what is the meaning of sonic point, mathematically & physically. is something to deal with sonic rarefaction?

The spatial location where the fluid reaches Mach one. It could also refer to the physical state of the fluid where sonic point is reached.

why only Mach one?

At mach one, fluid velocity = sound (sonic) speed, hence called sonic point.

colud you please explain to me this:-

fluid velocity = sound (sonic) speed

Hi,

The ratio of the velocity of the body/object to the local sound speed is the non-dimensional number called Mach(after the Austrian Physicist Ernst Mach). When the Mach number is less than 0.3(which is the case with liquids)all density variations can be neglected and the flow is treated as incompressible. Beyond that value compressiblity effects have to be taken into account. Then the flow can be either subsonic or transonic or sonic or supersonic or even hypersonic based on the different values of Mach number. Normally the flow is termed subsonic when M<1 but flow is termed transonic when Mach no lies anywhere between 0.75 to 1.2 and sonic when M is 1,supersonic for 1.2<M<5 and beyond which the flow is hypersonic. This no. might slighly vary. Physically Mach no describes the appearance of compressibility effects(hence need to solve the time dependent continuity eq as a part of the solution)and the associated changes in the flow(wrt shock waves). Catch hold of a good book on gas dynamics/compressible flow(Liepmann and Roshko for gas dynamics and A. Shapiro on compressible fluid flow)

hope this helps

Half the message got cut! Normally the flow is termed subsonic when M<1 but flow is termed transonic when Mach no lies anywhere between 0.75 to 1.2 and sonic when M is 1,supersonic for 1.2< M <5 and beyond which the flow is hypersonic. This no. might slighly vary(there is no precise cut off). Physically Mach no describes the appearance of compressibility effects(hence need to solve the time dependent continuity eq as a part of the solution)and the associated changes in the flow(wrt shock waves). Catch hold of a good book on gas dynamics or compressible flow(Liepmann and Roshko for gas dynamics and A. Shapiro on compressible fluid flow)

As stated before the sonic point is the place in a flow where the fluid velocity LOCALLY rises above the speed of sound (i.e. goes above Mach 1)

This is important for a couple of reasons. Downstream of the "sonic point" in the subsonic flow the partial differential equations that we use to predict the flow behaviour change from being "elliptic" to being "hyperbolic" in nature.

This means that pressure waves (which travel at the speed of sound max.) can no longer propagate (travel) upstream (against the supersonic fluid flow) and "shock waves" occur at the sonic point. This is caused by the pressure waves collecting at the interface between the subsonic (Mach < 1) and supersonic (Mach > 1) flow. The pressure at this point changes by a great deal over a VERY short distance and therefore can be very damaging.

The location of the sonic point in a flow depends mainly on the fluid velocity and therefore for flows that were initially subsonic, at a contraction or point of low pressure (top of wing) the fluid velocity can rise to above the velocity required for supersonic flow, and shock waves therefore occur at that point.

Theres a lot of good introductory stuff to CFD and fluids on the NASA website somewhere, it's been mentioned a couple of times on this website.

Hope this helps

Dr. Bob

can you explain

Downstream of the "sonic point" in the subsonic flow the partial differential equations that we use to predict the flow behaviour change from being "elliptic" to being "hyperbolic" in nature.

The comment before was based on the nature of the classification of Partial differential equations (PDE'S):

In the subsonic part of the flow (and away from walls) the equations describing the flow are elliptic. In an elliptic partial differential equation (PDE) the value of the dependent variable (i.e. the solution to the PDE) is dependent on the flow in all directions and at every part of the flow domain, for example in a subsonic flow if somebody shouted "oi!" you could hear it no matter where you are standing (as long as your fingers aren't in your ears!).

However, in a hyperbolic PDE the dependent variable (the PDE solution) is only dependent on the flow in a small region upstream (bounded by characteristic lines), i.e. it is directionally dependent. This is the supersonic flow situation, i.e. if somebody shouted "oi!" in a supersonic flow only people standing "downwind" or "downstream" of the person would hear them. Therefore from the 'sonic point' the pressure waves can only travel within the region of influence which is in the downstream direction. This is why the pressure waves trying to travel upstream collect at the sonic point and form the shock wave(s).

For example, the situation is like somebody trying to run the wrong way up an escalator (moving stairs). If the person doesn't run fast enough they are moved back to their original position by the escalator. To travel up the escalator the wrong way you must run FASTER than the escalator so that the escalator speed subtracted from your speed is still a positive value. In the same way, as the pressure waves can only move at a maximum speed of the speed of sound, if the oncoming fluid velocity is equal to or GREATER than the speed of sound (supersonic), they can only stay at the same position (if their speed is the same as the fluid flow) or move in the direction of the flow (if their speed is LESS than the fluid flow), assuming they are travelling in the opposite direction to the oncoming fluid. Therefore, the pressure waves only have an INLFLUENCE in the downstream direction. This is why the person shouting "oi!" in the supersonic flow can only be heard downwind of where they are standing.

Now you know why jet fighter pilots use a two-way radio

For more information on elliptic, hyperbolic and parabolic equations, the CFD book by J.D. Anderson (Jnr) is the best book to read. Alternatively, try putting the words "partial","differential", "equations","classification" and "hyperbolic" in the search facility on this web site, somebody must've explained it before.

Bye,

Dr. Bob

How is the speed of pressure wave in a media determined ? What would be the scenario if the media is water (or sea water) ? Thanks.

I cannot tell why jet fighters use a 2-way radio. Well, actually I don't know what a 2-way radio is. But I assume that it is a radio where the speakers are surrounding the pilot.

But I cannot see why the speed of the plane should affect the pilot. The acceleration, yes. But speed, no. Well, maybe if the pilot is flying with the window open

Cheers