8

2nd YEAR FLUIDS / COMPRESSIBLE FLOW

3

3.3 ISENTROPIC FLOW


3.3.1 REVISION OF BASIC THERMODYNAMIC RELATIONS

FOR AN IDEAL GAS.


P  = rR T, R  =  CP - CV      AND   g = CP/CV                    (3.5)



- FOR AIR :           R = 287 J/(kg�K)     g= 1.4     CV = 718 J / (kg�K)

  AND                     CP = 1005 J / (kg�K)

 

 

- SPECIFIC INTERNAL ENERGY u AND ENTHALPY h :

 

      du = CV dT     AND     dh = CP dT                             (3.6)



- FIRST LAW OF THERMODYNAMICS, HEAT TRANSFER dq :

dq = du + P dv                                                    

 

    SINCE            h = u + PV       :     dq = dh  -  vdP                       (3.7)


- FOR FRICTIONLESS FLOW :     dq = T ds                                (3.8)

   WHERE ds IS THE CHANGE IN ENTROPY


- FROM (3.7) AND (3.8), AS SHOWN IN THE APPENDIX :

   s2 - s1 = CP n ( T2/T1) - Rin (P2 / P1 )                       (3.9)

OR

    s2 - s1 = CV n ( T2/T1) - R n (2 / 1 )                             (3.10)

             Previous Page Main Menu Next Page