Nozzle Exit Velocity | Determine Gas Velocity

[Mathias Thomsen]

Homework Statement

Carbon dioxide gas flows through a well-insulated nozzle operating at steady state. Potential energy effects are neglected.

Inlet:
T1 = 500 K
p1 = 5 bar
v1 = 100 m/s

Outlet:
T2 = 460 K
p2 = 3 bar
v2 = ?

How do I determine the gas velocity at the nozzle exit?

Homework Equations

Bernoulli's equation?

The Attempt at a Solution

Bernoulli's equation, but it didn't give me the right answer. The result should be 265 [m/s] according to my lector.

My try:

rho₁:= p₁/(R·T₁)

rho₂:= p₂/(R·T₂)

p₁+(1/2)·rho₁·v₁^2 = p₂+(1/2)·rho₂·v₂^2

solved for v₂:

v₂ = 362 m/s

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[DM01]

Nozzle is a steady flow device. So, applying Steady Flow Energy Equation (S.F.E.E.) ,

h₁ + v₁²/2 + Z₁g + dQ/dm = h₂ + v₂²/2 + Z₂g + dW/dm

Here h₁ , h₂ → sp. enthalpy at inlet and outlet resp.
v₁ , v₂ → vel. at inlet and outlet resp.
Z₁ , Z₂ → elevation of inlet and oulet sections above arbitrary datum
dQ/dm → net heat transfer per kg of CO₂ thru Control Surface
dW/dm → net work transfer per kg of CO₂ thru C.S.

Potential energy changes are neglected ⇒ Z₁g =0 , Z₂g = 0
As nozzle is well insulated ⇒ dQ/dm = 0
Also dW/dm =0

⇒ h₁ + v₁²/2 = h₂ + v₂²/2 ... (1)

Now to find the values of h₁ and h₂ under given conditions you will have to refer to CO₂ property tables.
(Steam tables are the most common ones. I tried to look up for CO₂ tables on the net but couldn't find the right one. There are some online applications too where the user inputs values of P and T and the app display enthalpy & other thermodynamic prop. values under given conditions. It didn't work out for me. However, do check it for yourself.)

Once values of h₁ and h₂ are known simply substitute them in eqn. (1)

Hope this helps ! Thank you :) :)