Calculating Injector Flow rate

[joecar]

Marcin's spreadsheet is attached to this post (scroll down to bottom of post #1).

The math behind this is as follows (for those who want to know)...

Definitions

R0 = injector's rated flowrate measured at pressure P0
P0 = pressure at which the injector's rated flowrate R0 was measured (see Note below)
FP = regulator "base" gauge pressure

MAP = manifold absolute pressure
BARO = barometric absolute pressure = 101.3 kPa at sea level = 100 kPa approx. a little above sea level
MANVAC = manifold vacuum = BARO - MAP

gauge pressure = absolute pressure - BARO = value shown by pressure gauge
absolute pressure = gauge pressure + BARO

Pressure difference across an injector: this is the difference in the absolute pressures above and below the injector.

An unreferenced regulator has its pressure set constant; this pressure is FP (gauge) or FP + BARO (absolute).

A MAP-referenced regulator has a reference hose connected to the intake manifold,
so its pressure has MAP added to it; this pressure is FP + MAP (gauge) or FP + BARO + MAP (absolute);
with reference hose removed, this pressure becomes FP + BARO (guage) or FP + BARO + BARO (absolute).

The flowrate of an injector is directly proportional to the squareroot of the pressure difference across the injector (this is the Bernoulli pressure relationship).

Note on Injector Flowrate Measurement:
when R0 is measured on an injector flow bench, P0 is actually the pressure difference across the injector:
absolute pressure above injector = P0 + BARO; absolute pressure below injector = BARO; so then difference = P0.

Note regarding 1997-1998 Y-car:
The FPR is not MAP-referenced (follow the reference hose to verify it sees atmosphere/BARO).

Unreferenced Regulator (e.g. 1998-2002 F-car, 1997+ Y-car)

Pressure difference (of absolute pressures) across injector = (FP + BARO) - (MAP) = FP + BARO - MAP = FP + MANVAC

IFR = R0 * sqrt((FP + MANVAC) / P0) = varies/slopes with MANVAC

At the rail, absolute pressure is FP + BARO, so gauge pressure is FP.
--> Directly measure FP at rail with engine running (FP should be constant).

The spreadsheet calculates this equation (Example 1, post #3).

MAP-Referenced Regulator (e.g. trucks)

Pressure difference (of absolute pressures) across injector = (FP + BARO + MAP) - (MAP) = FP + BARO

IFR = R0 * sqrt((FP + BARO) / P0) = constant/flat regardless of MANVAC

At the rail, absolute pressure is FP + BARO + MAP, so gauge pressure is FP + MAP.

Remove reference hose, regulator is now exposed to barometric pressure (so MAP = BARO),
and rail absolute pressure is FP + BARO + BARO, so gauge pressure is FP + BARO.
--> With reference hose removed, directly measure FP + BARO at rail with engine running.

The spreadsheet calculates this equation at MANVAC=0 if measured FP + BARO is entered (Example 2, post #3).

Units

Rail pressure is measured in psi, and MAP or MANVAC is measured in kPa.
You need to convert one to the units of the other before calculating IFR.

Convert psi to kPa by multiplying by (100/14.5).

14.5 psi = 100 kPa

If injectors are rated in lb/hr:
convert lb/hr to g/s by multiplying by 0.125998 (can round to 0.1260).

1 lb/hr = 0.1260 g/s

If injectors are rated in cc/min:
convert cc/min to g/min by first multiplying by density of gasoline (typically 0.73 g/cc), and then dividing by 60.

1 cc/min = 0.0122 g/s (depending on density of gasoline)

[redhardsupra]

might wanna explain what P0 is, you have no idea how often do i get an email with 'so what do i put in where?' emails...

[joecar]

P0 is the pressure at which the injector's rated flowrate R0 is measured.

Note:
when R0 is measured, P0 is actually the pressure difference across the injector;
absolute pressure above injector = P0 + BARO;
absolute pressure below injector = BARO;
difference (above - below) = P0.

Examples:

An SVO 42 lb/hr injector is rated to flow 42 lb/hr at fuel pressure 43.5 psi across the injector;
so, by definitions (see post #1):
R0=42 lb/hr
P0=43.5 psi

Example 1 (unreferenced regulator):

Suppose measured rail pressure is 58 psi (gauge pressure), this is FP,
so, from post #1:
IFR
= R0 * sqrt((FP + MANVAC) / P0)
= 42 * sqrt((58 + MANVAC) / 43.5) <-- in psi
= 42 * sqrt((400 + MANVAC) / 300) <-- in kPa

As MANVAC varies from 0 kPa (0 psi) to 80 kPa (11.5 psi), IFR slopes upward.

Make sure MANVAC, FP, P0 have same units, and then calculate the IFR:
At MANVAC = 0.0 kPa (0.0 psi): IFR = 48.497 lb/hr = 6.111 g/s
At MANVAC = 80.0 kPa (11.6 psi): IFR = 53.088 lb/hr = 6.689 g/s

At MANVAC = 80kPa, you can see how vacuum "assists" the injector's flow rate by almost 10%.

Example 2 (MAP-referenced regulator):

Suppose, with reference hose removed, measured rail pressure is 58 psi (gauge pressure), this is FP + BARO,
so, from post #1:
IFR
= R0 * sqrt((FP + BARO) / P0)
= 42 * sqrt((58) / 43.5) <-- in psi
= 42 * sqrt((400) / 300) <-- in kPa
= 48.497 lb/hr
= 6.111 g/s

IFR is flat horizontal constant ("static") regardless of MANVAC.

Notice that this is the MANVAC=0 value calculated in example 1.

[Redline Motorsports]

Nice job guys! Great information!

Howard

[JezzaB]

Sounds like a great spreadsheet but the link is dead for me

Jez

[redhardsupra]

yea, that's why i hate direct links, and not pointing to the site that takes care of it :/
here's new linkage
http://www.marcintology.com/tuning/injectors.xls

[redhardsupra]

here's a new twist to injector fueling that i thought up yesterday:
AFR=Airmass/Fuelmass
Fuelmass=IPW * IFR

you got the formulas for IFR on top of this thread, i wanted to concentrate on the other contibuting member--IPW.

BIG QUESTION FOR PAUL/ROSS:
the IPW we can scan, is that the final IPW (after all modifiers, adders, offsets, etc), or is it IPW calculated to be needed to get desired AFR (pre-modifiers)?

if IPW is the 'premod' one, then we need to change
Fuelmass= (IPW+INJOFF) * IFR
in which case we could combine the two formulas with Fuelmass:
AFR=Airmass/(IPW+INJOFF)*IFR
and since we can scan for everything except the INJOFF, we could calculate it:
INJOFF=Airmass/(AFR*IFR) - IPW
once you have that, all you need to do is create a table just like the injector offset table (battery voltage vs manvac) use INJOFF as the data, and v'oile, you get an offset table.

does this make sense or am i completely off my rocker here?

[pkincy]

I wonder if as a group we could approach the mfgs through a retailer or wholesaler to get us offset tables.

It might be tedious but I can't imagine that Lucas, Bosch, etc. want this information secret if they are trying to sell fuel injectors.

Perry

[redhardsupra]

i've bugged every source on the planet i have an 'in' with to get this data, and no go. but then again maybe you got better contacts, so more power to you if you wanna to pry the data out of their cold dead hands

[WiseGuyZ06]

Im confused...