Pushing water down a pipe

[PeteThePen1]

Hi Everybody

I am not sure if this is the right place to post, but here goes anyway.

Context
I am starting to work on the design of the monotube boiler for the canoe project discussed elsewhere on this site and now logged on the Mono-tube.org.uk site. The engine I have is a Stuart Turner Cygnet minus any pumps. Given that the size of the engine is known it is possible to draw up a table of the amount of water the pump(s) would need to deliver at a range of engine speeds and boiler pressures. Using the SBA's Steamboat Register one can find details of the mono-tube boilers for the two listed canoes. Snipe has an engine of 1.5” X 1.625” and a 'coil' of 50ft of 5/16 cunifer brake pipe. Taniwha has a Cygnet engine (2.25" X 2") and a 'coil' of 36ft of 1/4" s/s (which has subsequently been replaced by a somewhat longer length). Both boats have been successful steamers for some years. Snipe is wood fired using supermarket compressed woodwaste logs while Taniwha uses a pot burner fueled by paraffin (kerosene). Having had a long history of domestic wood burners and a dislike of the smell of paraffin I am oriented towards the Snipe design.

The Problem
My calculations of the steam required for the Cygnet show that it is rather more greedy than Snipe's engine so that a straight copy of the boiler might not be sensible. Additionally, the mono-tube tradition of feeding cold water into the coils closest to the exhaust and extracting the useful steam from the coils closest to the fire is not happening in the Snipe boiler layout. A possible solution to that is to wind the pipe is a series of rectangular flat coils (the casing is rectangular not round) perhaps using a smaller bore for the cold water and adding two larger bore sections in the evaporation and post evaoration stage.

It strikes me, as a non engineer, that the limitation on this model will be how much water can be pushed into the smallest bore pipe and how much pump pressure is required to do that.

The (not quite) Solution
That wonderful information source the Internet and its 'super intelligent' daughter ChatGPT suggested that I need to use the Darcy-Weisbach equation. The latter offered the following definition:
"The Darcy-Weisbach equation is as follows:

ΔP = (f * (L/D) * (ρ * V^2)) / 2

Where:
ΔP is the pressure drop (input pressure - output pressure)
f is the Darcy friction factor
L is the length of the pipe
D is the inside diameter of the pipe
ρ is the density of the fluid
V is the velocity of the fluid

To solve for the input pressure, we rearrange the equation:

P_in = P_out + (f * (L/D) * (ρ * V^2)) / 2

Given your requirement of supplying 7.55 litres of water per minute (Q) down a 15.24 m long pipe, we can calculate the velocity (V) of the water using the following formula:

V = (Q / (A * 60))

Where:
Q is the flow rate in m^3/s (convert litres/min to m^3/s by dividing by 1000)
A is the cross-sectional area of the pipe (π * (D^2) / 4)

To calculate the input pressure required for each of the three pipe sizes, we need to determine the friction factor (f) for each pipe. The friction factor depends on the pipe roughness and flow regime, but for relatively smooth pipes, it can be estimated using empirical correlations such as the Colebrook-White equation:

1 / √f = -2 * log10((ε / (3.7 * D)) + (2.51 / (Re * √f)))

Where:
ε is the pipe roughness (assumed to be small for smooth pipes)
Re is the Reynolds number (ρ * V * D / μ)
μ is the dynamic viscosity of the fluid

[But when asked to do the actual calc ChatGPT decided to use a constant for F of 0.04]

With the given information, we can proceed with the calculations for each pipe size. We'll assume water at standard temperature and pressure for the fluid properties."

Some Parameters
D = 0.00334 [3/16" pipe]
Q = 0.000125833 cu/M/sec
L = 15.24M [50 ft]
P_out = 1 Bar
p = 1,000 kg/cu/M
μ = 0.001 kg/M/s
f = 0.04
A = 0.0000087651
V = 0.239269239

The Issue
The answer offered by ChatGPT appeared to be sensible (94.4782 bar) but being unwilling to just accept that I worked through every stage in a spreadsheet. Doing that identified one error in the evaluation of one of the parameters and substituting ChatGPT's figures into the final formula produced a completely different answer.

So can anybody familiar with this tool let me know what is going wrong? The basic data comprised a 3/16" pipe (3.34mm ID) in a length of 50ft (15.24 M) and a water requirement of 16.51 lbs/min (7.55 litres/min) output at 125 PSI and 500 RPM.

If I can get my head around this then I can correct my spreadsheet and sort out whether using smaller bore preliminary pipe is sensible, whether more tube than 50ft in (say) 1/4" will work, etc. The Darcy-Weisbach equation certainly looks as if it will be a useful tool.

Thanks for reading this far.

Regards

Pete

[dampfspieler]

Hi Peter,

... So can anybody familiar with this tool let me know what is going wrong? The basic data comprised a 3/16" pipe (3.34mm ID) in a length of 50ft (15.24 M) and a water requirement of 16.51 lbs/min (7.55 litres/min) output at 125 PSI and 500 RPM.

your calculations are wrong. The CYGNET will only use 892,22 ml/min (0,892 l/min), look to the sheet below.

Wasserverbrauch CYGNET_Peter.png (68.4 KiB) Viewed 10246 times

Your question is therefore irrelevant, because it was based on the wrong assumptions and water pipes with an internal width of 6, 7 and 8 mm are perfectly adequate.

This may not be the answer you were hoping for, but I hope it's helpful nonetheless.
---
Dietrich

[PeteThePen1]

Hi Dietrich

Many thanks for the post and the information. I am always happy to have my mistakes pointed out though slightly mbarassed that I should have got the water requirement figure wrong. That is not a difficult item to calculate (if one is paying attention!)

I will update everybody with what I have learned so far in case it is useful, but we are going our just now.

Regards

Pete