Rate of Vacuum Leak
Date: Summer 2011
I am an automotive diagnostic technician. A group of friends and I are discussing a phenomena with how on-board fuel control systems deal with "pirate air" (vacuum leak, air leak,
un-metered air leak, etc). We are coming up on the idea that even though the size of the leak (area?) may remain constant the amount it flows does not. The intake manifold acts as a low pressure (air) reservoir. Let us say at
idle there is 33kPa of pressure in said reservoir with a barometric pressure
of 100kPa. As engine RPM is raised initially pressure will increase but as the raise RPM is stabilized pressure typically drops, lets say to 28kPa, the flow of the leak will now increase, correct? I understand there are other
factors and am in no way fluent with fluid dynamics. But as a whole, is this
Yep, the pressure difference across an orifice (the hole) is the
primary determinant of gas flow, with the air flowing from high
pressure to low pressure, as you have described. It is not a linear
process though (e.g. if you double the pressure, you do not necessarily
double the gas flow / leak).
If you want to read more, I suggest you look up "fluid flow through an
orifice", which is essentially what you're talking about. There are
lots of resources on this topic.
Hope this helps,
A fine question, Matt.
This is probably relevant to you:
Also www.theleeco.com and other valve companies.
(They often give reference data on how much flow goes thru their valve when wide-open,
as a function of the pressure on each side.)
see Plot "For Air" on page 19 at the top
(The curves are strikingly non-linear!)
(never use water-flow curves to model an air-leak - they have completely different shape)
Some leaks are through relatively short, wide single passages.
Like the throat of a rocket nozzle, although not necessarily so well streamlined.
They tend to inject a jet-like stream of gas into their low-pressure side.
The gas accelerates into this trap-door-to-vacuum as fast as it can,
and the behavior is controlled by the mass and momentum of the gas.
(It's a lot like freeway traffic funneling through the one open lane around an accident.)
For hi-side to low-side pressure ratios greater than about 2.0,
The peak speeds at the throat actually approach the speed of sound.
The total flow is proportional to the hi-side pressure.
(The more gas there is, the more can fall into this hole).
So, surprisingly, the total flow is independent of low-side (downstream) pressure.
Into 40kPa or 0kPa, the flow from 100kPa will be the same.
It is said that pressure signals from the low side cannot propagate upstream
and have any effect on the hi-side or flow rate or pattern.
Other leaks are basically made of multiple leaks in series,
each with a pressure-ratio only a little over 1.0.
A thick rubber-wall hose with a pinhole or hairline crack
would fall into this category.
A toilet-paper filter from manifold to air would be the ultimate example.
I tend to call it a diffusive leak.
Think of it as a salmon-compatible stream:
so many intermediate surfaces for air-molecules to bounce off of,
and so much passage-width,
that the net speed is slower than sound
and some molecules actually can and do go upstream during the leak,
and the total flow can and does depend on downstream pressure,
being proportional to the difference between upstream and downstream pressure.
Longish open-end tubes tend to be in a similar category ,
or a category in between.
In between jet-like and diffusive is the Venturi-like leak:
a single throat with a pressure-ratio which is more than 1.1 but less than 1.8.
I am not so sure the flow varies just the way you are speculating.
Some leaks will vary, others will not.
I think the ones big enough to make a difference to the engine will often be jet like,
and then they would add a relatively constant current of air regardless of manifold pressure.
What is the typical big leak you see?
"Pirate air" might imply it's often a negligently open-ended tube.
I think these change with pressure, but slowly,
by a percentage maybe half of the percent change in the pressure ratio.
Try thinking it through with the presumption that the leak-flow does not change
(or changes < 20%) for 0-40kPa manifold pressure.
Even less for 28 to 33kPa.
See if that fits the engine behavior.
Yes, the amount of air leakage into an engine's intake system quite
clearly is not constant. This air leakage depends on two factors. The
first is the area of the holes where leakage is occurring, and second is
the degree of intake manifold vacuum. Although the leakage path area
is constant, the vacuum is definitely not, thus the volume of air leaking
varies strongly depending on manifold vacuum.
Inlet manifold vacuum depends primarily on throttle position and
engine RPM, and is highest at high RPM and closed throttle (such as
when descending a hill in a lower gear). In this situation, the motor is
acting as a pump, sucking air out of the manifold. But with a closed
throttle, the only air entering the manifold to replace that being sucked
out, is via the leakage you refer to. The result is a high manifold
vacuum, and greatest air leakage.
Opening the throttle (even a little) under the above conditions will allow
more air to enter the manifold, and this the degree of manifold vacuum
will be reduced. Similarly, even without opening the throttle, reducing
engine RPM will result in the engine sucking less air out of the
manifold, and thus also reducing vacuum. Either way... by either
opening the throttle, or by reducing engine RPM... manifold vacuum
and hence air leakage will be reduced.
As you were already hinting at, air leakage at low throttle openings and
higher RPM can be significant, and can upset the desired fuel mixture
and cause "trailing throttle misfiring". This is why most fuel injection
systems completely cut off all fuel being injected, whenever conditions
of a closed throttle and greater than about 2000 RPM are detected.
Laws of dry friction (of a bicycle tire in contact with the road)
The properties of sliding friction were discovered by experiment in the 15th
to 18th centuries and were expressed as three empirical laws:
Amontons' First Law: The force of friction is directly proportional to
the applied load.
Amontons' Second Law: The force of friction is independent of the
apparent area of contact.
Coulomb's Law of Friction: Kinetic friction is independent of the
But, Amontons' 2nd Law is an idealization assuming perfectly rigid and
inelastic materials. For example, wider tires on cars provide more traction
than narrow tires for a given vehicle mass because of surface deformation of
the tire.
 Dry friction
A highly pressurized bicycle tire will have less contact area with the
surface of the street than the same tire at a lesser pressurized level and
therefore will have less deformation, creating less braking friction. Under inflated tires have wider
contact with the road and therefore the case of the idealization of
Amontons' 2nd Law applies.
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Update: June 2012