

Fuel Pressure Regulator Flow  
John Estill Buickv6@prodigy.net


Introduction  
Several months ago Cal Hartline posed a question about the capacity of the fuel pressure regulator and the return line. That got me thinking and got my calculator working. Did a bunch of calculating, and with help from Cal and from Todd King I think we've got some reasonable results. We haven't actually proved this on a real live car (as far as I know at least), but I thought I'd share this with everyone anyway.
So, the question is, what is the limit of the fuel return line? At what point is the line too small? What about the regulator, when is it too small? 

Background  
Basically, the fuel rail is at some pressure fixed by the fuel pressure regulator. The tank is at atmospheric pressure or something pretty close to it. The difference in pressure between the two is the driving force that pushes the fuel through the regulator and return line to the tank.
The pressure drop from rail to tank is taken up in two parts. One part is in the return line. The fluid loses pressure as it flows through the line. The faster the fluid flows, the greater the pressure loss. The other part of the pressure drop is in the regulator. The total pressure drop from rail to tank is fixed (at a given rail pressure), and whatever pressure drop is not taken up in the return line is taken up by the regulator. For example, if the rail is at 35 psig, and the return line has 10 psi of pressure drop, the regulator has to have 25 psi drop across it so that the 10 psi line + 25 psi regulator = 35 psi from rail to tank. The regulator opens up just enough so that the pressure at the outlet is just the amount needed to push the return flow through the line. In doing so, for a given flow rate it can have a variable pressure drop. Say it needs to flow 50 gph; if the regulator is 20% open it will have a high pressure drop, if it is 50% open it will have less pressure drop, if it is 100% open it will have the lowest possible pressure drop. Think of it as a variable pressure drop device. The return line will have a certain pressure drop at some given flow rate. The regulator can have a variable pressure drop at a given flow rate depending on how open it is. If the return flow is 20 gph, and the regulator needs 30 psi drop, it opens up just the right amount to give 20 gph at 30 psi. That might be 20% open, it might be 50% open, it might be 90% open. Of course, the regulator can be 100% open, but once it gets to that point things aren't "in control" any more. When it gets to 100% open, then for a given flow rate the rail pressure is the sum of the regulator 100% open pressure drop + the return line pressure drop. The rail cannot be at a lower pressure than that, because that would mean there isn't enough pressure to push the flow rate needed through those two pieces. 

The "Problem"  
So anyway, a few months ago the discussion was on double pumpers. With the stock fuel lines both pumps cannot be run unless you're at WOT, otherwise the pressure in the rail rises uncontrollably and you go too
rich. So a Hobbs switch is used to turn on the second pump once some boost pressure is reached. Cal wondered if the fuel pressure could not be controlled due to a limitation of the fuel pressure regulator or a limit in the return line. Working with Todd and Cal I did some calculations and a little experiment. First I tested my Kenne Bell regulator. I'll leave out the details on that experiment, but let me say that you can describe the behavior of a wide open regulator with this equation: pressure drop = specific gravity x (gpm/Cv) squared. Cv is a constant that describes the relationship of the regulator's wide open pressure drop to the flow through it. I did an experiment and got a Cv of 0.504 for my Kenne Bell regulator. Knowing the Cv of the regulator, we can calculate the 100% open pressure drop for any flow rate we want. We can also calculate the pressure loss in the return line. If we set a flow rate, and we know the physical properties of the fluid (density, viscosity), and we know the diameter and length of the line, then we can calculate the amount of pressure loss from one end to the other. This is subject to some estimations and simplifications though. For example, anywhere there is a coupling where the diameter might change a little bit, or where there is a hose instead of a line, I didn't take into account. Plus the gasoline properties I used may not be exact. Anyway, the return line pressure drop plus the 100% open regulator drop is the absolute lowest fuel rail pressure that you can have. Here's the numbers for the stock 5/16" return line with the Kenne Bell regulator:
So suppose you've got a single intank stock pump. At idle the flow is about 40 gph, and the engine is using about 0.5 gph, so 39.5 gph has to be returned to the tank. We see from the list above that the minimum rail pressure for that flow is about 9.1 psig. Since we run the rail at 3540 psig, that is no problem at all, we're well above the minimum. Now we upgrade to a high performance single intank pump. This is flowing about 65 gph at idle. All but 0.5 gph must be returned to the tank, and we see from the list above that the minimum rail pressure for that flow is about 2223 psig. We are still running the rail at 3540 psig, but we can see that we are closer to the minimum possible rail pressure. The regulator is a lot more open now than before, but it is still in control. Now we go to the double pumper. With both pumps on, at idle, trying to keep the rail at 40 psig, the flow is about 100 gph. Again almost all of that has to be returned to the tank. But we look at the minimum rail pressure and we see that the minimum possible pressure for that flow is 52 psig. We cannot set the rail pressure to the 40 psig we want, even if the regulator is wide open the rail pressure will jump to the minimum pressure. It can't go any lower and still flow that 100 gph. This was confirmed by both Todd and Cal, they both reported that the rail pressure in their cars jumped to 5060 psig when the second pump was switched on at idle. 

