x 2 = 6.8 mm
SR 6.8 = 2.608 mm

?


----------



## TonyW (Jul 5, 2009)

What type of Garratt do you have Chris? If it is an Accucraft NGG16 you could just take the "blast pipe" (which it most certainly is not) out of the smokebox and, err..., throw it away! That will improve performance no end.

If you want to improve further, as I did with mine, replace the entire exhaust system pipework with something bigger. I think I used 3/16th OD tube. The result was: Gas consumption reduced, water consumption reduced, longer running time, more pulling power, increased top speed.


----------



## toddalin (Jan 4, 2008)

2.4042 mm diameter

(1.7 mm / 2)^2 x pi x 2 = 4.5394 mm^2

4.5394 mm^2 = pi r^2

1.4450 mm^2 = r^2

1.2021 = r

D = r x 2

D = 2.4042 mm


----------



## Chris Scott (Jan 2, 2008)

toddalin said:


> 2.4042 mm diameter
> 
> (1.7 mm / 2)^2 x pi x 2 = 4.5394 mm^2
> 
> ...



Todd; 
I probably missed something but could not duplicate your result with your formula. I cannot explain it but through primitive trial and error (little Excel help) at this; 

((1.7 mm / 2)^2 x pi)^2 x 2 = 2.404 mm

I'm not absolutely sure I copied the cell functions correctly

I wanted to duplicate the equation in Excel for future use and because I made a mistake originally; remeasured the ID is 1.9mm = 2.687mm (hopefully correct.) 


Thanks for the help.


----------



## Chris Scott (Jan 2, 2008)

TonyW said:


> What type of Garratt do you have Chris? If it is an Accucraft NGG16 you could just take the "blast pipe" (which it most certainly is not) out of the smokebox and, err..., throw it away! That will improve performance no end.
> 
> If you want to improve further, as I did with mine, replace the entire exhaust system pipework with something bigger. I think I used 3/16th OD tube. The result was: Gas consumption reduced, water consumption reduced, longer running time, more pulling power, increased top speed.


Tony;
I'm more into finesse than brute force.  

Besides, with the prices of metals so high why use more pipe than needed. 

I can accomplish the fix by simply boring out the existing Tee fitting to ~2.7mm and adding a Regner 5x5,0mm F/F coupling with a ~3.0mm ID blast pipe. Down the road somewhere sometime I'd like to try fitting a mini approximation of a Lempor exhaust to the Garratt so I'm saving all the hard rework effort for that and then. Crazy? Yes. But aren't we all?


----------



## TonyW (Jul 5, 2009)

Sorry Chris, I didn't realise that 12 inches of copper tube had a cost issue.

Before and after, with the tee bored out as you suggested:









And won't a Lempor exhaust create even more of the back pressure you are trying to avoid? Draughting a gas-fired loco causes combustion issues too.


----------



## zubi (May 14, 2009)

Folks, do not make it more complicated than it has to be. Area twice as large requires diameter larger by a square root of two.
Chris, if you wish to know more about flow through constricted pipe, there is a lot of physics there. For incompressible fluids (which steam strictly speaking is not) you can start with Bernoulli's principle: https://en.wikipedia.org/wiki/Bernoulli's_principle One nice application of this is the so called Venturi effect - probably still used to measure speed on aeroplanes for one example: https://en.wikipedia.org/wiki/Venturi_effect
Best wishes from Tokyo, Zubi


----------



## toddalin (Jan 4, 2008)

Chris Scott said:


> Todd;
> I probably missed something but could not duplicate your result with your formula. I cannot explain it but through primitive trial and error (little Excel help) at this;
> 
> ((1.7 mm / 2)^2 x pi)^2 x 2 = 2.404 mm
> ...



You said diameter of each pipe is 1.7 mm


The area of a circle is pi x r^2 (or r**2 in a spread sheet). I used the caret to denote superscript (squared), as is common practice.

Diameter is twice the radius.

1.7 mm dia / 2 = 0.85

0.85^2 (or 0.85**2, or 0.85 x 0.85) = 0.7225 mm^2 (or mm**2)

pi x 0.7225 = 2.2698 

There are two pipes so we double the value.

2.2698 x 2 = 4.5396 mm^2

If the pipes were different diameters, or there were a different number we would calculate each separately and add them up.

So we want to replace these pipes with one pipe with an area of 4.5396 mm^2

Again, the area of a circle is pi x r^2

4.5396 = pi x r^2

Divide both sides of the equation by pi

(4.5396 / pi) = ((pi x r^2) / pi)

1.4450 = r^2

So the square of the radius is 1.4450 mm and the radius is the square root of 1.4450 mm, or 1.2021 mm.

