Need help with a fluid system debate -Bernoulli

[Zooomer]

I am debating with a group in a message forum about fueling an engine.

Currently there is a pump running to a filter. The filter has two outlets, one returns fuel through a 60psi regulator then to the tank. The other outlet runs to the front of a car. All lines are 5/16". The fuel rail is 9/16" in diameter and 14" long and there are 4 injectors.

The debate is that they are claiming that the injector on the end of the fuel rail will put out the least fuel and starve that cylinder of gas. The solution proposed is to not return the fuel from the filter but to run all the way to the rail, then out the other side of the rail and back to the regulator before dumping in the tank.

This didn't make any sense to me as I proposed the fuel pressure would remain the same at all spots in the rail.

I figure it falls under Pascal's law or Bernoulli's principal

 

[gmax137]

The relative flow rates through the four injectors will depend on the exact geometry of the rail and also on the overall flow rate. Also, whether the injection is constant or intermittent (timed). But I think you are probably more correct than the others. They are likely relying on their 'intuition' which tells them the flow 'will follow the path of least resistance.' This intuition is misleading and really not correct.

Look for 'manifolds' in fluid mechanics textbooks to see how these are treated mathematically. One thing to realize is that the pressure in the manifold (rail) downstream of a given branch may increase due to the deceleration (since some fluid exits through the branch, the velocity in the (constant area) rail drops, and this raises pressure).

Also, friction losses in your 14 inch long, 9/16 diameter rail are going to be negligible relative to the losses in the long smaller diameter line from the filter to the rail.

 

[Zooomer]

This is what they are saying is happening and I told them it's not possible:

http://www.stevetek.com/Images/Figures/stockFuelSystem.gif

The explantion
"Notice in figure 1 that in this case the fuel pressure sender is in the small diameter restrictive section of the delivery system. Now the diameter of the fuel rail is much larger than the fuel line leading up to it. So when the injectors are at a high enough duty cycle as to approach the maximum capacity of the preceding delivery system, the pressure in the fuel rail will see a drop off at each successive injector as indicated by the wavy blue lines. There will be enough pressure to deliver sufficient fuel for the first two cylinders and probably the third. But the last cylinder (#1) will be starved and thus risks a lean condition. "

 

[rcgldr]

The pressure in a pipe only drops when there is flow, due to friction between the walls of the pipe and the fluid, and due to viscosity within the fluid. This pressure drop is small since the flow through that last fuel injector is momentary and also small compared to the related flow in the relatively large diameter fuel rail. Due to harmonics and momentum of the fluid, it's possible that at certain frequencies of injector operation, the pressure is actually higher at that last injector.