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# Sonic Velocity Calculation

## Sonic Velocity Calculation

(OP)
Please let me know how to solve.

T= 732.2F (389 C)
P= 3.67psia (190mmHg)
MW= 128.5

I can calculate Density that is 0.591395 kg/m3
ideal gas equation is applicated .

so how can I calculate. I don't know K=Cp/Cv this fact.
also there are some calculation sheet. I don't know what I have to apply any calculation sheet.

### RE: Sonic Velocity Calculation

johnsin20:

For an ideal gas:

cp - cv = R (the universal gas constant)

k = cp / cv = cp/(cv - R)

cp and cv are independent of temperature and pressure, so they are constant for a given gas. They are not universal constants, they will vary from one gas to gas another.

For a real gas:

cp and cv are dependent on the gas temperature and pressure, so they are not constant for any gas.

For ideal or real gases;

You cannot calculate cp. It must be experimentally measured or obtained from a correlation or a graph of experimental values.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

### RE: Sonic Velocity Calculation

mbeychok (Chemical)
For a perfect gas  cp - cv = R (the universal gas constant)
However, either Cp or Cv is temperature dependent.

Regards

### RE: Sonic Velocity Calculation

correction to above
pv=RT   perfect gas

Cp-Cv=R

For semi perfect gas Cp or Cv is function of temp
For ideal gas, Cp is generally assumed constant.

### RE: Sonic Velocity Calculation

try the computer programs available from NASA, distributed by Cosmic, such as :

<http://www.openchannelfoundation.org/projects/CET93_PC/>

The ability to calcualte the thremodynamic propoerties of any gas is fundamental to the process uses by the types of objects that Nasa designs, and the referenced program ( or its background references ) may provide a means to obtain a value for Cp/ Cv.

### RE: Sonic Velocity Calculation

To reduce confusion on mobeychok's post above

cp - cv = R

k= cp/c[sub]v/sub] = cp/ (cp - R)

(the equation above had (cv - R) in the denominator)

David

### RE: Sonic Velocity Calculation

zdas04:

David, thanks for picking up my typo.
======================================
sailoday28:

My posting very clearly said: (a) the the specific heats were constant and independent of temperature and pressure for ideal gases and (b) the specific heats were not constant and were dependent on temperature and pressure for real gases.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

### RE: Sonic Velocity Calculation

mbeychok (Chemical)
Yes for an ideal  gas Pv=RT   specific heats are constant.
For a semi-perfect gas, Pv=RT, specific heats are dependent upon temperature.

What I am trying to emphasize is that for pv=RT, gamma is temperature dependent. For the ideal gas, other than relying on tables, etc, how does one obtain the specific heats?

Regards

### RE: Sonic Velocity Calculation

sailoday28:

#### Quote:

What I am trying to emphasize is that for pv=RT, gamma is temperature dependent. For the ideal gas, other than relying on tables, etc, how does one obtain the specific heats?

#### Quote:

Yes for an ideal gas Pv=RT specific heats are constant.
For a semi-perfect gas, Pv=RT, specific heats are dependent upon temperature.
I don't understand why you are repeating information already included in my original response.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

### RE: Sonic Velocity Calculation

mbeychok (Chemical)
Sorry, but I didn't see where you addressed a semi-perfect gas, unless you are stating that pv=RT with a variable specific heat is a real gas.
My understanding is that a real gas approaches pv=RT as p approaches 0.

regards

### RE: Sonic Velocity Calculation

sailoday28:

Now you have really confused me. Are you saying that there are three types of gases: ideal, semi-perfect and real? Or are saying that all real gases are semi-perfect gases? Or what are you saying?

I just searched through 5 books on thermodynamics and none of them use the terminology "semi-perfect gas"?

Milton Beychok
(Visit me at www.air-dispersion.com)
.

### RE: Sonic Velocity Calculation

To give you a general idea about γ:

• For a gas containing simple particles -helium atoms, for example, or the electron-proton mixtures that characterize matter at very high temperatures- γ has the value 5/3.

• For diatomic molecules like those in air, γ takes the lower value 7/5. Since Cv = 5/2 R, and as stated by mbeychok Cp = Cv + R.

• For more complicated molecules γ is lower still; in triatomic CO2 or NO2, for example, γ is close to 4/3.

As an example. A mixture consisting of 2.0 mol of oxygen and 1.0 mol of argon the Cv = (1/n) ΔU/ΔT would be 6.5R/3.0 mol = 2.2R.

