Significance of Critical Pressure Ratio

*Consider a nozzle which connects vessel V_A and V_B. The vessel V_A contains steam at high pressure P_1. The vessel V_B contains steam but its pressure P₂ can be varied based on requirements.

*Initially the pressure P₂ be equal to the pressure P₁ in vessel V_A. By that time, there is no flow through nozzle.

*If the pressure P₂ is gradually reduced in vessel V_B, the discharge through the nozzle increases gradually.

*The pressure P₂, at which the discharge is maximum is called critical pressure.

*If the pressure P₂ is reduced further, the discharge through the nozzle will not increase and it remains at constant level.

* Hence it is confirmed that, at critical pressure ratio, the flow will be maximum.

*The velocity of steam at critical pressure is equal to sonic velocity. This condition will exist at throat cross section of the Convergent divergent nozzle.

Note;

*For convergent – Divergent nozzle, the flow of steam in the convergent portion of the nozzle is subsonic. i.e., the velocity of steam in the convergent section is less than the sound velocity.

*The steam flows in the divergent part of the nozzle is supersonic, i.e., the velocity of the steam in divergent portion is greater than velocity of sound.

Comparison of Otto, Diesel and Dual cycles

Based on Same Compression Ratio



# The comparison of Otto, Diesel and Dual cycle for the same compression ratio in p-v plot is shown below.

P-v plot

From p-v plot,

1247➡Otto cycle 

1267 ➨Diesel cycle

12357 ➡Dual cycle


# Here the compression ratio ‘r’ is equal for all cycles.

Compression ratio, r = V₂/V₁

Heat rejected is also equal for all cycles.


# We know that the efficiency of cyclic process is given by

η = 1- Q_R/ Q_S

Q_S - Heat supplied or absorbed

Q_R - Heat rejected

For constant heat rejection Q_R , the cycle efficiency increases with increases in the value of heat supplied, Q_S.

# In T-s plot, 

T-s Plot

The area under 1247 represents Q_S for Otto cycle

The area under 1267 represents Q_S for Diesel cycle

The area under 12357 represents Q_S for Dual cycle

Since,  Q_S)_Otto > Q_S)_Dual  > Q_S)_{Diesel ,}

η_Otto > η_Dual  > η_Diesel  , for same compression ratio



Note;

Area under p-v diagram represents Work done during the processes.

Area under T-s diagram represents heat transfer during the processes.

p = C ➡ Constant pressure processes.

v = C ➡ Constant volume processes.

Pv^Ɣ = C ➡ Isentropic processes.