9

2nd YEAR FLUIDS / COMPRESSIBLE FLOW

3

 

- FOR ISENTROPIC FLOWS :


          ( T₂/T₁)^1/(g-1) = (r₂/r₁)                                        (3.11)

          (P₂ / P₁) = (T₂ / T₁)^g/(g-1) = (r₂/r₁)^g                  (3.12)





3.3.2 STAGNATION STATE

• THE OBJECTIVE IS, FOR ISENTROPIC FLOW, TO RELATE, THROUGH THE MACH NUMBER :

   

• STAGNATION CONDITIONS FLOW CONDITIONS

CONSIDER A STREAM OF VELOCITY U, AND SPECIFIC ENTHALPY h :





 

• THE ENERGY EQUATION STATES THAT FOR :

- CONSTANT ELEVATION

- ZERO HEAT TRANSFER

- ZERO VISCOUS WORK

- ZERO SHAFT WORK

 

     h + U² / 2 = Const.                                        (3.13)





• WHEN THE FLOW IS ADIABATICALLY BROUGHT TO A STANDSTILL, THE ENTHALPY AT STAGNATION h_O IS :


       h_O =  h + U² / 2                                               (3.14)