Help with fluid dynamics

[CLB]

I am way outside my comfort zone with this topic so would appreciate some help if possible.

I have a fuel system for my outboard that currently uses 8mm ID fuel line and connectors with circa 6mm ID. The outboard uses a maximum of 12 litres per hour.
I want to put a valve in the system that requires me changing the pipe work to 6mm ID. I am sure this will be OK, but the valve has an ID of 4mm. Will that allow enough fuel to flow?

My research leads me to believe that ID, flow rate and velocity are interlinked and the fuel will simply flow faster to achieve the 12 lph rate required, but it can't be that simple can it? Surely there is a limit to the how small the pipework can get before it restricts flow to less than 12 lph.

I could just give it a go, which is probably what I'll do if I can't find an answer here, but I would like to be able to understand the physics of it if possible.

 

[cpedw]

Don't worry. My calculations suggest that 4mm diameter is plenty big enough.

According to a Rule of Thumb in Coulson & Richardson's Chemical Engineering vol 6, velocity of liquid in pumped pipelines should be 1 to 3 m/s.

Your case of volumetric flow rate of 12 l/h is 12/1000/3600 = 3.3*10^-6 m3/s [1000 litres in a cubic metre, 3600 seconds in an hour]
Velocity times pipe cross sectional area (CSA) gives volumetric flow rate. Aiming for 2m/s, CSA=3.3*10^-6/2=1.67*10^-6 m2.
Diameter is then √(4.CSA/pi) = 0.0015m or 1.5mm.

Looking another way, the velocity through the 4mm diameter is 3.3*10^-6/(pi.diameter^2/4) = 0.26 m/s

SO the pipe is comfortably oversized.

 

[lw395]

You should also look at the pressure drop.
The fuel pump may not like it.
There's an online calculator for this somewhere...

 

[TNT]

Low flow = high pressure
High flow = low pressure.
The pump will be the issue, can it cope with the incresed demand, ie, it will need to work harder to get the same amount of fuel through.

 

[CLB]

Don't worry. My calculations suggest that 4mm diameter is plenty big enough.

According to a Rule of Thumb in Coulson & Richardson's Chemical Engineering vol 6, velocity of liquid in pumped pipelines should be 1 to 3 m/s.

Your case of volumetric flow rate of 12 l/h is 12/1000/3600 = 3.3*10^-6 m3/s [1000 litres in a cubic metre, 3600 seconds in an hour]
Velocity times pipe cross sectional area (CSA) gives volumetric flow rate. Aiming for 2m/s, CSA=3.3*10^-6/2=1.67*10^-6 m2.
Diameter is then √(4.CSA/pi) = 0.0015m or 1.5mm.

Looking another way, the velocity through the 4mm diameter is 3.3*10^-6/(pi.diameter^2/4) = 0.26 m/s

SO the pipe is comfortably oversized.

Thank you for your comprehensive reply. That's the best thing about these forums, there is such a broad range of expertise. I cannot claim to understand any of what you said, but the last line brings me some comfort

You should also look at the pressure drop.
The fuel pump may not like it.
There's an online calculator for this somewhere...

Low flow = high pressure
High flow = low pressure.
The pump will be the issue, can it cope with the incresed demand, ie, it will need to work harder to get the same amount of fuel through.

Thanks for the heads up. I guess I won't know unless I try it.

 

[VicS]

Thank you for your comprehensive reply. That's the best thing about these forums, there is such a broad range of expertise. I cannot claim to understand any of what you said, but the last line brings me some comfort





Thanks for the heads up. I guess I won't know unless I try it.

I go along with cepdw's calculations. I did similar calcs and came to the same conclusion.


The length of the 4mm section will be short if its just the bore of the valve so the pressure drop will be small. I suppose it should be possible to calculate that too but its outside my comfort zone.

 

[cpedw]

I suppose it should be possible to calculate that too but its outside my comfort zone.

Indeed it's possible. It is late and I'm tired so I may get this wrong but let's try...
The worst case is complete loss of dynamic pressure through the constriction, the 4mm bit of valve (in practice, there will be some pressure recovery as the fuel slows down in the wider pipe downstream of the valve). The dynamic pressure is 0.5.density.speed^2.
Let's take density of fuel as 800kg/m^3. Speed worked out above was 0.26m/s so pressure loss is 27Pa.

To give that some context, static pressure change is given by density.g(9.81m/s^2).height change so 27Pa=800.9.81.height change. The pressure loss in the 4mm constriction is equivalent to 3.4mm change of fuel level in the tank (worst case calculation but that's ignoring pressure loss in the rest of the pipe - could be significant if it's several miles long). I think you're safe as you are.

Derek

 

[reeac]

The greatest constriction in the system must be at the carburettor jet ....if that's much less than 4 mm. diameter then you should be OK.

 

[CreakyDecks]

Instead of buying new hose, fittings and doing an hour's work, why don't you just buy a 5/16" valve instead of the 1/4" one?