is the study of exactly what you'd expect - the flow of
fluids where the effects of compression on the flow are significant.
This can include anything from high pressure gas delivery systems to
shock waves around supersonic jets, and is much more involved than the
few results relevant to my work that I will presents here. Let's first
take a look at an "incompressible flow," which is probably more
familiar in our daily lives. Image a pipe with water flowing through
it, and half way down the length of this pipe, it's diameter shrinks so
that it has only half of the cross-section of rest of the pipe.
1: Variable Diameter Pipe with Water Flow
understand that over any time period, the same volume and mass of
water passes through the cross-section of the wider section of pipe as
the narrower section of pipe. This volume is the product of the
cross-section of the pipe times the distance that the water travels in
that time period. We also understand that since the cross-section of
the narrower pipe is smaller than of the wide pipe, that the water must
then travel a longer distance over the same period of time, and
therefore is going faster than the water in the wider section of pipe.
This is why putting your thumb over the mouth of a garden hose causes
the water to come out much faster, but is only indirectly related to
why all the people around you are upset about being wet.
look at a similar example, but with the effects of
compressibility included. Let's take the same length of pipe as before,
but use air and put a pressure on the inlet that's greater than
atmospheric pressure but less than 1.89 atmospheres of pressure (ATMs.)
Fig. 2: Variable
Diameter Pipe With Unchoked Flow
Under these conditions,
if we increase the pressure on the inlet side,
more air will flow through the pipe. This makes sense and is consistent
with the previous water in pipe example. Now, let's increase the
pressure at the inlet to 1.89 ATMs.
Fig. 3: Choked Flow
These conditions are
specially chosen because they cause a choked flow,
which has some unexpected properties. The first difference is that the
air at the throat (the narrowest part of the pipe) will be traveling
at the speed of sound, and will form a shock wave. The second and most
important difference is that as long as the inlet pressure stays above
1.89 times the outlet pressure, the flow rate will only be a function
the inlet pressure and the throat cross-sectional area. Under these
conditions the throat may also be referred to as a critical orifice.
This is significant because the conditions at the outlet can change
(varying outlet pressure, longer pipe or tubing, kinked tubing, etc)
and the flow rate will remain unchanged. This is a very useful result
in applications where constant flow rates are necessary despite
changing outlet conditions. Think of gas welding, where the flow rates
of the welding gas and oxygen are carefully set to correspond to the
work that's being done, but longer tubing may be used or the tubes may
kink. If the welding regulator is designed to have a critical orifice
in it, then the gas delivery rate will not change unless the pressure
from the regulator is changed.
result of compressible flow occurs if the pipe from
our example expands again to its original diameter some distance after
Fig. 4: Expanded Flow
The shock wave
still occurs at the critical orifice, however, unlike in
the incompressible flow example, the flow increases in velocity after
the constriction. This seems counter-intuitive to our every day
experience, but this the same principle that rockets or any supersonic
nozzle works on.
[ Back to Main
Comments? Suggestions? E-Mail me at MyElectricEngine@gmail.com
Copyright 2007-2010 by Matthew Krolak - All Rights
Don't copy my stuff without asking first.