The diameter is twice the radius.

2 x 1.2021 = 2.4042 mm


Yes, 2.687 mm is the correct answer for two 1.9 mm pipes.


----------



## Chris Scott (Jan 2, 2008)

zubi said:


> Folks, do not make it more complicated than it has to be. Area twice as large requires diameter larger by a square root of two.
> Best wishes from Tokyo, Zubi


Todd;
Zubi is right, simple is better.

2^2 * ID =

Try it.

Thanks, Zubi


----------



## Kovacjr (Jan 2, 2008)

Chris a single 3mm pipe will not fix the problem. I put twin 1/8" piped on Stans and it was fine. The real issue is that the burners on his will not make sufficient steam. It only maintains 20-25 psi when running. The rear engine is a direct from the cab line unsuperheated.


----------



## Chris Scott (Jan 2, 2008)

Kovacjr said:


> Chris a single 3mm pipe will not fix the problem. I put twin 1/8" piped on Stans and it was fine. The real issue is that the burners on his will not make sufficient steam. It only maintains 20-25 psi when running. The rear engine is a direct from the cab line unsuperheated.



Somewhere between the gas can and the burner flame there's a problem. No way around it. You just haven't found the problem yet. No one said the problem is steam pressure. I get 80psi (factory operating spec.) with the factory exhaust and wet steam to the rear engine, same as Stan's. I'm sure Tony's Garratt (above) makes plenty of steam. The factory exhaust causes the Garratt to waste a lot of water and gas, and appear sluggish - still very beautiful - but has nothing to do with low steam pressure. Low steam pressure I've always traced to the fuel path. Most common probably is only one burner lit or missing something in looking for the cause.


----------



## HMeinhold (Jan 2, 2008)

I think I have to throw a monkey wrench into these calculations. It is not the total area which determines the flow resistance of two pipes, it is the radius/diameter. The resistance goes with the power of 4 of radius/diameter. So two pipes with the same area as the larger pipe still have more resistance, see: 
https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation
Regards


----------



## zubi (May 14, 2009)

Henner, you are correct of course, but Chris asked how to calculate the diameter which conserves flow. Flow conservation is conserved when area is conserved. Area is conserved when two pipes of diameter R are replaced with one pipe of diameter sqrt(2)*R or in other words 1.41*R. From Hagen–Poiseuille equation which you refer to you can calculate that the actual radius Chris needs is somewhat less than 1.41*R. I just wish Accucraft engineers had the necessary experience and know-how or knew how to calculate required diameters prior to production... Best wishes from Tokyo, Zubi


----------



## HMeinhold (Jan 2, 2008)

Zubi,
as you know of course, flow is also affected by the pressure difference (or loss). You always want to minimize this. As I pointed out, the larger tube with the same area as two smaller tubes has actually less resistance. I am currently looking into this, while I design the boiler for my ride-on Climax.
Regards


----------



## TonyW (Jul 5, 2009)

Kovacjr said:


> The rear engine is a direct from the cab line unsuperheated.


That will be a Batch 3 loco then, the same as mine. Batches 1 and 2 had superheat for the rear engine.


Chris Scott said:


> I'm sure Tony's Garratt (above) makes plenty of steam.


It does. Safety valves are set for 60psi and it will easily maintain 55psi+ while running.


Chris Scott said:


> The factory exhaust causes the Garratt to waste a lot of water and gas, and appear sluggish - still very beautiful - but has nothing to do with low steam pressure.


Exhaust back pressure kills them. They are the only loco I have ever come across that run faster with the cylinder drain cocks open (because then there is no back pressure).


----------



## zubi (May 14, 2009)

HMeinhold said:


> Zubi,
> as you know of course, flow is also affected by the pressure difference (or loss). You always want to minimize this. As I pointed out, the larger tube with the same area as two smaller tubes has actually less resistance. I am currently looking into this, while I design the boiler for my ride-on Climax.
> Regards