This is the result of applying the equipartition theorem for the total internal energy of the molecules (the average energy per molecule of a system in thermodynamic equilibrium is 1/2 kT for each degree of freedom):

for oxygen [O2] with 5 independent components of motion,
Uox = (2.0 mol)(5/2RT) = 5.0RT
for monoatomic argon [Ar]
Uar = (1.0 mol)(3/2RT) = 1.5RT
Utotal = 6.5RT
Cv = 6.5R/3.0 mol = 2.2R
Cp = 3.2R
Cp/Cv = 1.45

These assumptions seem to hold in the range of 250 to 750 K; outside these limits molecules show different degrees of freedom. This is explained by quantum mechanics (lack of rotation at low temperatures, and spring-like vibrations at higher temperatures).

### RE: Sonic Velocity Calculation

mbeychok (Chemical)
Pv=RT applies to gases as they  approach p=0.
From that definition, one obtains the simple relation between Cp and Cv. (and only applicable at low pressure)
The specific heats at low pressure are basically a function of only temperature.
My experience is that ideal and perfect gas assume Cp or Cv to be constant.
Semi-perfect uses the fact that with pv=RT, the specific heats are temperature dependent.
All the above are for Pv=RT.
As to where to look--
I don't have my texts available at present, but suggest you try Keenan, Osbourne and others- in addition to a google search. You will see that I have not dreamed up these terms. But in summary a real gas is a gas and becomes perfect or semi-perfect as p approaches zero pressure.

Regards

### RE: Sonic Velocity Calculation

(OP)
Thanks everyone. I appreciate that. but you guys don't have to be angle. just calm down

### RE: Sonic Velocity Calculation

Sailoday28:

As I said earlier, the cp of real gases are dependent on both temperature and pressure. See:

(1) Figure 3-4 on page 3-143 of the 6th Edition of Perry's Chemical Engineers' Handbook.
(2) "The Variation of the Specific Heats (cp) of Oxygen, Nitrogen and Hydrogen with Pressure", E. J. Workman, Physics Review, 37, 1345 - 1355 (1931)
(3) "Data Book on Hydrocarbons", J.B. Maxwell, D. Van Nostrand, 1950 (page 75, first sentence)

Also, the female of a species is either pregnant or not pregnant. There is no such thing as being semi-pregnant. The same hold true for gases, they are either ideal in their behavior or they are real gases in their behavior. There is no such thing as a "semi-real" or "semi-ideal" or "semi-perfect" gas.

Of course, as the pressure of a real gas approaches 0, its behavior approaches that of an ideal gas. There is no disputing that statement ... but the real gas is still a real gas until it becomes completely ideal in its behavior. There is reason to create a new term and call it a "semi-perfect" no matter who coined that new term. Just call it a real gas that is approaching a pressure of zero (or approaching a compressibility factor of 1).

I promise this is my last word in this thread.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

### RE: Sonic Velocity Calculation

Sailoday28:

Pardon my typographical error:

#### Quote:

There is reason to create a new term and call it a "semi-perfect" no matter who coined that new term. Just call it a real gas that is approaching a pressure of zero (or approaching a compressibility factor of 1).

There is no reason to create a new term and call it a "semi-perfect" no matter who coined that new term. Just call it a real gas that is approaching a pressure of zero (or approaching a compressibility factor of 1).

Milton Beychok
(Visit me at www.air-dispersion.com)
.

### RE: Sonic Velocity Calculation

mbeychok (Chemical)
You state---There is no such thing as a "semi-real" or "semi-ideal" or "semi-perfect" gas.

How did you come up up with semi-real, semi-ideal? I did not.  I am not playing with words.
I am not creating a new term--Perhaps you should look in other thermo texts, or do the google search that I previously suggested

Also, should we now, define the perfect gas as a gas that approaches a compressibility of one?

regards

Regards

### RE: Sonic Velocity Calculation

This interesting discussion is of semantic value.

To avoid confusion let me clarify that while pregnancy is a yes or no situation, real gases are the only option.

As far as I remember semi-perfect gases aren't real gases approaching perfection; on the contrary, they are actually defined as "ideal" gases deviating from perfection, in that their heat capacity [Cp] is only a function of temperature, and is independent of pressure.

Perfect or semi-perfect gases are just idealizations which may be approached asymptotically but are still abstractions.

In fact, Cp and Cv of real gases at low pressures rarely depart from the ideal gas values, and are estimated just as functions of temperature, namely as if they were semi-perfect gases.

### RE: Sonic Velocity Calculation

25362 (Chemical)
"In fact, Cp and Cv of real gases at low pressures rarely depart from the ideal gas values, and are estimated just as functions of temperature, namely as if they were semi-perfect gases."

