Question

P: I bar T-33'C Vor lex Tube P bar Sec P- to bar T;"-25.1
i need to find unknown flow rates of n2, and n3. is this the right way?

Answer 1

Hi

In this case of vortex tube , your assumption is correct.

Let us understand with a diagram

We have inlet pressure as 10 bar whereas Outlet pressure as 1 bar

But the assumption that since it is a liquid effect of pressure can be neglected

We can say enthalpy can be written as CpdT

Also you are taking the assumption that the the Cp is constant ,that is also realatic.

Doing overall mass balance

Taking 1 sec as basis

10=N2+N3

Let the enthalpy at 25 oc is Ho

So at 50 oc

Enthalpy =Ho+Cp*25

At -25 oc

Enthalpy = Ho –Cp*50

Uning enthakpy balanace

10*Ho= N2(Ho+Cp*25)+N3*( Ho –Cp*50)

10Ho= N2H0+N3Ho+N2 *25Cp- N1*50 Cp    (10 Ho= N2H0+N3Ho)

N2= 2N1

N1+N2= 10

N1= 3.33

N2 = 6.66

So the moles of N1= 0.33 moles per sec

Moles of N2 = 6.66 moles per sec .

T3 I am assuming – 25 o C ,as it is visible ,if it is different ,proceed with the similar steps

Feel free to comment in the comment section in the case of any doubt

Thank you