Henner, Let's forget your Climax for a moment and get back to this poor Garratt. The Hagen–Poiseuille equation is just too beautiful to leave Chris without more complete answer to his question. Let us take a look at the pipe in the photo which Tony shows a few posts above. There are two sections of this pipe: shorter one L1=5cm and longer one L2=25cm. Now, the resistance of the longer pipe is actually five times greater than that of the shorter pipe. And the pressure drop is five times greater on L2 than on L1. This makes a very unbalanced design. One of the principles of good design is balance. I guess every plumber knows the Hagen–Poiseuille equation and applies it in daily practice, apparently there are not enough plumbers in China or in the UK - wherever this Garratt was designed... Anyway, back to the pipes. In order to make this design balanced from the point of view of flow resistance, the longer pipe diameter should be greater than the diameter of the shorter pipe. By a factor of quartic root of five, which simply equals 1.5. That means that the diameter of the longer pipe should be 1.5 times that of the shorter one. This is what Tony suggests, more or less. Except that he made the shorter pipe also to have larger diameter, which brings us to 'square one' - his design is again unbalanced. Now what does this teach us in the context of the original question which Chris asked? Well, combining two flows (two pipes) into one flow (one pipe) increases the flow by factor 2. Chris wants to enlarge the exhaust pipe, because the exhaust pipe as it is, is of the same diameter as L1 and L2. But quartic root of two is only 1.2. Assuming that the exhaust pipe is short, say as short as L1, the real culprit is the long pipe L2. This is because the resistance on that pipe is 1.5 greater! So suppose that we sorted things out, and we replaced L2 with a pipe 1.5 times the original diameter. Then what Chris still needs to do to keep the resistance the same along the pipes - he needs to replace the exhaust pipe (lets make it of length L3) with a pipe of a diameter (2*L3/L1)^(1/4) or in other words quartic root of times two the ratio of L3 to L1. Please notice that _if_ the length of the exhaust pipe L3 is 0.84*L1 or less, there is no greater resistance on this exhaust pipe than on L1 (or the enlarged L2). So any exhaust pipe shorter than 84% of L1=5cm will be fine (i.e. 45mm or less), even if it has the same diameter as L1. I hope I made myself clear..., now back to your Climax;-)! Best wishes from Tokyo, Zubi


----------



## TLR (May 9, 2015)

Hi first post here, why don't you use 2 exhaust pipes instead of 1 then the back pressure caused by the shorter exhaust will not have any bearing on the longer exhaust pipe, I would follow TonyW and increase both diameters as shown in the picture, after all being gas fired it is of no consequence to drafting.

Shaun


----------



## Chris Scott (Jan 2, 2008)

TLR said:


> Hi first post here, why don't you use 2 exhaust pipes instead of 1 then the back pressure caused by the shorter exhaust will not have any bearing on the longer exhaust pipe, I would follow TonyW and increase both diameters as shown in the picture, after all being gas fired it is of no consequence to drafting.
> 
> Shaun


Articulated (2-6-2--2-6-2) the Garratt has two exhaust pipes merged into one blast pipe. Two blast pipes is an option but with a single stack one blast pipe is preferable. The exhaust pipes and blast pipe just have to be of the right size.


----------



## TLR (May 9, 2015)

As you only have a single chimney then a swept tee bringing the two exhaust pipes together is one option or blend the two exhaust pipes into one or another is to use the two exhaust pipes and bring the petticote pipe down to the level of the the blast pipes,that will allow you to still use a single chimney.


----------



## TonyW (Jul 5, 2009)

Chris Scott said:


> Two blast pipes is an option but with a single stack one blast pipe is preferable.


If your Garratt was fired by coal or internal alcohol I could understand why a blast pipe is important, but I'm struggling to see the relevance if it is not.

As supplied in gas-fired form the Accucraft Garratt, like all commercial gas-fired locos, has a great big hole in the bottom of the smokebox which is (a) essential to the correct operation of the gas burners, and (b) going to stop any partial vacuum being formed by the blastpipe.

If the hole is sealed and a blastpipe is installed then a partial vacuum will be created and it will attempt to draw the fire from the gas burners. This is not good: The burners will keep going out, or the gas combustion will be incomplete and will produce little heat but lots of unpleasant fumes.


----------



## bille1906 (May 2, 2009)

Lots of good (and technical) info here
1. no need for a blast pipe in poker burner engines, in fact, it just pulls heat from the tubes out the stack
2. exhaust piping can'r be too small
3. the longer the pipe, the more restriction you will have

One thing I found is that exhaust systems without a blast pipe have little or no risk of bad leaks and if they do, it doesn't hurt anything. Because of that, tube size can be increased merely by cutting the existing pipe close to the source and attaching a larger pipe either with silicone tubing or by sliding the next size over it. I use K&S
in non-metric sizes and often just slide a 5/32" over a 1/8" without soldering it. I would assume metric tubing is similar but if it isn't the short length of silicone tube will do the trick.
Making a new tube and fittings is the best way to go but many don.t have the skill or the tools to do that.


----------



## TLR (May 9, 2015)

TonyW I wasn't advocating making the smokebox airtight, just offering a few ideas to allow the use of a single chimney. I agree with you as can be seen from my first post.

Shaun


----------