Your point is will taken.  It is interesting to note, however, that for a VDW gas at all other conditions,  Cv is a function of only temperature.
Regards

### RE: Sonic Velocity Calculation

johnsin20:

what is the chemical description of this gas with a mole wt of 128.5 ?

### RE: Sonic Velocity Calculation

From thermodynamics the difference between molar heat capacities is:

Cp-Cv = T(∂P/∂T)V(∂V/∂T)P

which can be estimated using an EOS.

For a vdW gas, ie,, a gas that follows the equation (P+a/V2)(V-b) = RT

Cp-Cv = R + 2aP/RT2

### RE: Sonic Velocity Calculation

To sailoday28, of course, the result I gave for an vdW gas is a good approximation after eliminating negligible terms.

Using the Berthelot EOS using the same approach:

Cp-Cv ≈ R[1 + (27/16)(P/Pc)(Tc3/T3)]

where Pc and Tc are critical properties.

### RE: Sonic Velocity Calculation

25362 (Chemical)
I have no disagreement with your posting.  I was just pointing out that for VDW, Cv=Cv(T).  Cp and gamma are functions of two variables.
Relating to the original post.
Having an equation of state,Berthelot, VDW,etc
Cp or Cv at low pressure,
one may calculate the sound speed.

### RE: Sonic Velocity Calculation

(OP)
I'm Working on furnace company.
anyways I need to calculate sonic velocity.
I almost do it.
there is option which is

v=81.7(p/?)^0.5
V P ?
Where:
?=Density
P=Absolute essure
V=Sonic Velocity

the sonic velocity does not exceed 80% of sonic.
The conditions at the outlet of the furnace are:
?=0.0368lb/ft^3 (0.5895kg/m^3)
MW=128.5
P=3.67psia (190mmhg )
T=732.2F (389 C)
Per the above conditions, the Sonic Velocity is:
v=81.7*(3.67/0.0368)^0.5
V=816ft/s (249m/s)

I don't understand how calculated 81.7. tell me.
now I'm studying.
thank you.

### RE: Sonic Velocity Calculation

The factor is the result of units conversion in the following equation from metric to british units:

v = (γP/ρ)0.5

v, 1 m/s =  3.281 ft/s
P, 1 psia = 6,894.8 N/m2
ρ, 1 lb/cf = 16.02 kg/m3
γ = Cp/Cv ≈ 1.44

3.281× (1.44×6,894.8÷16.02)0.5 = 81.7

### RE: Sonic Velocity Calculation

Hello, all:

I really must explain why I keep repeating that the specific heat of a real gas is dependent on BOTH temperature and pressure.

Here is a partial copy of a Figure 3-14 from page 3-143 of the 6th Edition of Perry's Chemical Engineers' Handbook which I believe fully confirms that fact:

Milton Beychok
(Visit me at www.air-dispersion.com)
.

### RE: Sonic Velocity Calculation

I'm sure nobody denied mbeychok's statement on the dependence of real gases Cp on P and T. The only point I thought worth of attention was that the so-called semi-perfect gases aren't a sub-family of real gases. They are, contrarywise, members of the ideal gas tribe, and as such only arbitrary works of fiction.

### RE: Sonic Velocity Calculation

mbeychok (Chemical)
In the regions where P=P(v,T) in which VDW is met---  Cv is a function of only temperature.
Regards

### RE: Sonic Velocity Calculation

There are 2 ways to calculate the sonic velocity:

1) Vs=223*SQRT(k*T/M)
where Vs is ft/s
where SQRT is square root
where k is ratio of specifc heats (Cp/Cv)
where T is temperature in degrees Rankine
where M is gas mol weight

2) Vs=68.1*SQRT(k*P/rhov)
where Vs is ft/s
where SQRT is square root
where k is ratio of specific heat (Cp/Cv)
where P is pressure in psia
where rhov is vapour density in lb/ft3

### RE: Sonic Velocity Calculation

One way really.  These two equations are related via the ideal gas law T/M = 1/R x P/rho.  Multiplying 223 by (1/R)1/2 just happens to = 68.1

Good luck,
Latexman

### RE: Sonic Velocity Calculation

we now know why the term semi-perfect is not used

interesting discussion

### RE: Sonic Velocity Calculation

hacksaw (Mechanical)
I suggest you "google" the term and see if it not used.
You should be supprised.
Regards

### RE: Sonic Velocity Calculation

Hi

Can some explains me the Back Pressure on PSV.

Is it the Pressure immediately after the PSV minus the upstream pressure.

Is it the Pressure drop in the downstream pipeline.

What is the corelation of Back Pressure with Static Pressure.

Thanks

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