The "Solution"  
So what is the solution to the problem? Well, I won't say it's a exactly a problem, there is today's solution which is to run off one pump and have a Hobbs switch turn on pump #2. With just one pump running you can control the idle rail pressure. But wouldn't it be great if you could roll up to the starting line and turn on pump #2, not have to worry about it coming on at just the right time so you car doesn't either get a rich spot from coming on too early or go lean because came on too late (or didn't come on at all)?
The problem is not the regulator, the problem is the return line. Here is a table of flow rates and pressure drops for a 100% open regulator and 5/16" return line:
Obviously the return line, with it's much higher pressure drop, is the problem. At 100 gph, the regulator is responsible for only 7.6 psi of the total 52 psi drop from rail to tank. The return line has 44.4 psi drop! So what happens if we replace it with a 6 AN line, which has an inside diameter of 3/8"? Then the minimum rail pressure is:
Now you can see that if the double pumper at idle needs to return 100 gph, then the minimum possible rail pressure is 10.3 psig, so in theory you can turn the regulator all the way down to that pressure. Since we normally set it at 40 psig or so, then we should be able to have both pumps running and have the regulator control it, even at idle! Isn't that great! Well, maybe it is a solution in search of a problem, but I think it is a good idea anyway. The "Right" way to run a double pumper. Like I said at the start of this dissertation, to my knowledge neither Todd nor Cal has actually tried this out yet to make sure it works like I described, but I'm 95% confident that this is correct and fairly accurate. 

The Feed Line  
On a related issue, the feed line. A lot of people were a little disbelieving when Ron J. said he could support 1000 hp through a stock feed line with a double pumper. While that is not the "Right" way to do it, with a big enough pump you *could* do it. The regulator/return line has a fixed pressure difference to work with. The feed line doesn't, you can keep raising the pump discharge pressure (by adding pumps or installing bigger and better pumps) to get more flow. Here's some pressure drops and flow rates for the feed line, which is 3/8" and has an id of (I believe) about 0.315":
Joe Lubrant's chart on the web site says that to run 9.0 @ a BSFC of 0.5 in a 3700 lb car you need 1005 hp and 81 gph of fuel. Looks like the pressure drop of the feed line in that range is only 4.6 psi. Not too bad. I'd say that if the pump can put up that much flow at the required rail pressure, the stock feed line would work. On the other hand, that pressure drops above do not include the fuel filter, which probably offers a good bit of restriction. Anyway, let's crunch some numbers. Let's set the WOT rail pressure at 65 psig. Looking at the double pumper pump curves that are on the web site, at 65 psi the pumps are putting out about 80 gph. At that rate there is 4.6 psi difference between rail and pump outlet. So we add 4.6 to the rail pressure of 65 psig and get 69.6 psig, which we round off to 70 psig. That is what the pump is really pumping against (not including filter!); and at 70 psig the pump is really doing 75 gph, not 80. This tells us that if we had a larger feed line, we can pick up some flow. At the same rail pressure of 65 psig, with a larger feed line we could have up to 80 gph, so that feed line is costing us 5 gph. Since we are getting 75 gph, it looks like we are going to miss our 1000 hp fuel rate we needed. Sounds like a double pumper is pretty borderline for 1000 hp. Maybe with a bigger feed line, and big enough injectors that you can run at a lower rail pressure (60 psig at WOT?) and still get the fuel you need... And of course the 81 gph is at a BSFC of 0.50, if you want to run a little more conservative you need some more fuel... I don't think I'd recommend it. But I would not say that it is impossible! The limit is going to be the pumps though, not the feed line. Well, I'm done. Hope somebody got a little something out of all this! 
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