Sonic Velocity Calculation 1

[johnsin]

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.
Please help me.

 

[25362]

From thermodynamics the difference between molar heat capacities is:

Cp-Cv = T([∂]P/[∂]T)[sub]V[/sub]([∂]V/[∂]T)[sub]P[/sub]​

which can be estimated using an EOS.

For a vdW gas, ie,, a gas that follows the equation (P+a/V[sup]2[/sup])(V-b) = RT

Cp-Cv = R + 2aP/RT[sup]2[/sup]​

 

[25362]

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)(Tc[sup]3[/sup]/T[sup]3[/sup])]​

where Pc and Tc are critical properties.

 

[sailoday28]

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.

 

[johnsin]

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.

 

[25362]

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

v = ([γ]P/[ρ])[sup]0.5[/sup]​

v, 1 m/s = 3.281 ft/s
P, 1 psia = 6,894.8 N/m[sup]2[/sup]
[ρ], 1 lb/cf = 16.02 kg/m[sup]3[/sup]
[γ] = Cp/Cv [≈] 1.44

3.281[×] (1.44[×]6,894.8[÷]16.02)[sup]0.5[/sup] = 81.7​

 

[mbeychok]

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)
.

 

[25362]

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.

 

[sailoday28]

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

 

[Glenfiddich]

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

 

[Latexman]

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)[sup]1/2[/sup] just happens to = 68.1

Good luck,
Latexman

 

[hacksaw]

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

interesting discussion

 

[sailoday28]

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

 

[imran95109]

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