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Homework Help: Nozzle exit velocity

  1. Nov 2, 2014 #1
    1. The problem statement, all variables and given/known data
    Carbon dioxide gas flows through a well-insulated nozzle operating at steady state. Potential energy effects are neglected.

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

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

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

    2. Relevant equations

    Bernoulli's equation?

    3. 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
  2. jcsd
  3. Nov 7, 2014 #2
    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?
  4. Nov 10, 2014 #3
    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 :) :)
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