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Thermodynamics: Compressor Axial work

  1. Jun 17, 2015 #1
    1. The problem statement, all variables and given/known data

    Thermodynamics problem

    Air enters a compressor at a temperature of 290 Kelvin and pressure 100 kPa with a stable volume flow of 2.5 m^3/s. The output temperature of the compressor is is 400 Kelvin and the velocity of the flow is 30 m/s. Air is implied to be an ideal gas under those conditions. The cooling of the compressed is done with a refrigant that absorbs heat from the air with a speed of 750 kJ / min. If the changes in kinetic and dynamic energies are negligible and the flow is permanent then find the axial force needed for the compressor to work .

    Could someone help me with this problem? I'd really appreciate it , at least some help where i shoudl start from

    2. Relevant equations


    3. The attempt at a solution

    I'm having trouble where to start from , first thoughts where to find the state of air through the tables in the input and output of compressor , but beside that i haven't come to a better idea yet
     
  2. jcsd
  3. Jun 17, 2015 #2
    Let me guess. You're learning about the (open system) flow version of the first law of thermodynamics, correct? If so, please write down the relevant equation that applies to this situation. You are going to need to determine the outlet pressure. Based on the first sentence in the problem statement, what it the mass flow rate? If you want to find the axial force on the rotor, you are going to need to do a momentum balance also. How would you express that?

    Chet
     
  4. Jun 17, 2015 #3
    Q12 - W 12 = m [ h2 - h1 + (V22- V21)/2+ g (z2-z1)] (1)

    and since

    elD1wqJ.png

    we have kinetic and dynamic energies neglible
    Q12 = 0
    E(mass in-mass out) = 0 aswell

    so we take from 1

    W12= h2 - h1

    after working out a bit with it that's what i finished to , i find enthalpies from tables with linear intepollaration , but is this the axial work of compressor or i'm mistaken?
     
    Last edited: Jun 17, 2015
  5. Jun 17, 2015 #4
    Q is not zero. So

    Q - W = m(h2-h1)

    Do you know how to determine the mass flow rate, given the information in the first sentence of the problem statement?

    Chet
     
  6. Jun 17, 2015 #5
    I'm pretty sure we use the ideal gas law to find the density and then with multiplication of density with the volume flow rate we find the mass flow rate, now some questions as Q we use the heat that the refrigant absorbs so Q=-750KJ/min , the W we finally get is the axial work im looking for? Where should i use the velocity flow at that is given on the second sentence?
     
  7. Jun 17, 2015 #6
    Yes.
    Well, you are also asked to find the force on the rotor. This is where the velocity of flow would come in. So, a momentum balance would be involved. But I've been having trouble with this because there seems to be a piece of vital information missing (according to my judgement). I feel that, to do the momentum balance, you need to know either the inlet velocity or the cross sectional area of the compressor. The information at the outlet end seems adequate, when combined with the mass flow rate at the inlet end. Has anything been left out in the problem statement regarding the inlet or the cross sectional area?

    Chet
     
  8. Jun 18, 2015 #7
    Nothing has been left out
     
  9. Jun 18, 2015 #8
    Well, anyway, please try writing out algebraically a momentum balance on the gas, taking the entire compressor as the control volume and letting F be the force that the rotor exerts horizontally on the gas.
     
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