Understanding Steam Flow and Critical Pressure in Nozzles

When steam flows through a nozzle, its velocity increases as the cross-sectional area changes, converting thermal energy into kinetic energy. The flow rate depends on the pressure difference between the inlet and the exit (back pressure).

What is Critical Pressure?

For a given nozzle geometry and inlet steam conditions, there is a specific back pressure known as the critical pressure. The critical pressure is reached when the velocity of the fluid flow at the narrowest part of the nozzle (the throat, if it's a converging-diverging nozzle, or the exit for a converging nozzle) reaches the speed of sound (sonic velocity) for the local conditions.

Mass Flow Rate and Back Pressure

As the back pressure downstream of the nozzle is gradually reduced from the inlet pressure, the pressure ratio across the nozzle increases, and the mass flow rate of steam through the nozzle also increases. This continues until the back pressure reaches the critical pressure.

• When the back pressure is higher than the critical pressure, the flow is subsonic throughout the nozzle. The mass flow rate is dependent on the back pressure.
• When the back pressure equals the critical pressure, the velocity at the throat (or exit for a converging nozzle) becomes sonic. At this point, the mass flow rate reaches its maximum possible value for the given inlet conditions.
• If the back pressure is reduced further below the critical pressure, the velocity at the throat remains sonic, and the mass flow rate does not increase any further. The flow is said to be "choked". The expansion continues supersonically in the diverging section of a converging-diverging nozzle.

Conclusion on Mass Flow Rate at Critical Pressure

Therefore, the mass flow rate of steam through a nozzle is limited by the sonic velocity condition at the throat (or exit). This limiting condition occurs when the back pressure is equal to the critical pressure. Any further reduction in back pressure does not increase the mass flow rate.

This means that the mass flow rate achieves its highest possible value when the back pressure is exactly equal to the critical pressure.

Thus, if the back pressure is equal to the critical pressure, the mass flow rate of steam is maximum.