ten cubic meters of air in an area of 76 square millimeters

[Kaji]

I apologize for the question that may seem deprived of bases, but given the absence of staff asked me, that I am not engineer, to calculate the energy (better power) out if I introduce in a ten cubic meters air per minute to a pressure of 14 bar.
in the figure the vents crossed by the air are the colored ones of blue, the problem is that if I apply the trivial formula of the calculation of the speed according to the flow and the area of the nozzle I get an ipersonic speed that gives me a value of the disproportionate kinetic energy.
I believe that not being the convergent-divergent nozzle as are those for supersonal fluids, the speed once reached that of sound does not increase or perhaps decrease. Could you give me some confirmation and a few tips to solve this problem?
thanks to the availability and excuse if the message is unclear but I wrote in a hurry that I have to detach.

 

[paulpaul]

Hi.
to understand better: do you have to calculate the load losses of an air flow with a flow of 10 m3/min within the blue "anulating" duct?

 

[Kaji]

It would be enough for me to speed, because if the calculation with the formula of the fractual flow of the area, I get a measured value.
I know that the nozzle is geometrically wrong because it should be convergent-divergent, but it is not so in this case what happens: the speed reaches that of the sound then it freezes or decelles? Thank you for your concern.

 

[zeigs]

I'm going a little bit to spanne.
nozzle area: 75.6 mm2 =75.6e-6 m2
gas flow rate: 10 m3/min @ 14 bar = 10/15 m3 volumetric = 0.667 m3/min =0.011 m3/s
gas speed: 0.011/75.6e-6= 147 m/s

sound speed beats on 330 m/s

But I assumed that, as is often the case for those who treat gas, the 10 m3/min were considered at atmospheric pressure, otherwise yes, a speed value 15 times higher

Hi.

 

[paulpaul]

It would be enough for me to speed, because if the calculation with the formula of the fractual flow of the area, I get a measured value.
I know that the nozzle is geometrically wrong because it should be convergent-divergent, but it is not so in this case what happens: the speed reaches that of the sound then it freezes or decelles? Thank you for your concern.

you probably did not take into account the air density at 14 bar, which is about 18 kg/m3 (and not about 1.2 kg/m3 as in the case of atmospheric pressure). I also find the value of zeigs on the "small" duct (and I share the observation on the reference conditions of the flow, which in case of compressible fluids must always be specified).

since the section expands, you will have a decrease in speed. theoretically and accurately establish the load loss of this geometry is not simple. in literature (idel'cik, for example) you find load loss databases of numerous geometries.

 

[Kaji]

the pressure and flow are those of the compressor (it reaches up to 24 bar) or probably a little further downstream; As for the weight I also considered the perfect gas equation (by approaching the air to a perfect gas) finding the number of jets according to pressure and volume (in this case in the unit of time i.e. the flow) .
but the problem remains the speed that is disproportionate to me, so I wanted to know if it made sense to hypothesize that you are at the speed of the sound and then decline as suggested by you; on the internet I found some pdf on the nozzle of de laval and seemed very interesting to me the concept of stagnation, although perhaps the word is misleading.
thanks anyway for the interest

 

[paulpaul]

we start with order calculating the air density. Apart from that there are also online (nist for example) so many programs to calculate the density of a gas using one of the countless state equations for real gases, the equation of perfect gases in this case goes well, since in these conditions the air is well approximated to a perfect gas. I suggest that we leave the moles and write it in a more technical form, of the type p = rrt, where r is the density [kg/m3], press [Pa], t temperature [K], and r is the constant "specific" of the gas you are considering [J/kgK], which is given by the universal constant divided the molecular weight of the gas. avoiding the accounts (you can get it easily), for the air it is worth 287 j/kgk. Whereas t = 15 °c = 288 k and p = 15 bar = 1500000 pa (you must use absolute pressure) get r = 18 kg/m3, with a little approximation here and there.

 

[meccanicamg]

design all with solidworks and analyze fluid with flowsimulation

 

[paulpaul]

but the problem remains the speed that is disproportionate to me, so I wanted to know if it made sense to hypothesize that you are at the speed of the sound and then decline as suggested by you; on the internet I found some pdf on the nozzle of de laval and seemed very interesting to me the concept of stagnation, although perhaps the word is misleading.
thanks anyway for the interest

I answered you first: As the density goes to the denominator, if you take it too small the speed also becomes very high (at equal rate). But I think that calculating the speed is for you misleading, if you want to calculate the load loss. If you need to make an approximate calculation, take a localized loss coefficient of a similar geometry and throw it into a pressure drop type sw (which also models gases). If you want a more precise calculation and you have more time, flux or do a cfd.
the "restagno" speech is not related to the "sonic block" (chocking) with which perhaps you confuse: and anyway I would say that you do little here of these concepts...your conduit is - if I do not misinterpret the flow - basically always divergent (the section increases in the direction of the motion), the input speed is subsonic and therefore the fluid slows down, recovering therefore pressure (realizzi a "diffuser"). if the incoming speed was supersonic then the divergent would expand, and the fluid would accelerate. de laval is a converging followed by a divergent, used to speed up a subsonic flow at supersonal speed (it is the conformation that acquires an exhaust nozzle of a supersonic plane engine under certain flight conditions).