MRM:
Bernouli does not apply for supersonic flows over a body.  Shockwaves form in front of the body, instantaneously changing flow properties (pressure, temperature, etc.) from what are "freestream" to the properties over the body.  However, I do believe that it is still a valid equation once the shock is negotiated.   James John's: Gas Dynamics provides excellent explanations on this question as well as other equations that I'm sure will benefit you.  Hope this helps.

There is a "compressible form" of Bernoulli's equation for cases where Mach No > about 0.3. In such conditions density cannot be assumed to be constant.

FYI:
Compressibilty effects are not seen until M ~ 0.8.  Not sure where M > 0.3 would come from.

So you're saying that as you reach high velocity, i.e. Mach 0.8 or so, the air density changes (because of the compression)?  Adjustments to Bernoulli eqn can be made and it can still be used for approximate calculations?

Bernoulli's principle is valid for all fluids.  The atmosphere follows those principles when a body is travelling through it until the airflow reaches the speed of sound.

Air acts as a fluid and therefore is incompressable at speeds below the speed of sound but when a body travels at speeds approaching the speed of sound, the air speeds up to reach the speed of sound, and compresses.  It is then no longer a fluid and does not follow Bernoulli.

The point at which this first occurs on an aircraft is called the aircraft's critical Mach number (Mcrit).  Aircraft flying at speeds between where the airflow reaches Mcrit, and becomes fully supersonic are of most concern.  This range of flight is called the transonic range, and presents problems for aircraft designers.

The figure of M=0.8 is a guess at the speed at which Mcrit is reached.  The actual figure would depend on the aircraft.  In the early days of high speed flight, Mcrit was a closely guarded secret, and the guesstimate of 0.8 was often used.

There is further info available at http://www.rmcs.cranfield.ac.uk/aeroxtra/dtchispflt.htm

If you would like to see some pics of various aircraft flying in the transonic range then go to http://www.eng.vt.edu/fluids/msc/gallery/conden/pg_sing...

Glenn

www.metalbashatorium.com

GRUE:
Two points....

"Air acts as a fluid and therefore is incompressable at speeds below the speed of sound.."

How can you say this?  Where did you go to school?  Air (or any other gas for that matter), although behaves as a fluid, is extremely susceptable to compressibility effects!

...the air speeds up to reach the speed of sound, and compresses.  It is then no longer a fluid and does not follow Bernoulli.

Again, where do you come up with this?  You're saying that compressed (pressurized) air is not a fluid???  Explain to me how air at SSL is "compressed" compared to that at 50,000 ft, but each remains a "fluid".

MRM:
As for making "adjustments" to Bernouli, I'm not sure what you mean.  As stated earlier, when dealing with the trans/supersonic regime, the change in density MUST be accounted for.  You may not arbitrarily just increase the air density and then assume it to be constant.  It will not work.  You must have a state 1 density and a state 2 density.  For example, at M=1, the density ratio (rho/rho stagnation) is 0.6339 or roughly 63% at state 2 when compared to state 1. This is a significant change compared to a ratio of 0.9563 at M=0.3.

Regards,

aerobab,

Perhaps, in answering MRM's question, you would like to explain, briefly, in simple terms, what changes occur to the airflow over an aircraft as it approaches the speed of sound.

Was I wrong in saying that "The atmosphere follows those principles when a body is travelling through it until the airflow reaches the speed of sound."

Perhaps I should have have stated in the paragraph to which you refer: when air flows over a body at subsonic speeds it acts as a fluid (does not compress as a result of the flow around the body), however when the body approaches the speed of sound (M1), the air flowing around it speeds up to reach M1.  When this occurs the air undergoes compressibility affects and is no longer acting as a fluid.  Further explanation is available in the link.

I appologise if did not make it absolutely clear that I was referring to airflow around a body.
 
Glenn


www.metalbashatorium.com

Piston theory has been used for many years for high supersonic flows and it's derivation comes from solving the linearized form of the full potential equation and using Bernoulli's equation......look in any basic aerodynamic text.

There seems to be a lot of "loose talk" on this and other posts, mostly arising from the need to provide simple answers to people who have not had the benefit of a comprehensive course in fluid/aero-dynamics. To say that compressibility effects are not seen until M ~ 0.8 is an oversimplification; when the flow past an immersed body approaches M 0.8 shock waves can appear - the grossest of compressibility effects! It should be noted that when a bit of air flows past a body it may suffer compression (if it goes close to a stagnation point) or expansion (and reduction of density) if it flows close to the upper surface of a lifting wing. Even at M=0.3 the pressure changes are measurable - the density changes may be small but they are detectable - stagnation density is 5% above static in an airflow at M = 0.3.

GRUE : air is a fluid until it is cooled to a solid or (I think) until heated until it is a plasma. Air will act as a fluid for all but hypersonic Mach Numbers. Generally, it is a gas, but gas and liquid both qualify as fluid. For engineering puposes, liquids are usually assumed to be incompressible and would comply with Beroulli's (incompressible) equation provided their vicosity is sufficiently small. Gases are also assumed to be incompressible for "low Mach Number" flows. I chose M~0.3 as my boundary between low and high Machs - others may set the mark higher - it depends on the level of accuracy you need to maintain.

Hi Fellows!

I wonder why the maximal speed of the fascinating and famous WWII SPITFIRE stopped at 780 ~ 850 kmph, has something to be related with subsonic and transonic regimens structural implications !?

Of course an aeroplane will fly always in the middle of a wonderful vital fluid: air: (Otherwise, we will have crash accident situation against some solid, mountain, or into the space, with no fluid surrounding it, what-so-ever). Don´t forget to go back to visit the Basics, once for while.
Cheers, and Merry Christmas to All.
zzzo    

I find the terminology "incompressible" and "compressible" ambiguous.  In the fan/blower business we mostly deal with relatively low Mach No.s and often treat flow as incompressible to simplify some calculations.  However, we are also aware and take account of the static pressure and therefore density changes as air flows over and through (mostly closed) systems.  Effectively we recognise that air/gas is compressible even at low Mach No.s.

I am aware of the effects that occur as flow over a body or through a passage approaches Mach 1 and that this is generally referred to as compressible flow but since I rarely have to deal with this am a little light on the theory of what then happens.  I have presumed that Bernouli still applies behind the shock wave.

The back of any gasdynamics textbook would tabulate (for air) the effects of Mach number on pressure and density.
At Mach 0.3 (as has been stated in posts above), the ratio of static pressure to total pressure is about .94, and about .95 for the density.
For any serious calculations, the relationship of mass flow rate to pressure for airflow above Mach 0.3 should use compressible flow equations, not Bernoulli's equation. I once made this mistake and seriously miscalculated cooling airflow to a gas turbine component.

daveleo

First have an understanding of reynolds numbers and how they
relate to fluid (air) speeds.Then it will be easier to comprehend high speed fluids.