pintle vs. disc injector types

[Michael McBroom]

A70Duster at aol.com wrote:
> 
> The pintle type is pretty linear between 10% and about 80%.  At least with
> the pintle type, the fuel flow rate changes as the square root of the ratio
> of the different pressures.
> 
>                                Q2 = Q1 (P2/P1)^0.5

A follow-up to this, if I might.  In the turbocharged applications I'm
familiar with, a 1:1 fuel pressure regulator is used, which increases
fuel rail pressure in direct proportion to the increase in boost
pressure.  What I'm wondering is, if the presssure downstream of the
injector has increased by the same amount as the pressure upstream of
the injector, won't this affect the predicted outcome?  And if it will,
shouldn't a ratio of delta-Ps be used instead, where delta-P1 = [(fuel
rail pressure + atmospheric) - (atmospheric)] and delta-P2 = ([(fuel
rail pressure + atmospheric) + (boost * fpr ratio)] - [atmospheric +
boost])?  At a 1:1 fpr ratio, P2/P1 will equal 1, thus Q2 = Q1.  But at
a different fpr, which is a popular mod some folks use to increase fuel
flow, Q2 should increase, but only by the differential amount.  Right?

EG #1:

Given: 1:1 fpr
       0.8 bar boost
       Q1 = 300ml/min
       P1 = 3 bar + 1 bar (rail pressure + atmospheric pressure) 
       P2 = P1 + (boost * fpr ratio)

            P2 - (1 + 0.8)                   ([3 + 1] + [0.8 * 1]) - (1
+ 0.8)
Q2 = Q1 x (----------------)^0.5  =  300 x
(-----------------------------------)^0.5 = 300ml/min = Q1
               (P1 - 1)                               ([3 + 1] - 1)

EG #2:

Given: all of the above, but with a 2:1 rising rate fuel pressure
regulator

               ([3 + 1] + [0.8 * 2]) - (1 + 0.8)
 Q2 = 300 x (------------------------------------)^0.5 = 338ml/min
                         ([3 + 1] - 1)

-- 
Best,

Michael McBroom

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